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Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms — part I: A unified formulation. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 28(1), 26-37
Abstract
In optimization, multiple objectives and constraints cannot be
handled independently of the underlying optimizer. Requirements such as
continuity and differentiability of the cost surface add yet another
conflicting element to the decision process. While “better”
solutions should be rated higher than “worse” ones, the
resulting cost landscape must also comply with such requirements.
Evolutionary algorithms (EAs), which have found application in many
areas not amenable to optimization by other methods, possess many
characteristics desirable in a multiobjective optimizer, most notably
the concerted handling of multiple candidate solutions. However, EAs are
essentially unconstrained search techniques which require the assignment
of a scalar measure of quality, or fitness, to such candidate solutions.
After reviewing current revolutionary approaches to multiobjective and
constrained optimization, the paper proposes that fitness assignment be
interpreted as, or at least related to, a multicriterion decision
process. A suitable decision making framework based on goals and
priorities is subsequently formulated in terms of a relational operator,
characterized, and shown to encompass a number of simpler decision
strategies. Finally, the ranking of an arbitrary number of candidates is
considered. The effect of preference changes on the cost surface seen by
an EA is illustrated graphically for a simple problem. The paper
concludes with the formulation of a multiobjective genetic algorithm
based on the proposed decision strategy. Niche formation techniques are
used to promote diversity among preferable candidates, and progressive
articulation of preferences is shown to be possible as long as the
genetic algorithm can recover from abrupt changes in the cost landscape
... For example, in [12][13][14], the multiple objective functions are weighted and summed into a new objective function; then the multiobjective optimization problems are indirectly solved by single-objective methods. The other one is the evolutionary approach [15], such as ant colony optimization algorithm [16], genetic algorithm [17], particle swarm optimization algorithm [18], nondominated sorting genetic algorithm II [19], and multiobjective evolutionary algorithm based on decomposition [20]. The evolutionary approach tends to be stochastic and lacks theoretical guarantees. ...
... The aforementioned studies in [11][12][13][14][15][16][17][18][19][20][21][22] only provide centralized algorithms, where a center exists to collect and compute all objective functions. Noticeably, more objectives tremendously increase the computational burden of the center. ...
... In this subsection, we show the convergence analysis of the proposed algorithms (15)- (17). Firstly, from (15d), we know that the estimate ω k i (t) of the weighting factor for i ∈ V and k ∈ I K achieves predefinedtime convergence if the global decision variablex k of the constrained distributed optimization problem (6) for k ∈ I K achieves predefined-time convergence. ...
We consider the multiobjective optimization problem for the resource allocation of the multiagent network, where each agent contains multiple conflicting local objective functions. The goal is to find compromise solutions minimizing all local objective functions subject to resource constraints as much as possible, i.e., the Pareto optimums. To this end, we first reformulate the multiobjective optimization problem into one single-objective distributed optimization problem by using the weighted Lp preference index, where the weighting factors of all local objective functions are obtained from the optimization procedure so that the optimizer of the latter is the desired Pareto optimum of the former. Next, we propose novel predefined-time algorithms to solve the reformulated problem by time-based generators. We show that the reformulated problem is solved within a predefined time if the local objective functions are strongly convex and smooth. Moreover, the settling time can be arbitrarily preset since it does not depend on the initial values and designed parameters. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed algorithms.
... Breaking the ties between sites within a non-dominated front has been done using multiple methods, including minimizing the distance to a reference point (e.g. Euclidean distances: Fonseca & Fleming, 1998), or maximizing diversity (e.g. crowding distances: Emmerich & Deutz, 2018). ...
... Selecting a particular ranking method is a management decision, which is based on the planning objectives and the relative preferences of the managers and decision scientists. In this study, within a class, we gave the best rank to the solution closest to the goal or reference point using Euclidean distances (Fonseca & Fleming, 1998), which is a method consistent with the definition of climate refugia and our desire to find Climate Priority sites less affected by stressors. By calculating Euclidean distances to normalized data we are giving equal importance to each variable. ...
Climate change has become the greatest threat to the world's ecosystems. Locating and managing areas that contribute to the survival of key species under climate change is critical for the persistence of ecosystems in the future. Here, we identify ‘Climate Priority’ sites as coral reefs exposed to relatively low levels of climate stress that will be more likely to persist in the future. We present the first analysis of uncertainty in climate change scenarios and models, along with multiple objectives, in a marine spatial planning exercise and offer a comprehensive approach to incorporating uncertainty and trade‐offs in any ecosystem. We first described each site using environmental characteristics that are associated with a higher chance of persistence (larval connectivity, hurricane influence, and acute and chronic temperature conditions in the past and the future). Future temperature increases were assessed using downscaled data under four different climate scenarios (SSP1 2.6, SSP2 4.5, SSP3 7.0 and SSP5 8.5) and 57 model runs. We then prioritized sites for intervention (conservation, improved management or restoration) using robust decision‐making approaches that select sites that will have a benign climate under most climate scenarios and models. The modelling work is novel because it solves two important issues. (1) It considers trade‐offs between multiple planning objectives explicitly through Pareto analyses and (2) It makes use of all the uncertainty around future climate change. Priority intervention sites identified by the model were verified and refined through local stakeholder engagement including assessments of local threats, ecological conditions and government priorities. The workflow is presented for the Insular Caribbean and Florida, and at the national level for Cuba, Jamaica, Dominican Republic and Haiti. Our approach allows managers to consider uncertainty and multiple objectives for climate‐smart spatial management in coral reefs or any ecosystem across the globe. We identify priority reefs that will be more likely to survive climate change impacts in the future. Our approach is novel because it solves two important issues when selecting sites for conservation. It allows considering multiple desirable properties that an ideal site should have and choosing a site that is best for all, not only best for some. Also, it makes use of all the uncertainty around future climate change and chooses sites that will have a benign climate under all climate scenarios and models.
... • Fonseca-Fleming [32,37]. The objective functions of the MOO problem are ...
In this work, the author presents a novel method for finding descent directions shared by two or more differentiable functions defined on the same unconstrained domain space. Then, the author illustrates an alternative Multiple-Gradient Descent procedure for Multi-Objective Optimization problems that is based on this new method. In particular, the proposed method consists in finding the shared descent direction solving a relatively cheap Linear Programming (LP) problem, where the LP's objective function and the constraints are defined by the gradients of the objective functions of the Multi-Objective Optimization problem. More precisely, the formulation of the LP problem is such that, if a shared descent direction does not exist for the objective functions, but a non-ascent direction for all the objectives does, the LP problem returns the latter. Moreover, the author defines a new backtracking strategy for Multiple-Gradient Descent methods such that, if the proposed LP is used for computing the direction, the ability to reach and/or explore the Pareto set and the Pareto front is improved. A theoretical analysis of the properties of the new methods is performed, and tests on classic Multi-Objective Optimization problems are proposed to assess their goodness.
... To illustrate the three indicators and evaluate the effectivity and efficiency of a hybrid of customised VNS and NSGA II, we consider a simple test problem, FON (Fonseca and Fleming 1998;Fonseca and Fleming 1995) problem shown in Equations (18-20), which is a bi-objective optimisation problem with a known theoretical Pareto front shown in Equation (21). Figure 5 shows the non-dominated solutions and the theoretical Pareto front after one, two, three, and five generations of NSGA denoted as Algo.1 and the proposed hybrid NSGA II and VNS denoted as Algo.2. The red line labelled as PFture represents the theoretical Pareto front. ...
... To address diverse gaps and objectives in the literature, following [21,25], the Multi-Objective Genetic Algorithm (MOGA) is used in optimizing diesel/wind systems with aims to curtail emissions and fuel expenses. Furthermore, the Strength Pareto Evolutionary Algorithm (SPEA) is utilized to optimize HRES size and power management as suggested in [26][27][28]. ...
This paper addresses the optimal sizing of Hybrid Renewable Energy Systems (HRESs), encompassing wind, solar, and battery systems, with the aim of delivering reliable performance at a reasonable cost. The focus is on mitigating unscheduled outages on the national grid in Iraq. The proposed On–off-grid HRES method is implemented using MATLAB and relies on an iterative technique to achieve multi-objectives, balancing reliability and economic constraints. The optimal HRES configuration is determined by evaluating various scenarios related to energy flow management, electricity prices, and land cover effects. Consumer requirements regarding cost and reliability are factored into a 2D optimization process. A battery model is developed to capture the dynamic exchange of energy among different renewable sources, battery storage, and energy demands. A detailed case study across fifteen locations in Iraq, including water, desert, and urban areas, revealed that local wind speed significantly affects the feasibility and efficiency of the HRES. Locations with higher wind speeds, such as the Haditha lake region (payback period: 7.8 years), benefit more than urban areas (Haditha city: payback period: 12.4 years). This study also found that not utilizing the battery, particularly during periods of high electricity prices (e.g., 2015), significantly impacts the HRES performance. In the Haditha water area, for instance, this technique reduced the payback period from 20.1 to 7.8 years by reducing the frequency of charging and discharging cycles and subsequently mitigating the need for battery replacement.
... Upon inputting training data into the network, we derive a performance index function dependent on the network parameters. These parameters are then determined by optimizing (using particle swarm optimization (PSO) [9][10][11][12]) the objective function, thus constructing the new algorithm [13,14]. GNNs, as an enhancement of the original concept, have broad application potential. ...
Utilizing granular computing to enhance artificial neural network architecture, a new type of network emerges—the granular neural network (GNN). GNNs offer distinct advantages over their traditional counterparts: The ability to process both numerical and granular data, leading to improved interpretability. This paper proposes a novel design method for constructing GNNs, drawing inspiration from existing interval-valued neural networks built upon NNNs. However, unlike the proposed algorithm in this work, which employs interval values or triangular fuzzy numbers for connections, existing methods rely on a pre-defined numerical network. This new method utilizes a uniform distribution of information granularity to granulate connections with unknown parameters, resulting in independent GNN structures. To quantify the granularity output of the network, the product of two common performance indices is adopted: The coverage of numerical data and the specificity of information granules. Optimizing this combined performance index helps determine the optimal parameters for the network. Finally, the paper presents the complete model construction and validates its feasibility through experiments on datasets from the UCI Machine Learning Repository. The results demonstrate the proposed algorithm’s effectiveness and promising performance.
... This function was selected as it is the primary global multi-objective optimisation solver offered with MATLAB, which uses a robust optimisation technique to perform a global search in the solution space for the global optimum point [55,56]. GA multi-objective optimisations and their use in parametric optimisation have been widely researched and are discussed within the literature such as [57][58][59][60]. Additionally, the limitations of mathematical models are discussed in [61]. ...
Human Centrifuge Systems (HCSs) are an effective training tool to improve the G-acceleration and Spatial Disorientation (SD) tolerance of aircrew. Though highly capable HCSs are available, their structure and performance are yet to be fully optimised to efficiently recreate the G-vectors produced using Aircraft Combat Manoeuvres (ACMs). To achieve this improvement, the relationship between configurational design and HCS performance should be profoundly investigated. This work proposes a framework for identifying the optimal configurational design of an active four Degree-of-Freedom (DoF) HCS. The relationship between configurational design parameters and objective criteria is established using inverse kinematics and dynamics. Then, a multi-objective evolutionary optimiser is used to identify the optimum arm length and seat position, minimising the Coriolis effect, relative acceleration ratio, and cost. The results of the work show that the applied optimisation step can significantly contribute to (1) efficiently replicating the aircraft motion, (2) minimising the detrimental effects generated during HCS motion, and (3) reducing the overall cost of the system. The applied methodology can be adapted to HCSs with different structures and DoFs.
... The MOGA multi-objective genetic algorithm introduces the concept of Pareto rank for fitness allocation, thus maintaining population diversity and increasing the search efficiency of the algorithm, etc. [37]. The MOGA, by introducing the concept of fitness sharing [38] and the method of mating restrictions [39], is capable of well solving the problem of 'genetic drift' that can exist in multi-peak optimisation problems due to premature maturity. ...
... Most evolutionary algorithms employ the concept of Pareto dominance with an iterative solving procedure, meaning that they can produce Pareto optimal solutions from the very first trial. This research employs two well-known and efficient MOEAsmulti-objective genetic algorithm (MOGA) [35] and nondominated sorting genetic algorithm (NSGA-II) [36]-as well as multi-objective bonobo optimizer (MOBO) [37], a new MOEA, to solve the proposed mathematical model. For interested readers, the source code for NSGA-II and MOBO can be accessed by forwarding an email to Hasan, K.W. ...
... The algorithm continues to create successive generations till a termination criterion is satisfied. A flow chart illustrating GA procedure is shown in Fig. 7. Generally, GA has been developed to handle multiple objectives simultaneously instead of formulating the optimization problem as a series of singleobjective optimization problems [40]. Consequently, a set of optimum solutions is obtained called the Pareto solution set, which provides an important degree of flexibility in choosing the best optimum solution based on additional defined criterion. ...
In this study, multi-objective optimum energy management strategies are developed for pre- and post-transmission parallel hybrid electric vehicles. The first strategy aims to improve fuel economy and electric system efficiency, while the second strategy adds the improvement in battery performance and life. Multi-objective genetic algorithm is adopted to solve the formulated optimum energy management problems, hence generates optimum control inputs for each drivetrain configuration. Mathematical models of vehicle dynamics and drivetrain components are integrated with the developed strategies in a simulation environment. Results for both strategies are compared to a baseline rule-based energy management strategy, commonly used as a benchmark in literature. Additionally, both drivetrain configurations are compared and analyzed through different standard driving cycles. The results show the significant improvement in battery performance due to its consideration in the energy management strategy, with either null or positive effect on fuel consumption. Additionally, the results of pre-transmission drivetrain configuration show noticeable improvement in battery performance as compared to the post-transmission results.
... The model is subjected to simulation on MATLAB by applying multi-objective optimization with the inversion technique. As opposed to the single-objective optimization approach of Fonseca and Fleming (1998), this model introduces sequential quadratic programming (SQP) and multiobjective genetic algorithm (MOGA) to solve nonlinear constrained optimization problems. More importantly, the inversion technology is applied to MOGA for the first time. ...
Aiming at the key design variables of journal bearings, a novel optimization scheme is proposed to minimize oil leakage and power loss. For the first time, the inversion technology is introduced into the multi-objective optimization genetic algorithm under thermohydrodynamics. Using the hybrid optimization method (sequential quadratic programming and multi-objective optimization genetic algorithm) and the pareto optimal frontier method, the journal bearing model under the oil supply condition of oil groove (Model A) and oil hole (Model B) is optimized. More importantly, the oil leakage (QL) formula is exhaustively deduced, and good prediction results are obtained by simulating the data in literature. The optimization test results show that compared with the maximum errors (13% and 25%) of the power loss and leakage flow prediction results in literature, the maximum errors of this prediction model are 8% and 14%, respectively. In addition, compared with hybrid optimization method, the pareto optimal frontier has better advantages under inversion technology. Both methods can give good prediction results. The accuracy of this model is proved by comparing experimental data in the literature.
... To illustrate the three indicators and evaluate the effectivity and efficiency of a hybrid of customised VNS and NSGA II, we consider a simple test problem, FON (Fonseca and Fleming 1998;Fonseca and Fleming 1995) problem shown in Equations (18-20), which is a bi-objective optimisation problem with a known theoretical Pareto front shown in Equation (21). Figure 5 shows the non-dominated solutions and the theoretical Pareto front after one, two, three, and five generations of NSGA denoted as Algo.1 and the proposed hybrid NSGA II and VNS denoted as Algo.2. The red line labelled as PFture represents the theoretical Pareto front. ...
The first-mile transportation system connects scattered requests in residential areas to mass transit networks and provides convenient and high-quality travelling services. The complicated road network and passenger mobility lead to potential multiple selections of passengers when choosing pick-up locations, which is ignored in the literature. This study develops a multi-objective optimisation model for the first-mile transportation system considering requests' preference ranks for multiple boarding stops. The objectives are to minimize the system cost and the number of unserved requests as a proxy for service quality, respectively. We devise a hybrid solution approach combining the fast elitist non-dominated sorting genetic algorithm (NSGA II) with a variable neighbourhood search (VNS) improvement method. The method is tested and compared with the classical NSGA II and an exact method on a number of instances. We also examine the effect of multiple stops and the discount scheme on the system performance.
... These functions have been used in many previous studies in this field. Veldhuizen [12] used a set of these functions and two of them were selected (FON) [13], and (KUR) in our case, in addition to (POL) [14] and (SCH). In 1999 Deb [15] proposed methodological approaches for developing test functions of multi-objective optimization algorithms, Zitzler and his colleagues [16] followed this methodology and proposed six optimization functions, five of them were used in this research ZDT1, ZDT2, ZDT3, ZDT4, ZDT6. ...
The 3D reconstruction process is very important in a variety of computer vision applications. Bundle adjustment has a significant impact on 3D reconstruction processes, namely in Simultaneously Localization and Mapping (SLAM) and Structure from Motion (SfM). Bundle adjustment, which optimizes camera parameters and 3D points as a very important final stage, suffers from memory and efficiency requirements in very large-scale reconstruction. Multi-objective optimization (MOO) is used in solving a variety of realistic engineering problems. Multi-Objective Particle Swarm Optimization (MOPSO) is regarded as one of the state of the art for meta-heuristic MOO. MOPSO has utilized the concept of crowding distance as a measure to differentiate between solutions in the search space and provide a high level of exploration. However, this method ignores the direction of the exploration which is not sufficient to effectively explore the search space. In addition, MOPSO starts the search from a fully randomly initialized swarm without taking any prior knowledge about the initial guess into account, which is considered impractical in applications where we can estimate initial values for solutions like bundle adjustment. In this paper, we introduced a novel hybrid MOPSO-based bundle adjustment algorithm that takes advantage of initial guess, angle quantization technique, and traditional optimization algorithms like RADAM to improve the mobility of MOPSO solutions; the results showed that our algorithm can help improve the accuracy and efficiency of bundle adjustment (BA).
... This study applied the multi-objective choice function-great deluge hyper-heuristic (HHMO_CF_GDA) approach proposed by Maashi et al. [5]. HHMO_CF_GDA controls and combines three multi-objective evolutionary algorithms including the multi-objective genetic algorithm (MOGA) [22,23], the non-dominated sorting genetic algorithm (NSGAII) [24,25], and the strength Pareto evolutionary algorithm (SPEA2) [26]-which acting as low-level heuristics in the hyper-heuristic framework [27]. As a selection method, we utilized a choice function with a high-level strategy that adaptively ranks the performance of three low-level heuristics, choosing which one to call at each decision point. ...
Software maintenance is an important step in the software lifecycle. Software module clustering is a HHMO_CF_GDA optimization problem involving several targets that require minimization of module coupling and maximization of software cohesion. Moreover, multi-objective software module clustering involves assembling a specific group of modules according to specific cluster criteria. Software module clustering classifies software modules into different clusters to enhance the software maintenance process. A structure with low coupling and high cohesion is considered an excellent software module structure. In this study, we apply a multi-objective hyper-heuristic method to solve the multi-objective module clustering problem with three objectives: (i) minimize coupling, (ii) maximize cohesion, and (iii) ensure high modularization quality. We conducted several experiments to obtain optimal and near-optimal solutions for the multi-objective module clustering optimization problem. The experimental results demonstrated that the HHMO_CF_GDA method outperformed the individual multi-objective evolutionary algorithms in solving the multi-objective software module clustering optimization problem. The resulting software, in which HHMO_CF_GDA was applied, was more optimized and achieved lower coupling with higher cohesion and better modularization quality. Moreover, the structure of the software was more robust and easier to maintain because of its software modularity.
... We selected 16 bi-objective minimization test problems commonly used in literature. These problems are: Schaffer N. 1 (SCH1) and N. 2 (SCH2) (Schaffer 1985), Fonseca-Fleming (FON) (Fonseca and Fleming 1998) (Srinivas and Deb 1994), Tanaka (TNK) (Tanaka et al 1995), and Constr-Ex (CONSTR) (Deb 2001). The first twelve problems are unconstrained, while the last four are constrained. ...
Multiobjective optimization has a wide range of applications in science and engineering. Various multiobjective optimization algorithms work fine for bi-objective problems with few variables. However, many problems involve several functions that handle many variables each, and there is no efficient mathematical method to solve these types of problems. Quantum computers offer an exponential speed-up for such problems when they take full advantage of quantum phenomena. At present, quantum multiobjective problem solvers for quantum computers do not exist. This paper presents a formal statistical analysis of two state-of-the-art classical multiobjective evolutionary algorithms and three quantum-inspired multiobjective optimization algorithms to determine whether quantum solvers can provide comparatively optimal quality solutions or if they are limited. One of the quantum-inspired algorithms tested is a novel proposal that uses fewer qubits. The paper also presents contributions to the state of the art by modifying two original, quantum-inspired algorithms to perform in continuous search spaces. The purpose of this paper is to settle the first step of multiobjective quantum optimization for quantum computers from quantum-inspired algorithms by providing valuable results that can assist in future research along the way in this field. The results indicated that the quantum-inspired algorithms tested performed as well as the NSGA-II, and the proposed method outperforms the other quantum-inspired algorithms in problems with constraints and complicated Pareto sets.
... In general, the multi-objective deterministic optimization design (MDOD) model can be expressed as follows [29,30]: ...
The planetary gear train is often used as the main device for decelerating and increasing the torque of the drive motor of electric vehicles. Considering the lightweight requirement and existing uncertainty in structural design, a multi-objective uncertainty optimization design (MUOD) framework is developed for the planetary gear train of the electric vehicle in this study. The volume and transmission efficiency of the planetary gear train are taken into consideration as optimization objectives. The manufacturing size, material, and load input of the planetary gear train are considered as uncertainties. An approximate direct decoupling model, based on subinterval Taylor expansion, is applied to evaluate the propagation of uncertainties. To improve the convergence ability of the multi-objective evolutionary algorithm, the improved non-dominated sorting genetic algorithm II (NSGA-II) is designed by using chaotic and adaptive strategies. The improved NSGA-II has better convergence efficiency than classical NSGA-II and multi-objective particle swarm optimization (MOPSO). In addition, the multi-criteria decision making (MCDM) method is applied to choose the most satisfactory solution in Pareto sets from the multi-objective evolutionary algorithm. Compared with the multi-objective deterministic optimization design (MDOD), the proposed MUOD framework has better reliability than MDOD under different uncertainty cases. This MUOD method enables further guidance pertaining to the uncertainty optimization design of transportation equipment, containing gear reduction mechanisms, in order to reduce the failure risk.
... Furthermore, the framework includes coding three sets of benchmarking mathematical functions with an MOO and/or variable-length nature. Two sets of multiobjective benchmarking functions with a V-length attribute, namely CEC 2020 [13] and Fonseca & ZDT [14], [15], were used. The third one includes basic unimodal and multimodal test functions [16]. ...
Wireless Sensor Network (WSN) management has several NP-hard optimization problems with multiobjective space and variable solution space nature. Such problems are considered challenging and require a carefully developed and well-understood algorithm in behavior and performance. This article presents an open-source benchmarking framework that enables comparison within supporting multiobjective optimization metrics and networking measures. As the first of its type, the framework is designated as Variable-length Multiobjective Optimization (VLMOO). It includes three sets of mathematical benchmarking problems, WSN deployment problem with multiobjective, and variable-length nature. It is extensible and flexible in enabling interfacing with other algorithms with rich visualization graphs generation for the metrics.
When real-world engineering challenges are examined adequately, it becomes clear that multi-objective need to be optimized. Many engineering problems have been handled utilizing the decomposition-based optimization approach according to the literature. The performance of multi-objective evolutionary algorithms is highly dependent on the balance of convergence and diversity. Diversity and convergence are not appropriately balanced in the decomposition technique, as they are in many approaches, for real-world problems. A novel Multi-Objective Artificial Algae Algorithm based on Decomposition (MOAAA/D) is proposed in the paper to solve multi-objective structural problems. MOAAA/D is the first multi-objective algorithm that uses the decomposition-based method with the artificial algae algorithm. MOAAA/D, which successfully draws a graph on 24 benchmark functions within the area of two common metrics, also produced promising results in the structural design problem to which it was applied. To facilitate the design of the "rectangular reinforced concrete column" using MOAAA/D, a solution space was derived by optimizing the rebar ratio and the concrete quantity to be employed.
Data-driven models are now successfully used to solve complex multi-objective optimisation problems in materials mechanics. This chapter deals with the creation of surrogate models and its subsequent application for optimisation by evolution-based algorithms. Models representing curved beams or frames fabricated from composite tubes with circular cross sections are discussed here. Some learning strategies based on Evolutionary Neural Network (EvoNN), Bi-objective Genetic Programming (BioGP), and Evolutionary Deep Neural Net (EvoDN2) algorithms were applied. The surrogate models obtained from these algorithms were subsequently subjected to multi-optimisation for computing the Pareto fronts as the resulting output. Simple geometries could be very efficiently trained and optimised by each of the above-mentioned approaches, but more complex configurations (e.g., curved beams and frames made up of more tubes or tubes with additional layers) were effectively solved only by the EvoDN2 algorithm, as demonstrated in examples.
This chapter introduces basic procedures for designing and optimizing an electric motor for electric vehicle applications using the example of an axial flux induction motor. The analytical model for the motor is derived firstly, which can provide output values close to that provided by finite element analysis in ANSYS Maxwell with a much shorter simulation time. Then, based on the developed analytical model, the corresponding optimization and solution will be formulated to help optimize the motor to meet all design requirements and achieve excellent performance. Finally, the optimized motor design will be validated by ANSYS Maxwell.
Subpixel mapping (SPM) aims to reconstruct a subpixel-level class distribution map from the pixel-level abundance maps, which is an under-determined problem that has non-unique solutions. To address this, the spatiotemporal SPM uses the abundance, spatial, and temporal constraints to reduce the uncertainty of the mapping solutions, so the spatiotemporal SPM is essentially a constrained optimization problem. However, it is hard to find the optimal weighting parameters to combine the three joint constraints. In addition, the existing spatiotemporal SPM methods mainly use the temporal information either for the unchanged subpixels detection or for the subpixel classification, which is insufficient in the utilization of the temporal information. In this paper, a novel multiobjective optimization-based spatiotemporal SPM algorithm (STSPM_MO) is proposed. STSPM_MO is composed of an unchanged subpixels detection stage and a multiobjective spatiotemporal mapping stage. In the former stage, the historical thematic map is used for identifying the unchanged subpixels. In the latter stage, the historical thematic map is further used for providing the temporal dependence, so that the temporal information can be more fully utilized. Moreover, to solve the constrained optimization problem of the spatiotemporal SPM, the abundance, spatial and temporal constraints are modeled as three objectives and are dynamically fused through the subfitness-based multiobjective evolution, to generate the optimal subpixel classification map. Both synthetic and real-data experiments have been conducted and the results show the proposed method and its two variants are superior, stable, and effective.
Planar super-oscillatory lens (SOL), a far-field subwavelength-focusing diffractive device, holds great potential for achieving sub-diffraction-limit imaging at multiple wavelengths. However, conventional SOL devices suffer from a numerical-aperture-related intrinsic tradeoff among the depth of focus (DoF), chromatic dispersion and focusing spot size. Here, we apply a multi-objective genetic algorithm (GA) optimization approach to design an apochromatic binary-phase SOL having a prolonged DoF, customized working distance (WD), minimized main-lobe size, and suppressed side-lobe intensity. Experimental implementation demonstrates simultaneous focusing of blue, green and red light beams into an optical needle of ~0.5λ in diameter and DOF > 10λ at WD = 428 μm. By integrating this SOL device with a commercial fluorescence microscope, we perform, for the first time, three-dimensional super-resolution multicolor fluorescence imaging of the “unseen” fine structures of neurons. The present study provides not only a practical route to far-field multicolor super-resolution imaging but also a viable approach for constructing imaging systems avoiding complex sample positioning and unfavorable photobleaching.
Many-objective optimization problems (MaOPs) are problems that feature four or more objectives, criteria or attributes that must be considered simultaneously. MaOPs often arise in real-world situations and the development of algorithms for solving MaOPs has become one of the hot topics in the field of evolutionary multi-criteria optimization (EMO). However, much of this energy devoted to MaOP research is arguably detached from the challenges of, and decision analysis requirements for, MaOPs. Motivated by this gap, the authors of this chapter organized a Lorentz Center workshop in 2019 entitled Many-Criteria Optimization and Decision Analysis—MACODA—bringing researchers and practitioners together to reflect on the challenges in many-objective optimization and analysis, and to develop a vision for the next decade of MACODA research. From the workshop arose the MACODA book, for which this chapter forms the introduction. The chapter describes the organizers’ perspectives on the challenges of MaOP. It introduces the history of MaOP principally from the perspective of EMO, from where the terminology originated, but drawing important connections to pre-existing work in the field of multi-criteria decision-making (MCDM) which was the source or inspiration for many EMO ideas. The chapter then offers a brief review of the present state of MACODA research, covering major algorithms, scalarization approaches, objective-space reduction, order extensions to Pareto dominance, preference elicitation, wider decision-maker interaction methods and visualization. In drawing together the vision for MACODA in 2030, the chapter provides synopses of the unique and varied contributions that comprise the MACODA book and identifies further under-explored topics worthy of consideration by researchers over the next decade and beyond.
In multi-objective optimisation, it is common to transform the multi-objective optimisation problem into a (sequence of) single-objective problems, and then compute or approximate the solution(s) of these transformed problems. Scalarisation methods are one such example where a set of solutions is determined by solving a sequence of single-objective problems. Another example are indicator-based methods where the aim is to determine, at once, a set of solutions that maximises a given set-quality indicator, i.e., a single-objective function. The aim of this chapter is to explore the connections between set-quality indicators and scalarisations, and discuss the corresponding theoretical properties. In particular, the connection between the optimal solutions of the original multi-objective problem and the optimal solutions of the single-objective problems into which it is transformed is considered.
The insights and benefits to be realised through the optimisation of multiple independent, but conflicting objectives are well recognised by practitioners seeking effective and robust solutions to real-world application problems. Key issues encountered by users of many-objective optimisation (>3 objectives) in a real-world environment are discussed here. These include how to formulate the problem and develop a suitable decision-making framework, together with considering different ways in which decision-makers may be involved. Ways to manage the reduction of computational load and how to reduce the sensitivity of candidate solutions as a result of the inevitable uncertainties that arise in real-world applications are addressed. Other state-of-the-art topics such as the use of machine learning and the management of complex issues arising from multidisciplinary applications are also examined. It is recognised that optimisation in real-world applications is commonly undertaken by users and decision-makers who need not have specialist expertise in many-objective optimisation decision analysis methods. Advice is offered to experts and non-experts alike.
This paper proposes an enhancement to the Harris’ Hawks Optimisation (HHO) algorithm. Firstly, an enhanced HHO (EHHO) model is developed to solve single-objective optimisation problems (SOPs). EHHO is then further extended to a multi-objective EHHO (MO-EHHO) model to solve multi-objective optimisation problems (MOPs). In EHHO, a nonlinear exploration factor is formulated to replace the original linear exploration method, which improves the exploration capability and facilitate the transition from exploration to exploitation. In addition, the Differential Evolution (DE) scheme is incorporated into EHHO to generate diverse individuals. To replace the DE mutation factor, a chaos strategy that increases randomness to cover wider search areas is adopted. The non-dominated sorting method with the crowding distance is leveraged in MO-EHHO, while a mutation mechanism is employed to increase the diversity of individuals in the external archive for addressing MOPs. Benchmark SOPs and MOPs are used to evaluate EHHO and MO-EHHO models, respectively. The sign test is employed to ascertain the performance of EHHO and MO-EHHO from the statistical perspective. Based on the average ranking method, EHHO and MO-EHHO indicate their efficacy in tackling SOPs and MOPs, as compared with those from the original HHO algorithm, its variants, and many other established evolutionary algorithms.
div class="section abstract"> Further advancing key technologies requires the optimization of increasingly complex systems with strongly interacting parameters—like efficiency optimization in engine development for optimizing the use of energy. Systematic optimization approaches based on metamodels, so-called Metamodel-Based Design Optimization (MBDO), present one key solution to these demanding problems. Recent advanced methods either focus on Single-Objective Optimization (SoO) on local metamodels with online adaptivity or Multiobjective Optimization (MoO) on global metamodels with only limited adaptivity. In the scope of this work, a fully online adaptive (“in the loop”) optimization approach, capable of both SoO and MoO, is developed which automatically approximates the global system response and determines the (Pareto) optimum. A combination of a new Design of Experiment (DoE) method for sampling points, Neural Networks as metamodel/Response Surface Model (RSM), and a Genetic Algorithm (GA) for global optimization performed on the RSM enables very high flexibility. Key features of the presented MBDO methodology are as follows: A new fully online, adaptive approach working in iterative loops combined with successive refinements of the RSM; Two novel boundary treatment approaches for handling arbitrarily complex constraints; A novel approach to automatically adapt the number of neurons of the Neural Network to the system complexity; An innovative uncertainty-based DoE method to maximize information gain for each new sample point; Comprehensive additional sampling strategies. Detailed benchmarks to popular DoE methods and MBDO approaches from the literature are conducted. The benchmarks show comparable to slightly better performance to current state-of-the-art SoO MBDO approaches with the significant benefit that a global RSM is obtained, providing valuable insight into the system behavior. Compared to state-of-the-art MoO MBDO approaches, the benchmark highlights a considerably better performance in terms of the needed number of samples (i.e., simulations or experiments), significantly fewer resources required, and high accuracy approximation of the Pareto front.
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In practical multi-criterion decision-making, it is cumbersome if a decision maker (DM) is asked to choose among a set of trade-off alternatives covering the whole Pareto-optimal front. This is a paradox in conventional evolutionary multi-objective optimization (EMO) that always aim to achieve a well balance between convergence and diversity. In essence, the ultimate goal of multi-objective optimization is to help a decision maker (DM) identify solution(s) of interest (SOI) achieving satisfactory trade-offs among multiple conflicting criteria. Bearing this in mind, this paper develops a framework for designing preference-based EMO algorithms to find SOI in an interactive manner. Its core idea is to involve human in the loop of EMO. After every several iterations, the DM is invited to elicit her feedback with regard to a couple of incumbent candidates. By collecting such information, her preference is progressively learned by a learning-to-rank neural network and then applied to guide the baseline EMO algorithm. Note that this framework is so general that any existing EMO algorithm can be applied in a plug-in manner. Experiments on 48 benchmark test problems with up to 10 objectives and a real-world multi-objective robot control problem fully demonstrate the effectiveness of our proposed algorithms for finding SOI.
Selection hyper-heuristics have emerged as high level general-purpose search methodologies that mix and control a set of low-level (meta)heuristics. Previous empirical studies over a range of single objective optimisation problems have shown that the number and type of low-level (meta)heuristics used are influential to the performance of selection hyper-heuristics. In addition, move acceptance strategies play an important role and can significantly affect the overall performance of a hyper-heuristic. In this paper, we introduce an adapted variant of an existing learning automata based multiobjective hyper-heuristic from the literature. We investigate the performance and generality level of the proposed method, and another learning automata based selection hyper-heuristic, operating over a search space of multiobjective evolutionary algorithms (MOEAs) across two well-known multiobjective optimisation benchmarks. The experimental results demonstrate that, regardless of the number and type of low-level metaheuristics available, the learning automata based hyper-heuristics outperform each constituent MOEA individually, and an online learning and random choice selection hyper-heuristic from the literature. This performance and generality is shown to be consistent across a number of different move acceptance strategies.
Most real-world problems involve some type of optimization problems that are often constrained. Numerous researchers have investigated several techniques to deal with constrained single-objective and multi-objective evolutionary optimization in many fields, including theory and application. This presented study provides a novel analysis of scholarly literature on constraint-handling techniques for single-objective and multi-objective population-based algorithms according to the most relevant journals and articles. As a contribution to this study, the paper reviews the main ideas of the most state-of-the-art constraint handling techniques in population-based optimization, and then the study addresses the bibliometric analysis, with a focus on multi-objective, in the field. The extracted papers include research articles, reviews, book/book chapters, and conference papers published between 2000 and 2021 for analysis. The results indicate that the constraint-handling techniques for multi-objective optimization have received much less attention compared with single-objective optimization. The most promising algorithms for such optimization were determined to be genetic algorithms, differential evolutionary algorithms, and particle swarm intelligence. Additionally, “Engineering,” “Computer Science,” and “ Mathematics” were identified as the top three research fields in which future research work is anticipated to increase.
It is inefficient and time-consuming to begin the search from scratch for each optimization task. Evolutionary multitasking optimization (EMTO) handles multiple tasks simultaneously, aiming at improving the solving quality of every task via the evolutionary algorithm (EA) and inter-task knowledge transfer. Thus, suitable evolutionary operators and inter-task effective knowledge transfer are two key factors for the success of EMTO. As one of the representative EMTO algorithms, the multifactorial evolutionary algorithm (MFEA) has attracted a lot of attention. However, MFEA has suffered from the issue of premature convergence and negative knowledge transfer among tasks with a low correlation. To handle these issues, this article enhances MFEA with two proposed strategies, namely a carefully-designed opposition-based learning (OBL) strategy and a carefully-designed differential evolution (DE) strategy, named MFDE-OBL for short. Both the proposed OBL and the proposed DE contain an inter-task strategy and an intra-task strategy. To improve the effectiveness of knowledge transfer, the inter-task OBL strategy learns a linear subspace mapping among task/tasks’ subpopulations to transfer different search scales among tasks, while the inter-task DE strategy uses genetic information from another task to improve the population diversity with different scales and directions. Besides, the intra-task generalized-opposite-point-based OBL is used to enhance the global search ability, while the intra-task DE strategy consists of two complementary DE strategies to maintain a good balance between exploitation and exploration. Finally, the proposed algorithm is tested on both single-objective and multi-objective multi-tasking test suites. Experimental results have shown the efficiency and effectiveness of the proposed algorithm compared with both classical and state-of-the-art algorithms.
With the vast existence of multi-objective optimization problems to the scientific research and engineering applications, Many-objective Evolutionary Algorithms (MaOEAs) demand to systematically perpetuate population diversity and convergence distributions in the objective space with high dimensionality. To fulfill the balance in the relationship between convergence, distributions, and diversity, this paper proposes a directed search many-objective optimization algorithm embodied with kernel clustering strategy (DSMOA-KCS) in decision space where some mechanisms such as adaptive environmental selection which efficiently assimilates design for control of diversity and convergence in the distribution of the solutions in the decision scopes. DSMOA-KCS is a stochastic, multi-start algorithm using clustering to increase efficiency. DSMOA-KCS finds the starting point in the regions of interest. Then, it improves them by the directed search method. DSMOA-KCS is compared with several existing state-of-the-art algorithms (NSGA-III, RSEA, and MOEADPas) on many-objective problems with 5 to 30 objective functions using the Inverted Generational Distance (IGD) performance metric. DSMOA-KCS evaluation results illustrate that it is competitive and promising, performing better with some problems. Then, even distribution, convergence, and diversity are maintained.
Multi-objective optimization (MOO) is widely used for solving various engineering real-life problems. Meta-heuristic optimization has been regarded as an effective solution for such problems because it enables the successful examination of a broad range of candidate solutions and the selection of optimal ones. However, there is a high probability of the algorithms becoming ensnared in local minima due to the complex optimization surface and the unlimited number of viable solutions. Therefore, to provide the decision-maker with the optimal non-dominated set of solutions, significant improvements must be made to the search process, where the efficient exploration of the population has a vital role in maintaining a good non-dominated solution in evolutionary algorithms. MOPSO is regarded as one of the states of the art for meta-heuristic MOO. MOPSO has adopted the concept of crowding distance as a measure that can leverage the characteristics of the distribution of solutions in the search space and provide a high level of exploration. However, this method is not sufficient to effectively explore the search space because it ignores the direction of the exploration. In addition, MOPSO starts the search from a fully randomly initialized swarm without taking any prior knowledge about the searching space into account which is considered impractical in applications where we can estimate initial values for solutions. In this paper, the crowding angle concept was introduced which can help in directing the search to explore wider areas inside the searching space, in addition to an initialization mechanism that takes the advantage of initial guesses based on the prior knowledge of the searching space, both improvements were merged inside Guess aided Angle quantization based Multi-Objective Particles Swarm Optimization (GAMOPSO). which preserves equal exploration in all directions and exploits the initial guesses to boost the search operations, especially in high-dimensional spaces. Three variants of the algorithm were implemented and tested on a set of standard benchmark MOO functions. The results show that the GAMOPSO variants are superior to the traditional MOPSO on the most of evaluation measures for MOO used for the comparisons.
An increase in computing power available from modern processors and GPUs has allowed more complex design optimization problems to be solved. This increase in complexity typically results in a difficult optimization problem with a highly non-linear objective function topology. In this work a robust optimization algorithm is presented capable of efficiently traversing higher-dimensional objective function space to find Pareto optimal solutions. It is well known that no single optimization algorithm performs best for all problems. Therefore, the developed method, a many-objective hybrid optimizer (MOHO), uses five constitutive algorithms and actively switches among them throughout the optimization process to accelerate the convergence, avoid local minima and arrive at a diverse set of optimal designs. MOHO monitors the progress made by each of the five algorithms and allows the best performing algorithm more attempts at finding the optimum. The MOHO algorithm was tested on 13 unconstrained and five constrained analytical test problems, of up to 15 objectives, from the DTLZ and WFG test suite. The MOHO algorithm performed, on average, better than the five constitutive algorithms in 52% of the unconstrained DTLZ+WFG problems and in 70% of the constrained DTLZ test problems.
Constraint violation has been a building block to design evolutionary multi-objective optimization algorithms for solving constrained multi-objective optimization problems. However, it is not uncommon that the constraint violation is hardly approachable in real-world black-box optimization scenarios. It is unclear that whether the existing constrained evolutionary multi-objective optimization algorithms, whose environmental selection mechanism are built upon the constraint violation, can still work or not when the formulations of the constraint functions are unknown. Bearing this consideration in mind, this paper picks up four widely used constrained evolutionary multi-objective optimization algorithms as the baseline and develop the corresponding variants that replace the constraint violation by a crisp value. From our experiments on both synthetic and real-world benchmark test problems, we find that the performance of the selected algorithms have not been significantly influenced when the constraint violation is not used to guide the environmental selection. The supplementary material of this paper can be found in https://tinyurl.com/23dtdne8.
KeywordsConstrained multi-objective optimizationConstraint handling techniquesEvolutionary multi-objective optimization
Community detection is an important topic in complex network analysis which can explore valuable relationships in the networks, such as protein-protein interactions, advertisement recommendations, etc. Recently, the structure and attributes of a network are expected to be integrated to obtain a more accurate community division. But existing community detection algorithms based on multiobjective optimization evolutionary algorithms (MOEAs) for attributed networks have two common problems. First, their encoding strategies completely depend on the network structure, which limits their use of attribute information in search. Second, the calculation of the attribute objective function is time-consuming. In this paper, we propose a novel algorithm that combines the nodes’ embedding vectors generated by a Skip-Gram model with an attention-based multiobjective optimization evolutionary algorithm to discover overlapping communities on networks with attributes. With the help of embedding vectors, the attention-based encoding strategy can overcome the problem of the limited searching capability of traditional MOEAs’ encoding schemes that depend only on a network structure, and an attribute objective function based on embedding vectors is designed which can be calculated in linear time to improve the computational efficiency. The statistical results in artificial and real-world networks demonstrate the feasibility and effectiveness of the proposed method.
Chemical reactors are employed to produce several materials, which are utilized in numerous applications. The wide use of these chemical engineering units shows their importance as their performance vastly affects the production process. Thus, improving these units will develop the process and/or the manufactured material. Multi-objective optimization (MOO) with evolutionary algorithms (EA’s) has been used to solve several real world complex problems for improving the performance of chemical reactors with conflicting objectives. These objectives are of different nature as they could be economy, environment, safety, energy, exergy and/or process related. In this review, a brief description for MOO and EA’s and their several types and applications is given. Then, MOO studies, which are related to the materials’ production via chemical reactors, those were conducted with EA’s are classified into different classes and discussed. The studies were classified according to the produced material to hydrogen and synthesis gas, petrochemicals and hydrocarbons, biochemical, polymerization and other general processes. Finally, some guidelines are given to help in deciding on future research.
Balancing constraints and objective functions in constrained evolutionary multiobjective optimization is not an easy task. Over-emphasis on constraints satisfaction may easily lead to the search to get stuck in local optimal regions, and over-emphasis on objectives optimization may lead to substantial search resources wasted on infeasible regions. This paper proposes a constrained multiobjective optimization algorithm, called CMOEA-SDE, aiming to achieve a good balance between the above two issues. To do so, CMOEA-SDE presents a strictly constrained dominance relation and a constrained shift-based density estimation strategy. Specifically, the former defines a new dominance relation that considers both constraint satisfaction and the objective functions. It favors good feasible solutions but still leaves room for infeasible solutions to be selected.
Unlike most density estimation methods, which only consider the diversity of solutions, our shift-based density estimator covers both the feasibility and the diversity of solutions. That is, our estimator shifts the solutions’ positions based on the extent of the constraints they violate so that solutions violating constraints more severely are shifted to crowded areas, thus being eliminated early. Systematic experiments were conducted on four benchmark test suites and six real-world constrained multiobjective optimization problems. The experimental results suggest that the proposed algorithm can achieve very competitive performance against state-of-the-art constrained multiobjective evolutionary algorithms.
This chapter introduces a new class of optimization problems, called Mixed Pareto-Lexicographic Multi-objective Optimization Problems (MPL-MOPs), to provide a suitable model for scenarios where some objectives have priority over some others. Specifically, this work focuses on two relevant subclasses of MPL-MOPs, namely optimization problems having the objective functions organized as priority chains or priority levels. A priority chain (PC) is a sequence of objectives ordered lexicographically by importance; conversely, a priority level (PL) is a group of objectives having the same importance in terms of optimization, but a lexicographic ordering exists between the PLs. After describing these problems and discussing why the standard algorithms are inadequate, an innovative approach to deal with them is introduced: it leverages the Grossone Methodology, a recent theory that allows handling priorities by means of infinite and infinitesimal numbers. Most interestingly, this technique can be easily embedded in most of the existing evolutionary algorithms, without altering their core logic. Three algorithms for MPL-MOPs are shown: the first two, called PC-NSGA-II and PC-MOEA/D, are the generalization of NSGA-II and MOEA/D, respectively, in the presence of PCs; the third, named PL-NSGA-II, generalizes instead NSGA-II when PLs are present. Several benchmark problems, including some from the real world, are used to evaluate the effectiveness of the proposed approach. The generalized algorithms are compared to other famous evolutionary ones, either priority-based or not, through a statistical analysis of their performances. The experiments show that the generalized algorithms are consistently able to produce more solutions and of higher quality.
Tuning Proportional-Integral-Derivative Computed Torque controllers (PID-CTC) for trajectory tracking control of Robotic Manipulators is a multi-objective optimization problem. Besides selecting a suitable optimization algorithm among various choices, forming an appropriate objective function is also essential. This work investigates the impact of different single and multi-objective optimization strategies for complex trajectory tracking control of a 6DOF robotic manipulators in simulation. By an attempt of optimizing the PID-CTC for two different complex trajectory tracking, this work initiates a multi-trajectory tracking optimization approach.KeywordsRobot manipulator controlPID-CTCMulti-objective optimizationGenetic algorithm
Sectorization problems have significant challenges arising from the many objectives that must be optimised simultaneously. Several methods exist to deal with these many-objective optimisation problems, but each has its limitations. This paper analyses an application of Preference Inspired Co-Evolutionary Algorithms, with goal vectors (PICEA-g) to sectorization problems. The method is tested on instances of different size difficulty levels and various configurations for mutation rate and population number. The main purpose is to find the best configuration for PICEA-g to solve sectorization problems. Performance metrics are used to evaluate these configurations regarding the solutions’ spread, convergence, and diversity in the solution space. Several test trials showed that big and medium-sized instances perform better with low mutation rates and large population sizes. The opposite is valid for the small size instances.KeywordsSectorization problemsCo-Evolutionary AlgorithmsMany-objective optimisation
To improve the maintenance and quality of software product
lines, efficient configurations techniques have been proposed. Nevertheless,
due to the complexity of derived and configured products in a product line,
the configuration process of the software product line (SPL) becomes timeconsuming
and costly. Each product line consists of a various number of
feature models that need to be tested. The different approaches have been presented
by Search-based software engineering (SBSE) to resolve the software
engineering issues into computational solutions using some metaheuristic
approach. Hence, multiobjective evolutionary algorithms help to optimize
the configuration process of SPL. In this paper, different multi-objective
Evolutionary Algorithms like Non-Dominated Sorting Genetic algorithms
II (NSGA-II) and NSGA-III and Indicator based Evolutionary Algorithm
(IBEA) are applied to different feature models to generate optimal results
for large configurable. The proposed approach is also used to generate the
optimized test suites with the help of different multi-objective Evolutionary
Algorithms (MOEAs).
Teaching–Learning-Based Optimization (TLBO) was developed to solve single-objective optimization problems. It is inspired by the theory of teaching–learning mechanism, which works better for unimodal problems. However, TLBO’s exploration is weak, and hence its performance is not better for multimodal problems. To solve multimodal problems and maintain good exploration, we made significant changes to the operators of basic TLBO. The changes we made are to add multiple teachers in the Teacher phase and Euclidean distance in the Student phase. With this modification to TLBO, we developed a multi-objective variant of TLBO to produce more diverse solutions to solve multi-objective optimization problems. The proposed algorithm, named multi-objective generalized TLBO (MOGTLBO), is tested on standard benchmark test problems. The simulated result of the proposed algorithm is compared with the other existing multi-objective optimization algorithms, and it is found that MOGTLBO performs better comparatively.
Higher education is one of the scarcest social resources, with high demand and low supply, and higher education is currently in limited supply in our country, making it difficult to resolve this contradiction. In addition to increasing investment in higher education as much as possible, the most important thing is to maximize the benefits of education through the rational allocation of resources. An evaluation index system of educational resource input-output was constructed, and a multiobjective function model of educational resource utilization efficiency and allocation efficiency was proposed. We should rationalize the allocation of resources and maximize the benefits of innovation and entrepreneurship education in colleges and universities. By combining particle swarm optimization with genetic algorithm, we can simulate and solve the model. The simulation results suggest that by optimizing the usage and allocation efficiency of innovation, it may be increased. College and university entrepreneurship education resources have increased by 18.72 percent and 20.98 percent, respectively, on average, and tend to be in a balanced state, which can realize the optimization of education resources allocation.
Diversification of investment is a well-established practice for reducing the total risk of investing. Portfolio optimization is an effective way for investors to disperse investment risk and increase portfolio return. Under the assumption of no short selling, a bi-objective minimizing portfolio optimization model, in which the first objective is a semi-absolute deviation mean function used to measure the portfolio risk, and the second objective is a maximum entropy smooth function used to measure the portfolio return, is given in this paper. Also, a maximum entropy multi-objective evolutionary algorithm is designed to solve the bi-objective portfolio optimization model. In order to obtain a sufficient number of uniformly distributed portfolio Pareto optimal solutions located on the true Pareto frontier and fully exploit the useful asset combination modes which can lead the search process toward the frontier direction quickly in the objective space, a subspace multi-parent uniform crossover operator and a subspace decomposition mutation operator are given. Furthermore, a normalization method to deal with the tight constraint and the convergence analysis of the proposed algorithm are also discussed. Finally, the performance of the proposed algorithm is verified by five benchmark investment optimization problems. The performance evaluations and results analyses illustrate that the proposed algorithm is capable of identifying good Pareto solutions and maintaining adequate diversity of the evolution population. Also, the proposed algorithm can obtain faster and better convergence to the true portfolio Pareto frontier compared with the three state-of-the-art multi-objective evolutionary algorithms. The result can also provide optimal portfolio plan and investment strategy for investors to allocate and manage asset effectively.
The Siluro-Devonian adaptive radiation of jawed vertebrates, which underpins almost all living vertebrate biodiversity, is characterized by the evolutionary innovation of the lower jaw. Multiple lines of evidence have suggested that the jaw evolved from a rostral gill arch, but when the jaw took on a feeding function remains unclear. We quantified the variety of form in the earliest jaws in the fossil record from which we generated a theoretical morphospace that we then tested for functional optimality. By drawing comparisons with the real jaw data and reconstructed jaw morphologies from phylogenetically inferred ancestors, our results show that the earliest jaw shapes were optimized for fast closure and stress resistance, inferring a predatory feeding function. Jaw shapes became less optimal for these functions during the later radiation of jawed vertebrates. Thus, the evolution of jaw morphology has continually explored previously unoccupied morphospace and accumulated disparity through time, laying the foundation for diverse feeding strategies and the success of jawed vertebrates.
Abstract
A specialized genetic algorithm, which was introduced in the GLEAM concept for "intuitive learning" by C.Blume at the lst PPSN, is applied to two task planning and learning applications. The first one is to move the tool center point of a simulated industrial robot to a given location on a "good” path avoiding obstacles and the second one is to control the behavior of an autonomous vehicle. The results of applying the ideas of population structures as described by M.Gorges-Schleuter to the task planning genetic algorithm are outlined and compared to the first implementation based on a panmictic population model. The influence of some selected parameters of the genetic algorithm on convergence and computing load have been investigated and are presented. The robot task has been varied in order to find out how the already learned plans can help to solve new tasks. A parallel implementation, which exploits the inherent parallelism of the used neighborhood model, is under development. Finally the concept for controlling an autonomous vehicle is presented as an outlook to future work.
Abstract Three main streams of Evolutionary Algorithms (EAs), i.e. probabilistic optimization algorithms based on the model of natural evolution, are compared with each other in this article: Evolution Strategies (ESs), Evolu- tionary Programming (EP), and Genetic Algorithms (GAs). The comparisonis performed with respect to certain characteristic components of EAs, i.e. the representation scheme of object variables, mutation, recombination, and the selection operator. Furthermore, each algorithm is formulated in a high-level notation as an instance of the general, unifying basic algorithm, and the fundamental theoretical results on the algorithms are presented. Finally, after presenting experimental results for three test functions representing a unimodal and a multimodal case as well as a step function with discontinuities, similarities and differences of the algorithms are elaborated, and some hints to open research questionsare sketched.
This paper describes the use of multiobjective genetic algorithms
(MOGAs) in the design of a multivariable control system for a gas
turbine engine. It is shown how the MOGA confers an immediate advantage
over conventional multiobjective optimization methods by evolving a
family of Pareto-optimal solutions allowing the control engineer to
examine the trade-offs between the different design objectives. In
addition, the paper demonstrates how the genetic algorithm can be used
to search in both controller structure and parameter space thereby
offering a potentially more general approach to optimization in
controller design than traditional numerical methods
Many, if not most, optimization problems have multiple objectives.
Historically, multiple objectives have been combined ad hoc to form a
scalar objective function, usually through a linear combination
(weighted sum) of the multiple attributes, or by turning objectives into
constraints. The genetic algorithm (GA), however, is readily modified to
deal with multiple objectives by incorporating the concept of Pareto
domination in its selection operator, and applying a niching pressure to
spread its population out along the Pareto optimal tradeoff surface. We
introduce the Niched Pareto GA as an algorithm for finding the Pareto
optimal set. We demonstrate its ability to find and maintain a diverse
“Pareto optimal population” on two artificial problems and
an open problem in hydrosystems
This paper describes the use of multiobjective genetic algorithms
(MOGAs) in the design of a multivariable control system for a gas
turbine engine. The mechanisms employed to facilitate multiobjective
search with the genetic algorithm are described with the aid of an
example. It is shown that the MOGA confers a number of advantages over
conventional multiobjective optimization methods by evolving a family of
Pareto-optimal solutions rather than a single solution estimate. This
allows the engineer to examine the trade-offs between the different
design objectives and configurations during the course of an
optimization. In addition, the paper demonstrates how the genetic
algorithm can be used to search in both controller structure and
parameter space thereby offering a potentially more general approach to
optimization in controller design than traditional numerical methods.
While the example in the paper deals with control system design, the
approach described can be expected to be applicable to more general
problems in the fields of computer aided design (CAD) and computer aided
engineering (CAE)
He consider a cone dominance problem: given a "preference" cone lP and a set n X ~ R of available, or feasible, alternatives, the problem is to identify the non dominated elements of X. The nonzero elements of lP are assumed to model the do- nance structure of the problem so that y s X dominates x s X if Y = x + P for some nonzero p S lP. Consequently, x S X is nondominated if, and only if, ({x} + lP) n X = {x} (1.1) He will also refer to nondominated points as efficient points (in X with respect to lP) and we will let EF(XJP) denote the set of such efficient points. This cone dominance problem draws its roots from two separate, but related, ori gins. The first of these is multi-attribute decision making in which the elements of the set X are endowed with various attributes, each to be maximized or minimized.
The evolutionary approach to multiple function optimization formulated in the first part of the paper (1) is applied to the optimization of the low-pressure spool speed governor of a Pegasus turbine engine. This study illustrates how a technique such as the mUltiobjective Genetic Algorithm can be applied and exemplifies how design requirements can be defined as the algorithm runs.
Several objective functions and associated goals express design concerns in direct form, i.e., as the designer would state them. While such a designer-orientated formulation is very attractive, its practical usefulness depends heavily on the ability to search and optimize cost surfaces in such a class much broader than usual, as already provided to a large extent by the Genetic Algorithm (GA).
The two instances of the problem studied, demonstrate the need for preference articulation in cases where many and highly competing objects lead to a non dominated set too large for a finite population to sample effectively. Further, it is sown that only a very small portion of the non-dominated set is of practical relevance, which further substantiates the need to supply preference information to the GA. The paper concludes with a discussion of the results.
This paper describes multicriteria decision models with several types of goal interpretations. We consider decision makers who simultaneously
maximize several objective functions,
wish to attain several goals as close as possible,
want to reach several aspiration levels,
pursue several well-defined fixed goals.
Literature on Multiple Objective Decision Making (MODM) methods and their applications have been reviewed and classified systematically.
This survey provides readers with a capsule look into the existing methods, their characteristics, and applicability to analysis of MODM problems.
The basic MODM concepts are defined and a standard notation is introduced in Part II to facilitate the review.
A system of classifying about two dozen major MODM methods is presented. of these methods have been proposed by various researchers
in the last few years, but here for the first time they are presented together. The basic concept, the computational procedures, and the characteristics of each of these methods are presented concisely in Part III. The computational procedure of each method is illustrated by solving a simple numerical example.
Part IV of the survey deals with the actual or proposed applications of these MODM methods. The literature has been classified into 12 major topics based on the area of applications. Summary of each reference on applications is given.
An updated bibliographical listing of 24 books, monographs or conference proceedings, and 424 papers, reports or theses is presented.
In this work, a multiobjective genetic algorithm is applied in the identification of polynomial models for a real non-linear system. The approach is shown to allow multiple performance, complexity, and validity criteria to influence the selection of candidate model structures, leading to the production of various preferable alternatives. The various models produced by the algorithm enable a better informed selection of the final identified model.
Non-linear model term selection is identified as a novel field of application for genetic algorithms (GAs). After formulating the problem as a subset selection problem, a suitable representation for subsets and the corresponding genetic operators are presented. While earlier approaches searched the space of terms in order to gradually build a model of increasing complexity, the subset GA actually searches the much larger space of all models with a given number of terms, having the ability to find not only a good model, but a family of models.
The subset GA is successfully applied to two different problems. A family of low residual variance models is identified and posteriorly evaluated according to other measures of performance and validated before the final model is chosen. Directions for further work are identified.
Two important solution concepts in the theory of multicriteria decision making are Pareto optimum and Lexicographic optimum.
An abstract is not available.
The present paper describes an implementation of genetic search methods in multicriterion optimal designs of structural systems with a mix of continuous, integer and discrete design variables. Two distinct strategies to simultaneously generate a family of Pareto optimal designs are presented in the paper. These strategies stem from a consideration of the natural analogue, wherein distinct species of life forms share the available resources of an environment for sustenance. The efficacy of these solution strategies are examined in the context of representative structural optimization problems with multiple objective criteria and with varying dimensionality as determined by the number of design variables and constraints.
The target vector criterion was combined with a genetic algorithm as a parallel and evolutionary search technique. In this way a multicriteria optimization technique was obtained. In a number of numerical simulations the method was compared with classical optimization techniques used in analytical chemistry such as grid search, modified simplex, steepest ascent, overlapping resolution map, pattern search and simulated annealing according to their computational expenditure and speed, their ability to find global and local optima, their on-line applicability in analytical instrumentation and number of experiments needed. Then the technique was experimentally demonstrated for the simulataneous optimization of intensities of six atomic emission lines of trace elements in alumina powder as a function of spectroscopic excitation conditions.
In the design of dynamical systems, such as automatic regulators and electrical networks, a system is required to satisfy constraints and specifications, which can be represented by a set of simultaneous algebraic inequalities. It is shown how typical design problems lead naturally to the formulation of a set of inequalities, any solution of which characterizes an acceptable system. A numerical process for obtaining a solution of a system of inequalities is developed. Applications of the method of inequalities to the design of automatic control systems are discussed. Specific control problems, in single-variable and multivariable systems, are considered, and designs, obtained by methods of inequalities, are compared with those obtained by standard methods of Nyquist, root locus and optimization.
Finding a controller for a given plant in order to achieve a number of design objectives is a common control design problem. As well as closed loop plant stability, design objectives often include measures such as rise time, settling time, overshoot, asymptotic tracking, decoupling and regulation, gain and phase margins, small disturbance response and bounds on frequency response magnitudes. Genetic algorithms have previously been shown to be useful in addressing ill-behaved optimization problems, being able to cope with discontinuities, multimodality and uncertain function evaluations, and their single objective formulation has been extended by the authors to include multiple objectives. The paper shows how genetic search can be interactively used to design controllers of given complexity, in a multiobjective sense, while learning about the trade-off between the design objectives.
For part I see ibid., 26-37. The evolutionary approach to multiple
function optimization formulated in the first part of the paper is
applied to the optimization of the low-pressure spool speed governor of
a Pegasus gas turbine engine. This study illustrates how a technique
such as the multiobjective genetic algorithm can be applied, and
exemplifies how design requirements can be refined as the algorithm
runs. Several objective functions and associated goals express design
concerns in direct form, i.e., as the designer would state them. While
such a designer-oriented formulation is very attractive, its practical
usefulness depends heavily on the ability to search and optimize cost
surfaces in a class much broader than usual, as already provided to a
large extent by the genetic algorithm (GA). The two instances of the
problem studied demonstrate the need for preference articulation in
cases where many and highly competing objectives lead to a nondominated
set too large for a finite population to sample effectively. It is shown
that only a very small portion of the nondominated set is of practical
relevance, which further substantiates the need to supply preference
information to the GA. The paper concludes with a discussion of the
results
Many, if not most, optimization problems have multiple objectives. Historically, multiple objectives have been combined ad hoc to form a scalar objective function, usually through a linear combination (weighted sum) of the multiple attributes, or by turning objectives into constraints. The genetic algorithm (GA), however, is readily modified to deal with multiple objectives by incorporating the concept of Pareto domination in its selection operator, and applying a niching pressure to spread its population out along the Pareto optimal tradeoff surface. We introduce the Niched Pareto GA as an algorithm for finding the Pareto optimal set. We demonstrate its ability to find and maintain a diverse "Pareto optimal population " on two artificial problems and an open problem in hydrosystems. I. Introduction Genetic algorithms (GAs) have been applied almost exclusively to single-attribute 1 problems. But a careful look at many real-world GA applications reveals that the objective functions...
The Genetic Algorithm (GA) is generally portrayed as a search procedure which can optimize pseudo-boolean functions based on a limited sample of the function's values. There have been many attempts to analyze the computational behavior of the GA. For the most part, these attempts have tacitly assumed that the algorithmic parameters of the GA (e.g. population size, choice of genetic operators, etc.) can be isolated from the characteristics of the class of functions being optimized. In the following, we demonstrate why this assumption is inappropriate. We consider the class, F, of all deterministic pseudo-boolean functions whose values range over the integers. We then consider the Genetic Algorithm as a combinatorial optimization problem over f0; 1g l and demonstrate that the computational problem it attempts to solve is NP-hard relative to this class of functions. Using standard performance measures, we also give evidence that the Genetic Algorithm will not be able to efficiently appr...
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