No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
Evolutionary Search under Partially Ordered Fitness Sets
Abstract
The search for minimal elements in partially ordered sets is a generalization of the task of finding Pareto-optimal elements in multi-criteria optimization problems. Since there are usually many minimal elements within a partially ordered set, a population-based evolutionary search is, as a matter of principle, capable of finding several minimal elements in a single run and gains therefore a steadily increase of popularity. Here, we present an evolutionary algorithm which population converges with probability one to the set of minimal elements within a finite number of iterations. 1 Introduction The search for minimal elements in partially ordered sets is a generalization of the task of finding Pareto-optimal elements in multi-criteria optimization problems. Since there are usually many minimal elements within a partially ordered set, a population-based evolutionary search is, as a matter of principle, capable of finding several minimal elements simultaneously and gains therefore a s...
... Now, the problem of the simultaneous accounting of the several quality indicators can be successfully solved using the multiobjective optimization algorithms, including, multiobjective evolutionary algorithms (MOEAs). First of all, it is necessary to say about the multiobjective genetic algorithms [4][5][6][7][8][9][10][11][12][13] and the multiobjective clonal selection algorithms [14][15][16][17][18][19][20]. These algorithms provide a solution of the account's problem of the several objective functions (criteria, quality indicators) at the analysis of various applied problems. ...
... The essential interest has been to introduce elitism to enhance the convergence properties of a MOEA. Among the existing elitist MOEAs, Zitzler and Thiele's SPEA (Strength Pareto Evolutionary Algorithm) [8], Knowles and Corne's PAES (Pareto Archived Evolution Strategy) [9], and Rudolph's elitist GA [10] are well studied. They appeared at the end of 1990s. ...
In this paper a novel approach for time series forecasting with multi-objective clonal selection optimization and modeling has been considered. At first, the main ideas of development of the forecasting models on the base of the strictly binary trees and the modified clonal selection algorithm have been discussed. Herewith, it is suggested, that the principles of development of the forecasting models on the base of the strictly binary trees can be applied to develop the multi-factor forecasting models, if we are aware of the presence of the several interrelated time series. It will allow increasing the forecasting accuracy of the main factor (the forecasting time series) on the base of the additional information on the auxiliary factors (the auxiliary time series). Then, it is offered to make the multiobjec-tive modified clonal selection algorithm on the base of the notion of the " Pareto dominance " , and use the affinity indicator based on the average forecasting error rate, and the tendencies discrepancy indicator in the role of the objective functions in this algorithm. It will allow to improve the results of the solution of a problem of the short-term forecasting and to receive the adequate results of the middle-term forecasting. This multiobjective modified clonal selection algorithm can be applied for solving problems of individual and groups' forecasting. Also, the application of the principles of the attractors' forming on the base of the long time series to creation of the training data sequence with the adequate length has been discussed. In this case, it is possible along with the reduction of the time expenditures on the forecasting models development to minimize the values of the forecasting errors thanks to refusal from the attempt to pick up a forecasting model based on the original data sequence of the big length, which may fail due to the specifics of the applied mathematical tools. The experimental results which confirm the efficiency of the offered novel approach for time series forecasting have been given. 2
... GA are typically characterized by an initial population consisting of a number of individuals (predictor sets) which evolves throughout a series of generations (iterations) until a certain termination condition is attained. Inspired by the evolution theory of genetics, GA typically consider four stages within each generation, namely fitness, selection, crossover and mutation (see e.g., [80]). During fitness, the cost function (here the prediction RMSE) is evaluated by means of a regression tool. ...
This work presents a novel hybrid (physics-and data-driven) model for short-term (intra-day and day-ahead, 3h-24h) wind power forecasting (STWPF). Traditionally, STWPF predictors admitted very few meteorological variables only from the grid points closest to the turbines. Here, with the aim to further capture the underlying atmospheric processes ruling the wind variability in the wind farm, the approach relies on drastically expanding the predictor space, composed of numerous meteorological variables throughout a large geographical domain, retrieved from a weather forecasting model (COSMO-1). An ad-hoc genetic algorithm that optimizes the selection of predictors is designed and combined with feed-forward artificial neural networks for its cost function evaluation. The introduced model is compared to multiple benchmark models in a 16-turbine wind farm in the Swiss Jura mountains. For +12h and +24h lead times, the new approach shows a root-mean squared error normalized to the installed wind farm capacity of 11% and 11.6%, respectively. These values entail ∼16% higher forecasting skill compared to state-of-the-art predictor frameworks. Results highlight the ability of the presented approach to systematically select as predictors different variables with a well-known impact on the wind farm performance, such as the turbulent kinetic energy or the vertical wind shear. Clustering the data according to the wind direction provides substantial benefit. In addition, it provides a better understanding of the attained improvement: largest performances occur in those wind directions affected by highly complex terrain. This indicates that the proposed model can be especially suitable for wind farms in complex terrain.
... To produce better solutions, the elitism strategy is adopted (Zitzler et al., 1994). Some elitist MOEA examples include Strength Pareto Evolutionary Algorithm (SPEA) (Zitzler & Thiele, 1998), Pareto-archived Evolution Strategy (PAES) (Knowles & Corne, 1999) and elitist objective genetic algorithm (Rudolph, 2001). ...
This study proposes a combinatorial double auction bi-objective winner determination problem for last mile delivery using drone. Prior studies are limited on solving mixed integer model, which are not efficient for large-scale scenario. However, this is not practical in real cases as the computation time to obtain the solution is longer due to number of combinations of packages and participants anticipated in the last mile delivery platform. Four multi-objective evolutionary algorithms (MOEAs) with the decomposed winner determination problem model are experimented. This study is able to yield Pareto optimal solutions from multiple runs of mixed linear integer programming (MILP) using different objectives weights in the model. Unmanned aerial vehicle, or drone, has potential to reduce cost and save time for last-mile logistic operations. The result positively shows MOEAs are more efficient than MILP in yielding a set of feasible solutions for undertaking complex winner determination problem models. This is likely an unprecedented research in drone where combinatorial double auction is applied to complex drone delivery services and MOEAs are used to solve the associated winner determination problem model.
... A multi-objective evolutionary algorithm that included a method for preserving variety called Rudolph's Multi-objective Elitist Evolutionary Algorithms (MEEA) was proposed [63]. The primary disadvantage of this method is that it does not assure that the produced solutions are diverse. ...
This paper proposes a variant of the Gray Wolf Optimizer (GWO) called the Cross-Dimensional Coordination Gray Wolf Optimizer (CDCGWO), which utilizes a novel learning technique in which all prior best knowledge is gained by candid solutions (wolves) is used to update the best solution (prey positions). This method maintains the wolf's diversity, preventing premature convergence in multimodal optimization tasks. In addition, CDCGWO provides a unique constraint management approach for real-world constrained engineering optimization problems. The CDCGWO's performance on fifteen widely used multimodal numerical test functions, ten complex IEEE CEC06-2019 suit tests, a randomly generated landscape, and twelve constrained real-world optimization problems in a variety of engineering fields, including industrial chemical producer, power system, process design, and synthesis, mechanical design, power-electronic, and livestock feed ration was evaluated. For all 25 numerical functions and 12 engineering problems, the CDCGWO beats all benchmarks and sixteen out of eighteen state-of-the-art algorithms by an average rank of Friedman test of higher than 78 percent, while exceeding jDE100 and DISHchain1e+12 by 21% and 39%, respectively. For all numerical functions and engineering problems, the Bonferroni-Dunn and Holm's tests indicated that CDCGWO is statistically superior to all benchmark and state-of-the-art algorithms, while its performance is statistically equivalent to jDE100 and DISHchain1e+12. The proposed CDCGWO might be utilized to solve challenges involving multimodal search spaces. In addition, compared to rival benchmarks, CDCGWO is suitable for a broader range of engineering applications.
... The implementation of elitism in genetic algorithms can significantly accelerate performance [28]. It prevents premature loss of good solutions, according to results presented in [29,30]. The first approach uses elitism is SPEA in [29]. ...
Refrigeration systems based on cooling towers and chillers are widely used equipment in industrial buildings, such as shopping centers, gas and oil refineries and power plants, among many others. Cooling towers are used to recover the heat rejected by the refrigeration system. In this work, the refrigeration is composed of cooling towers dotted with ventilators and compression chillers. The growing environmental concerns and the current scenario of scarce water and energy resources have lead to the adoption of actions to obtain the maximum energy efficiency in such refrigeration equipment. This backs up the application of computational intelligence to optimize the operating conditions of the involved equipment and cooling processes. In this context, we utilize multi-objective optimization algorithms to determine the optimal operational setpoints of the cooling system regarding the cooling towers, its fans and the included chillers. We use evolutionary multi-objective optimization to provide the best trade-offs between two conflicting objectives: maximization of the effectiveness of the cooling towers and minimization of the overall power requirement of the refrigeration system. The optimization process respects the constraints to guarantee the correct and safe operation of the equipment when the evolved solution is implemented. In this work, we apply three evolutionary multi-objective algorithms: Non-dominated Sorting Genetic Algorithm (NSGA-II), Micro-Genetic Algorithm (Micro-GA) and Strength Pareto Evolutionary Algorithm (SPEA2). The results obtained are analyzed under different scenarios and models of the cooling system’s equipment, allowing for the selection of the best algorithm and best equipment’s model to achieve energy efficiency of the studied refrigeration system.
... This concept of elitism ensures that the best solution in an iteration does not deteriorate. The speed up of the performance of genetic algorithm due to this elitism is well documented in [52,73]. Detail of the proposed genetic algorithm based approach is presented in this section. ...
Multimodal biometric systems are highly used over unimodal biometric systems. The multimodal systems fuse information from multiple biometric traits to overcome the limitations, like, inter-class similarities, non-universality of unimodal biometric systems. This fusion significantly enhances the overall performance of the biometric systems. One of the ways of fusing information for multimodal biometrics is rank level fusion. In this paper, rank level fusion is formulated as an optimization problem. A novel genetic algorithm (GA) based method is proposed for rank level fusion of multimodal biometrics. It minimizes the distances between an aggregated rank list and each input rank list being derived from individual biometric trait. The proposed method uses Spearman footrule distance measure to find the said distance between a pair of rank lists. Superiority of the proposed method over several existing rank level and score level fusion methods is demonstrated experimentally.
... Different from the single-objective optimization problem, the multiobjective optimization problem needs vector comparison. e multiobjective optimization strategy adopted in this paper is similar to the method of NGSA-II [25][26][27], but some changes have been made. All scheduling schemes are divided into three types. ...
Multiaccess edge computation (MEC) is a hotspot in 5G network. The problem of task offloading is one of the core problems in MEC. In this paper, a novel computation offloading model which partitions tasks into subtasksis proposed. This model takes communication and computing resources, energy consumption of intelligent mobile devices, and weight of tasks into account. We then transform the model into a multiobjective optimization problem based on Pareto that balances the task weight and time efficiency of the offloaded tasks. In addition, an algorithm based on hybrid immune and bat scheduling algorithm (HIBSA) is further designed to tackle the proposed multiobjective optimization problem. The experimental results show that HIBSA can meet the requirements of both the task execution deadline and the weight of the offloaded tasks.
... All of the described procedures can replace the entire parent population with the new individuals, but this may result in the best individual's loss. The results of [85,86] had shown that elitism could significantly speed up the GA's performance, which can also help prevent the loss of good solutions once they are found. To achieve this and reach a better convergence, the worst offspring (20% of the population size) is replaced by the best parent individuals [64]. ...
Due to their distinctive presence in everyday life and the variety of available built-in sensors, smartphones have become the focus of recent indoor localization research. Hence, this paper describes a novel smartphone-based sensor fusion algorithm. It combines the relative inertial measurement unit (IMU) based movements of the pedestrian dead reckoning with the absolute fingerprinting-based position estimations of Wireless Local Area Network (WLAN), Bluetooth (Bluetooth Low Energy—BLE), and magnetic field anomalies as well as a building model in real time. Thus, a step-based position estimation without knowledge of any start position was achieved. For this, a grid-based particle filter and a Bayesian filter approach were combined. Furthermore, various optimization methods were compared to weigh the different information sources within the sensor fusion algorithm, thus achieving high position accuracy. Although a particle filter was used, no particles move due to a novel grid-based particle interpretation. Here, the particles’ probability values change with every new information source and every stepwise iteration via a probability-map-based approach. By adjusting the weights of the individual measurement methods compared to a knowledge-based reference, the mean and the maximum position error were reduced by 31%, the RMSE by 34%, and the 95-percentile positioning errors by 52%.
... They are most widely applied in practice, but in general no mathematical proof of convergence exists. However, some results on convergence for evolutionary methods, provided that the method satisfies some very general conditions, have been published for single- [20] and multi-objective [21] problems. ...
This chapter gives a brief introduction to the formulation of optimisation problems and solving algorithms. After mentioning the different classes of problems, such as continuous/discrete, local/global and single-/multi-objective, and introducing some of the useful terminology, the chapter is split in two main parts: (1) formulations and algorithms for continuous problems, including optimal control, and (2) formulations and algorithms for integer and mixed-integer problems. Both sections first consider standard deterministic methods that have been derived starting by optimality criteria, then more recent heuristics derived by experience and sometimes inspired by nature. This gives the basis to better read and understand some of the following chapters on more advanced topics.
... The research of [16] [17] shows that the elitism of GA can improve the convergence speed. However, the increased number of remained elitism individuals can increase the evolution pressure which may cause premature convergence [18]. ...
This paper presents a Genetic Algorithm approach to solve a specific examination timetabling problem which is common in Japanese Universities. The model is programmed in Excel VBA programming language, which can be run on the Microsoft Office Excel worksheets directly. The model uses direct chromosome representation. To satisfy hard and soft constraints, constraint-based initialization operation, constraint-based crossover operation and penalty points system are implemented. To further improve the result quality of the algorithm, this paper designed an improvement called initial population pre-training. The proposed model was tested by the real data from Sophia University, Tokyo, Japan. The model shows acceptable results, and the comparison of results proves that the initial population pre-training approach can improve the result quality.
... In an influential article, introduced a faster elitist, multi-objective GA: "NSGA-II". Elitism, i.e. keeping in the next generation the current best chromosome in the population, speeds up the convergence speed of the GA and allows to prevent the "catastrophic forgetting" of good solutions (Rudolph, 2001, Zitzler et al., 2000. The NSGA-II algorithm (Deb, Pratap, Agarwal, Meyarivan, and Fast, 2002) limited computational complexity to O(M N 2 ) using domination count, and a sharing rule for draws that gives preference to diversity. ...
This review intends to summarise the key qualities, current challenges and future perspectives faced by the GA technique. Their implicit parallelism and evolutionary operators allow an optimal balance between exploration and exploitation. They thrive in identifying good solutions in large, rugged search spaces. They have desirable convergence properties, offer high flexibility, and impose very few assumptions on the nature of the solutions being evolved. They allow a realistic modelling of evolutionary systems and innovation dynamics. Often criticised for their computational complexity, GAs' computational efficiency is a first challenge to address to handle dynamic or more complex problems, likely with further use of parallelism and GPU computing. The difficult configuration of GAs parameters, determinant to their performance, remains an open area of investigation. The specifications of the canonical GA, notably the choice of individual representation, the design of the fitness landscape, and initial population sampling, impose some implicit constraints on the search space being explored, and the solutions being evolved, requiring further innovations to achieve open-ended evolution and robustness. Most of GAs achievements have so far been achieved from a restricted subset of our knowledge on natural evolution and genetics. We argue that a deeper, renewed inspiration from the state of the art of biology and genetic research, carries the potential for fundamental discoveries in GA design. The evolution of evolvability, the ability to produce the most improving kind of variation for selection, interactions between mutations, pleiotropy, the modularity of biological networks, are only few examples of such many promising future directions. By expanding self-adaptation, a novel class of GAs oriented towards artificial life and open ended evolution can emerge.
... Individuals use real-number coding. According to our experiments and the literatures[63] [64], for the DTLZ problems, compared algorithms use SBX crossover[53] [65], and the polynomial variation for mutation op- ...
With the number increase of optimization objectives, the selection pressure begins to decrease, and the performance of multi-objective evolutionary algorithms becomes gradually inefficient. A decomposition method based on random objective division (ROD) is proposed in this paper for MOEA/D optimizing many-objective problems. We abbreviate MOEA/D using ROD decomposition as MOEA/DROD for easy expression. MOEA/D-ROD adopts a random objective partitioning method transforming a many-objective problem into multiple multi-objective problems. Furthermore, each multi-objective problem utilizes the assigned decomposition method to transform itself into multiple single-objective optimization problems for collaborative optimization. Therefore, different decomposition methods can be combined at the same time to balance diversity and convergence of the algorithm. Three sets of experiments are carried out on two sets of scalable problems DTLZ 1 - 4 and WFG 1 - 9, with the number of objectives from 3-8, 10 and 15. The experimental results verify the effectiveness of the proposed ROD decomposition method in solving those many-objective optimization problems.
... The fitness value decided the rank of the solutions that directed the exploration process towards the nondominated solution. Rudolph [21] proposed a simple elitist [22] multi-objective EA based on a comparison between the parent population and the child population. At each iteration, the candidate parent solutions were compared with the child nondominated solution, and a final non-dominated solution set was formed to participate as the parent population for the next iteration. ...
Real-world problems such as scientific, engineering, mechanical, etc., are multi-objective optimization problems. In order to achieve an optimum solution to such problems, multi-objective optimization algorithms are used. A solution to a multi-objective problem is to explore a set of candidate solutions, each of which satisfies the required objective without any other solution dominating it. In this paper, a population-based metaheuristic algorithm called an artificial electric field algorithm (AEFA) is proposed to deal with multi-objective optimization problems. The proposed algorithm utilizes the concepts of strength Pareto for fitness assignment and the fine-grained elitism selection mechanism to maintain population diversity. Furthermore, the proposed algorithm utilizes the shift-based density estimation approach integrated with strength Pareto for density estimation, and it implements bounded exponential crossover (BEX) and polynomial mutation operator (PMO) to avoid solutions trapping in local optima and enhance convergence. The proposed algorithm is validated using several standard benchmark functions. The proposed algorithm’s performance is compared with existing multi-objective algorithms. The experimental results obtained in this study reveal that the proposed algorithm is highly competitive and maintains the desired balance between exploration and exploitation to speed up convergence towards the Pareto optimal front.
... However, in this work, crossover has been subject to an elitist sub-condition. The idea is inspired by the elitist genetic strategy from the NSGA-II algorithm [75], after different contributions made it evident that "elitism can speed up the performance of the GA significantly, whereas it can help with preventing the loss of good solutions once they are found" [76,77]. Specifically, in this work, we propose an elitist mechanism adapted to the particularities of WFLO, as done in González et al. [48]. ...
Wind Farm Layout Optimization (WFLO) can be useful to minimize power losses associated with turbine wakes in wind farms. This work presents a new evolutionary WFLO methodology integrated with a recently developed and successfully validated Gaussian wake model (Bastankhah and Porté-Agel model). Two different parametrizations of the evolutionary methodology are implemented, depending on if a baseline layout is considered or not. The proposed scheme is applied to two real wind farms, Horns Rev I (Denmark) and Princess Amalia (the Netherlands), and two different turbine models, V80-2MW and NREL-5MW. For comparison purposes, these four study cases are also optimized under the traditionally used top-hat wake model (Jensen model). A systematic overestimation of the wake losses by the Jensen model is confirmed herein. This allows it to attain bigger power output increases with respect to the baseline layouts (between 0.72% and 1.91%) compared to the solutions attained through the more realistic Gaussian model (0.24–0.95%). The proposed methodology is shown to outperform other recently developed layout optimization methods. Moreover, the electricity cable length needed to interconnect the turbines decreases up to 28.6% compared to the baseline layouts.
... The technique of preserving the elite should also constantly update the set of non-dominated solutions and get rid of individuals that are dominated by newly generated non-dominated ones. The examples of elitist MOEAs are Rudolph's algorithm [53], strength Pareto evolutionary algorithm (SPEA) [54], strength Pareto evolutionary algorithm 2 (SPEA2) [55] and multi-objective micro GA [56]. ...
Return on Equity is an important factor from the perspective of formulating and implementing a company’s financial strategies. It is also one of its evaluation criteria. It presents to investors the effectiveness of using their capital. Increasing profitability may be treated as a symptom of shareholder wealth, while its reduction may be a signal indicating a deterioration of the financial situation of the company. An investment in a company will be attractive to investors if the results obtained by it will enable the benefit from the dividend to be paid and if the share prices will show an upward trend. Therefore, profit and profitability are categories dependent on the company and affect the wealth of its owners. The Return on Equity ratio is synthetic and is linked to, among others with the size of sales, asset use activity and the size of the company’s debt. However, the decisions regarding the capital structure of a company should be made not only by purely economic and financial analyses but also should take into account the social and environmental effects of economic activities. To take into account not only shortterm financial goals but also long-term sustainable development goals during the decision-making process, we need intelligent and creative multi-criteria decision support tools. Bio-inspired artificial intelligence techniques—like evolutionary algorithms, deep neural networks or swarm algorithms, to give only a few examples—are gaining more and more popularity in the recent years. Evolutionary algorithms are optimization techniques that are modeled on the processes of evolution that are taking place in natural populations. They can find approximate solutions to the NP-hard global, multi-modal and multi-objective optimization problems. In this paper, we propose an innovative approach—an agent-based bio-inspired system supporting decisions in the area of corporate finance, which takes into account not only financial goals but also sustainable development goals. The system will allow for multi-objective optimization with the use of bio-inspired algorithms. In this paper, we will concentrate on one module of the proposed system—the evolutionary algorithm optimizing the Return on Equity factor. During the experiments, we will verify the ability of the proposed algorithm to provide decision makers with reasonable, useful and at the same time also innovative and non-obvious solutions concerning the desired capital structure of a given company, which usually operates in a rapidly changing environment. The proposed system will allow for taking into account more than one criteria and perform multi-objective optimization with the use of an evolutionary algorithm or an agent-based co-evolutionary algorithm, so it will be possible to include also the long-term goals of sustainable development in the future.
... The non-dominated sorting genetic algorithm (NSGA) and the NSGA-II are between the most famous of them based on the Pareto optimality concept. The NSGA that is presented by Deb and Srinivas has some shortcomings as (i) the high complexity, of the non-dominated sorting, which is O(mN 3 ) at each iteration, (ii) the lack of elitism and (iii) the diversity adjustment requirement [13][15] [35][54]. ...
Many evolutionary algorithms have been used to solve multi-objective scheduling problems. NSGA-II is one of them that is based on the Pareto optimality concept and generally obtains good results. However, it is possible to improve its performance with some modifications. In this paper, two modified NSGA-II algorithms have been suggested for solving the multi-objective flexible job shop scheduling problem. The neighborhood structures defined for the problem are integrated into the algorithms to create better generations during the iterations. Also, their initial populations are created with an effective heuristic. In the first modified NSGA-II, after the creation of the offspring population, a neighbor of each individual in the parent population is constructed, and then one of them is selected according to the domination state of the solutions. Then the populations are merged to create a new population. In the second modified NSGA-II, only the solutions on the first and second fronts of the parent population and also their neighbors are merged with the offspring population. Other operators of the algorithms like the non-dominated sorting and calculating the crowding distances are as the classic NSGA-II. A comparison is done with a classic NSGA-II based on two metrics. The results show that as it is in the first modified NSGA-II, including neighbors of more individuals of the population provides better results because it increases diversity and intensity of the search.
... The component costs comprise two parts: availability-associated cost and performance-associated cost. Non-dominated sorting genetic algorithm-II (NSGA-II) is selected for solving the optimization problem [43], [44]. Finally, a practical pumping system is considered as an example to illustrate the availability model and optimal component design. ...
As one of the most typical multistate systems, weighted k-out-of-n system has been extensively studied in recent years. This paper presents a new kind of multistate weighted k-out-of-n system, which simultaneously considers performance requirements of each component and the system performance (cumulative performance threshold of all components). Then, we establish a new dynamic availability model by combining the Markov process and universal generating function. Moreover, an optimal design is proposed to achieve a trade-off between system reliability/availability and cost. Non-dominated sorting genetic algorithm-II is used to optimize the probability and performance of components in different states. Finally, an example is illustrated to evaluate system availability and optimize component design. The optimization design can be referred as an optimal standard in system update. OAPA
... In order to speed up the convergence, we follow the popular elitism heuristic [25,80,109] by keeping, besides a population of n candidate solutions, also a population of n top candidate solutions generated so far in previous iterations, and combine these two populations to generate a new generation of candidate solutions so that the top candidate solutions are carried over from one generation to the next unaltered. ...
This preprint is available on arXiv.org as well:
https://arxiv.org/abs/1512.09347
This is a method to find reoccuring patterns in the single cell cryo-electron tomograms. The paper is under review at Structure.
... Cet algorithme est souvent cité comme meilleur que ses concurrents (Zitzler. E, 2001) (Knowles, 1999) (Rudolph, 1999). ...
Le bâtiment contribue majoritairement aux enjeux de la transition energétique. Pour mieux réduire ses consommations, assurer un meilleur confort, répondre aux exigences environnementales et règlementaires, tout en minimisant le prix total, nous proposons d’outiller la conception (des phases d’esquisse à la phase de conception plus avancées, …) par des solutions offrant une vision globale du bâtiment et permettant de faire des choix optimaux. La conception en bâtiment est caractérisée par de nombreux modèles et outils de simulation experts complémentaires, mais indépendants et hétérogènes. En réponse à cette problématique d’interopérabilité, nous proposons une approche orientée service, basée sur l’Internet, pour couvrir les aspects de modèlisation globale et d’aide à la décision. Nous abordons plus particulièrement les problématiques liées aux stratégies et algorithmes de co-simulation, d’optimisation multi-objectif hybride discret/continu et l’aide à la décision multicritère. Ce travail est réalisé dans le cadre de l’ANR COSIMPHI en partenariat fort avec le CSTB.
... The approach presented in this paper is referred to as an elitist multiobjective evolutionary algorithm (NSGA) [Deb, 2001]. This procedure was suggested but not simulated by [Rudolph, 1999] to develop a selection method for multiobjective evolutionary algorithms [Deb, 2001]. Deb et al. [2002] refined Rudolph's algorithm, referred to as NSGA-II, which is available in Matlab [The MathWorks Inc., 2013b]. ...
The evaluation of the seismic safety and reliability of buildings and building contents within a probabilistic framework often requires response history analyses using site-specific ground motion records. The ground motion selection method proposed in this paper addresses this issue by a stochastic search procedure in which record sets are selected such that first- and second-order statistics satisfy predefined ground motion spectrum targets over a wide period range. The methodology enables the ground motion selection process to be independent of the structural properties of the building, i.e., information such as fundamental period is not required. Once a ground motion record set is selected, it can be used for seismic assessment of a broad class of buildings within the target period range at the given location. The method is illustrated herein for a site located in Century City (Los Angeles), California, USA.
... It is an addition to many selection methods that forces the GA to retain some number of the best individuals at each generation. Some studies [45,46] show that elitism can increase the performance of GA by preventing the loss of good solutions once they are found. ...
The choice of the best optimization algorithm is a hard issue, and it sometime depends on specific problem. The Gravitational Search Algorithm (GSA) is a search algorithm based on the law of gravity, which states that each particle attracts every other particle with a force called gravitational force. Some revised versions of GSA have been proposed by using intelligent techniques. This work proposes some GSA versions based on fuzzy techniques powered by evolutionary methods, such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE), to improve GSA. The designed algorithms tune a suitable parameter of GSA through a fuzzy controller whose membership functions are optimized by GA, PSO and DE. The results show that Fuzzy Gravitational Search Algorithm (FGSA) optimized by DE is optimal for unimodal functions, whereas FGSA optimized through GA is good for multimodal functions.
... The essential interest has been to introduce elitism to enhance the convergence properties of a MOEA. Among the existing elitist MOEAs, Zitzler and Thiele's SPEA (Strength Pareto Evolutionary Algorithm) [12], Knowles and Corne's PAES (Pareto Archived Evolution Strategy) [13], and Rudolph's elitist GA [14] are well studied. They appeared at the end of 1990s. ...
The multiobjective modified clonal selection algorithm based on the use of the notion "Pareto dominance", which can be applied for the development of the forecasting models on the base of the strictly binary trees has been offered. It is suggested to use the affinity indicator based on the average forecasting error rate, and the tendencies discrepancy indicator in the role of the objective functions of this algorithm. The multiobjective modified clonal selection algorithm can be applied for solving problems of individual and groups' forecasting. The experimental results which confirm the efficiency of the offered algorithm in comparison with the basic modified clonal selection algorithm have been given.
... The essential interest has been to introduce elitism to enhance the convergence properties of a MOEA. Among the existing elitist MOEAs, Zitzler and Thiele's SPEA (Strength Pareto Evolutionary Algorithm) [13], Knowles and Corne's PAES (Pareto Archived Evolution Strategy) [14], and Rudolph's elitist GA [15] are well studied. They appeared at the end of 1990s. ...
In this paper, a multiobjective modified clonal selection algorithm based on the use of the notion «Pareto set», which can be applied for the development of the forecasting models on the base of the strictly binary trees has been offered. It is suggested to use the affinity indicator based on the average forecasting error rate, and the tendencies discrepancy indicator in the role of the objective functions. The results of experimental studies which confirm the efficiency of the offered multiobjective clonal selection algorithm have been given.
... This strategy consists simply of copying integrally the fittest chromosome of the current population into the following one. Some empirical results show that elitism has a considerable impact on the performance of GAs [41]. It specially ensures that the best fitness of the population can never be reduced throughout generations. ...
The portfolio optimization problem has become a standard financial engineering problem since the pioneering work of Markowitz on Modern Portfolio Theory. It aims to find an optimal allocation of capital among a set of assets by simultaneously minimizing the risk and maximizing the return of the investment. In the theoretical case of linear constraints, this problem is basically solved by quadratic programming. However, real-life financial market imposes some nonlinear constraints such as cardinality constraints, which limit the number of assets held in the portfolio, minimum transaction lots constraints, which require holding discrete units in assets , multiples of minimum lots, e.g., 100 or 200 shares, or transaction costs, which tend to eliminate small holdings. If we take into account these constraints, our problem becomes computationally intractable in theoretical sense, e.g., NP-hard. GA, genetic algorithm, is a collective term describing family of stochastic algorithms based on the natural selection principle – survival of the fittest, and is widely adopted in many fields. In fact, many empirical studies have reported that GA can find good approximate solutions for NP-hard problems. Already various GA-based approaches have been proposed to solve portfolio optimization problems. We survey more than 10 state-of-the-art approaches on the topic, categorize them, compare their computational results and provide brief descriptions of the techniques involved. The aim of this paper is to provide a good guide to the application of GA to portfolio optimization.
... This strategy consists simply of copying integrally the fittest chromosome of the current generation into the following population. Some empirical results show that elitism, when applied, has a considerable impact on the performance of GAs [130]. It especially ensures that the best fitness of the population can never be reduced throughout generations. ...
Solving ill-defined optimization problems, where the actual values of some input parameters are unknown or unknowable, as well as predicting the behavior of algorithms that exhibit sensitive dependence to initial conditions are deemed fundamental issues in several disciplines of science. Such ‘butterfly effects’ often occur in various scientific fields, including economic and financial problems, where the input parameters are usually estimations and thus error-prone. In this case, the problem solutions overfit the past data used for the parameter estimation, rather than forecasting or solving for the future. The solution results actually in poor performance for the ‘true’ data. Injecting some randomness in the solving process would be an advantageous feature. Computer simulation, which is an efficient approach used to randomly generate scenarios of the uncertain parameters, enables to better manage the problem uncertainty. In the current thesis, we address the robustness of the solutions of optimization under uncertainty, and of the outputs of sensitive algorithms, by designing a simple simulation module. The role of our simulation process is solely intended to assess robustness, in the sense that the simulation results are encapsulated within two simple robustness criteria that we propose.
Two separate application domains are conveyed in this thesis. First, the financial problem of portfolio optimization is discussed. After examining the robustness of several evolutionary algorithms (EA) using a simple robustness measure computed over multiple sampling scenarios, we turned to integrating our simulation process for robustness assessment into genetic algorithms (GA), the most robust among the examined EAs, through what is commonly known in the metaheuristic field as hybridization. Robustness in this second step is extended to a bi-criteria assessment. Our empirical experiments, where the hybrid GA is compared to well-established paradigms of optimization under uncertainty such as stochastic programming and robust optimization show encouraging results. As the topic of GA application to portfolio optimization is redundantly present in the thesis, a survey of some state-of-the-art approaches on the matter is provided. The second application of the thesis concerns clustering methods applied to global supply-chain networks, which are generally complex networks. The insight of such application for CO2 emission networks is to find environmentally significant clusters, and thus entry points for international climate change mitigation, as reported in Kagawa et al. (2015) study. However, due to the presence of algorithms sensitive to initialization such as k-means in the body of clustering methods of non-negative matrix factorization and spectral clustering, the yielded cluster assignments are actually sensitive. We employ our bi-criteria simulation module, altered for this problem context, to solve for robust clusterings. Empirical findings of the proposed approach are compared with Kagawa et al. (2015) findings. The environmental implications are reported as well.
... In order to prevent possible negative aspects of the evolution process and hence drive the solutions to get better over time, at each step of the optimization process, the best individuals (a given, userdefined percentage of the population size) are selected to become part of an elite group which is unchanged in the next generation. This technique, in addition to avoiding the possibility to obtain worse generation during the process, enhances its convergence properties [34,35]. The optimization procedure is iterated until either the chromosomes similarity (bit-string affinity) achieves a user-defined value [36], or the maximum number of iterations is reached. ...
An optimal procedure for the design of rotor blade that generates low vibratory hub loads in nonaxial flow conditions is presented and applied to a helicopter rotor in forward flight, a condition where vibrations and noise become severe. Blade shape and structural properties are the design parameters to be identified within a binary genetic optimization algorithm under aeroelastic stability constraint. The process exploits an aeroelastic solver that is based on a nonlinear, beam-like model, suited for the analysis of arbitrary curved-elastic-axis blades, with the introduction of a surrogate wake inflow model for the analysis of sectional aerodynamic loads. Numerical results are presented to demonstrate the capability of the proposed approach to identify low vibratory hub loads rotor blades as well as to assess the robustness of solution at off-design operating conditions. Further, the aeroacoustic assessment of the rotor configurations determined is carried out in order to examine the impact of low-vibration blade design on the emitted noise field.
... NSGA over the years has been widely criticized. The main criticisms are the high computational complexity of non dominated sorting, the lack of elitism (Zitzler et al. 2000;Rudolph 1999) and finally the need for specifying the sharing parameter (Fonseca and Fleming 1998). In Deb et al. (2002) proposed an improved version of NSGA, called NSGA2 which introduced a fast non dominated sorting algorithm. ...
The paper presents strategies optimization for an existing automated warehouse located in a steelmaking industry. Genetic algorithms are applied to this purpose and three different popular algorithms capable to deal with multi-objective optimization are compared. The three algorithms, namely the Niched Pareto Genetic Algorithm, the Non-dominated Sorting Genetic Algorithm 2 and the Strength Pareto Genetic Algorithm 2, are described in details and the achieved results are widely discussed; moreover several statistical tests have been applied in order to evaluate the statistical significance of the obtained results.
... In order to speed up the convergence, we follow the popular elitism heuristic [25,80,109] by keeping, besides a population of n candidate solutions, also a population of n top candidate solutions generated so far in previous iterations, and combine these two populations to generate a new generation of candidate solutions so that the top candidate solutions are carried over from one generation to the next unaltered. ...
Cryo-electron tomography enables 3D visualization of cells in a near native state at molecular resolution. The produced cellular tomograms contain detailed information about all macromolecular complexes, their structures, their abundances and their specific spatial locations in the cell. However, extracting this information is very challenging and current methods usually rely on templates of known structure. Here, we formulate a template-free visual proteomics analysis as a de novo pattern mining problem and propose a new framework called "Multi Pattern Pursuit" for supporting proteome-scale de novo discovery of macromolecular complexes in cellular tomograms without using templates of known structures. Our tests on simulated and experimental tomograms show that our method is a promising tool for template-free visual proteomics analysis.
... This makes NSGA computationally expensive for large population sizes. 2. Lack of elitism: The research results [34,35] show that elitism can significantly speed up the performance of the GA, which also can help in preventing the loss of good solutions once they are found. ...
Tuned Mass Dampers (TMDs) are a well-accepted control device widely used by the civil engineering community. The main purpose of this study is the robust multi-objective optimization design of this device using Genetic Algorithms (GAs) to control the structural vibrations against earthquakes. To enhance the performance of the TMD system, its parameters, including mass, stiffness, and damping ratio, have been optimally designed using multi-objective genetic algorithms. For doing this, three noncommensurable objective functions, namely: maximum displacement, maximum velocity, and maximum acceleration of each floor, are considered, which are to be minimized simultaneously. For this purpose, a fast and elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) approach is used to find a set of Paretooptimal solutions. Moreover, in order to take into account the uncertainties existing in the system, a robust design optimization procedure is performed using the Hammersley sequence sampling approach. In this study, the example building is modeled as a 3-D frame, and its responses are evaluated using coupled multi-mode analysis. From the numerical results of the study, it is found that the robust TMD system is capable of providing a reduction of about 28% on maximum displacement of the building. © 2013 Sharif University of Technology. Production and hosting by Elsevier B.V. All rights reserved.
Besides solving the continuous optimization problems, this chapter introduces the evolutionary multitasking algorithm for solving the complex combinatorial optimization problems. In particular, in this chapter, we first present a generalized variant of vehicle routing problem with occasional drivers, i.e., Vehicle Routing Problem with Heterogeneous capacity, Time window and Occasional driver (VRPHTO), which is inspired by today’s “crowdshipping” and “sharing economy” in vehicle routing. Next, to further conceptualize the cloud-based optimization service that is capable of catering to multiple VRPHTOs requests at the same time, we present an evolutionary multitasking algorithm (EMA) to optimize multiple VRPHTOs simultaneously.
Multi‐objective evolutionary algorithms (MOEAs) have been applied to water distribution system (WDS) optimization problems for over two decades. The selection strategy is a key component of an MOEA that determines the composition of a population, and thereby the evolutionary search process, which imitates natural selection by granting fitter individuals an increasing opportunity to reproduce. This paper proposes the convex hull contribution (CHC) selection strategy for generational MOEAs (CHCGen) as a novel selection strategy that is based on the CHC of solutions to the Pareto front in the objective space. Numerical experiments using a general MOEA framework demonstrate that the CHCGen selection strategy is able to outperform existing popular selection strategies (e.g., crowding distance, hypervolume contribution, and hybrid replacement selection). Moreover, it is illustrated that the CHCGen selection strategy is able to improve the performance of existing MOEAs such as NSGA‐II and GALAXY. The conclusions are based on the results of six bi‐objective WDS problems.
This study proposes a combinatorial double auction bi-objective winner determination problem for last-mile delivery using drone. Prior studies are limited on solving mixed integer model, which are not efficient for large-scale scenario. However, this is not practical in real cases as the computation time to obtain the solution is longer due to number of combinations of packages and participants anticipated in the last-mile delivery platform. Four multi-objective evolutionary algorithms (MOEAs) with the decomposed winner determination problem model are experimented. This study is able to yield Pareto optimal solutions from multiple runs of mixed linear integer programming (MILP) using different objectives weights in the model. Unmanned aerial vehicle, or drone, has potential to reduce cost and save time for last-mile logistic operations. The result positively shows MOEAs are more efficient than MILP in yielding a set of feasible solutions for undertaking complex winner determination problem models. The percentage of improvement in terms of time spent identifying the best option is almost 100%. This is likely an unprecedented research in drone where combinatorial double auction is applied to complex drone delivery services and MOEAs are used to solve the associated winner determination problem model.
Two significant concerns need to be addressed to handle multimodal problems: classifying various local/global optima and preserving these optimum values until the termination. Besides, a comprehensive local search ability is also a need to achieve the exact global optima. Chimp Optimization Algorithm (ChOA) is a recently swarm intelligence algorithm that needs less parameter tuning. The ChOA, on the other hand, is prone to early convergence and fails to strike a balance between exploration and exploitation when it comes to resolving multimodal challenges. In order to overcome these concerns, this paper embeds the niching technique in ChOA (NChOA) that includes the personal best qualities of PSO and a local search technique. To evaluate the NChOA’s performance, we analyze it against fifteen frequently utilized multimodal numerical test functions, ten complex IEEE CEC06-2019 suit tests, and twelve constrained real-world optimization problems in a variety of engineering fields, including industrial chemical producer, process design and synthesis, mechanical design, power system, power-electronic, and livestock teed ration problems. The results indicate that the NChOA outperforms several benchmark algorithms and sixteen out of eighteen state-of-the-art algorithms by an average rank of Friedman test greater than 81% for 25 numerical functions and twelve engineering problems while outperforming jDE100 and DISHchain1e+12 by 22% and 41%, respectively. The Bonferroni-Dunn and Holm tests demonstrated that NChOA outperforms all benchmark and state-of-the-art algorithms for all numerical functions and engineering tasks while performing comparably to jDE100 and DISHchain1e+12. The proposed NChOA, we believe, can be used to address difficulties involving multimodal search spaces. Additionally, NChOA is more broadly applicable than rival benchmarks to a broader range of engineering applications.
In many diagnostic imaging settings, including positron emission tomography (PET), images are typically used for multiple tasks such as detecting disease and quantifying disease. Unlike conventional image reconstruction that optimizes a single objective, this work proposes a multi-objective optimization algorithm for PET image reconstruction to identify a set of images that are optimal for more than one task. This work is reliant on a genetic algorithm to evolve a set of solutions that satisfies two distinct objectives. In this paper, we defined the objectives as the commonly used Poisson log-likelihood function, typically reflective of quantitative accuracy, and a variant of the generalized scan-statistic model, to reflect detection performance. The genetic algorithm uses new mutation and crossover operations at each iteration. After each iteration, the child population is selected with non-dominated sorting to identify the set of solutions along the dominant front or fronts. After multiple iterations, these fronts approach a single non-dominated optimal front, defined as the set of PET images for which none the objective function values can be improved without reducing the opposing objective function. This method was applied to simulated 2D PET data of the heart and liver with hot features. We compared this approach to conventional, single-objective approaches for trading off performance: maximum likelihood estimation with increasing explicit regularization and maximum a posteriori estimation with varying penalty strength. Results demonstrate that the proposed method generates solutions with comparable to improved objective function values compared to the conventional approaches for trading off performance amongst different tasks. In addition, this approach identifies a diverse set of solutions in the multi-objective function space which can be challenging to estimate with single-objective formulations.
Greenhouse cultivation has gained a lot of growers’ interest because of higher yield achieved by maintaining desired environment and provision for additional protective measures. Greenhouses degrade with time, which is caused by mechanical deterioration of construction elements and equipment, as well as by severe climate conditions. These factors are responsible for the gradual change of greenhouse parameter. Therefore, parameters are commonly re-tuned periodically to ensure desired model accuracy for realistic control action generation. The limitation of conventional parameter estimation is that while minimizing the deviation from sensors’ measurements, it ignores the fact that parameters change slowly, and hence, it can overfit to noisy measurements. This paper presents a re-tuning strategy , which utilizes the prior knowledge contained in the previously tuned parameters. For this, the strategy incorporates the deviation from the prior tuned parameters as an objective along with deviation from the sensor measurements, which may be beneficial in overcoming the overfitting of parameters. Multi-objective algorithms were considered for re-tuning , as objectives are of conflicting nature. Multi-objective particle swarm optimization (MOPSO) and non-dominated sorting genetic algorithm (NSGA)-II were used to obtain the Pareto fronts for multiple runs and different population sizes. The Pareto fronts obtained by NSGA-II were found favourable compared to MOPSO regarding the approximation quality of the Pareto front. The selection of the desired parameter set was made based on the balance amongst objectives.
This paper proposes a multi-objective optimization method of a primary double-D pad for Inductive Power Transfer (IPT) systems. First, a parametric sweep analysis is conducted to choose the crucial design parameters. Then, using the non-dominated sorting genetic algorithm II (NSGA-II), the structure of the double-D pad can be optimized based on two key objectives; ensuring a good coupling coefficient while minimizing the worst-case stray leakage magnetic fields. Several useful design guidelines are found from the optimization results, including how the dimensions of both the coil and layers affect the coupling coefficient and stray leakage magnetic fields around the pad. A practical coil suitable for wireless charging of electric vehicles at level 2, similar to that recommended in SAE J2954, is used as the reference and also as the starting point for the optimization. Two of the coil structures resulting from the optimization are chosen and investigated further to assess their performance with different secondary pad misalignments using finite element methods. Finally, an experimental setup is built to validate the optimal pad structures.
With the emergence of
crowdshipping
and
sharing economy
, vehicle routing problem with occasional drivers (VRPOD) has been recently proposed to involve occasional drivers with private vehicles for the delivery of goods. In this article, we present a generalized variant of VRPOD, namely, the vehicle routing problem with heterogeneous capacity, time window, and occasional driver (VRPHTO), by taking the capacity heterogeneity and time window of vehicles into consideration. Furthermore, to meet the requirement in today’s cloud computing service, wherein multiple optimization tasks may need to be solved at the same time, we propose a novel evolutionary multitasking algorithm (EMA) to optimize multiple VRPHTOs simultaneously with a single population. Finally, 56 new VRPHTO instances are generated based on the existing common vehicle routing benchmarks. Comprehensive empirical studies are conducted to illustrate the benefits of the new VRPHTOs and to verify the efficacy of the proposed EMA for multitasking against a state-of-art single task evolutionary solver. The obtained results showed that the employment of occasional drivers could significantly reduce the routing cost, and the proposed EMA is not only able to solve multiple VRPHTOs simultaneously but also can achieve enhanced optimization performance via the knowledge transfer between tasks along the evolutionary search process.
Intense seismic excitations might be considered as one of the
most important loading cases imposed on offshore jacket platforms. To perform seismic assessments for these structures, appropriate suites of ground motions can be selected by different methodologies. Since time history analyses of fixed offshore platforms are truly time consuming, number of selected records can considerably change the computational expenses. This paper quantitatively investigates the effects of sample size of ground motions on seismic performance of these structures. Thus, several samples of record suites with different sample sizes are selected from a target population so that the differences between the statistical properties of their response spectra become minimum using Genetic Algorithm. The results show that the drift or collapse fragility curves based on the suites with larger sample sizes are closer to the target fragility. Nevertheless, according to the results of the investigated case study, some suites with smaller sample sizes (e.g. 20 or 25) could lead to relatively acceptable accuracy at almost half the computational expenses. Also, the correlation coefficients between the collapse fragilities of the selected record sets and the target one are very close to unity, indicating that these collapse fragilities are linearly correlated with the target one.
In this paper we consider multi-objective optimization problems (MOOP) from the point of view of Bayesian analysis. MOOP problems can be considered equivalent to certain statistical models associated with the specific objectives and constraints. MOOP that can explore accurately the Pareto frontier are Generalized Data Envelopment Analysis and Goal Programming. In turn, posterior analysis of their associated statistical models can be implemented using Markov Chain Monte Carlo (MCMC) simulation. In addition, we consider the minimax regret problem which provides robust solutions and we develop similar MCMC posterior simulators without the need to define scenarios. The new techniques are shown to work well in four examples involving non-convex and disconnected Pareto problems and to a real world portfolio optimization problem where the purpose is to optimize simultaneously average return, mean absolute deviation, positive and negative skewness of portfolio returns. Globally minimum regret can also be implemented based on post-processing of MCMC draws.
In this paper, a multiobjective modified clonal selection algorithm based on the use of the notion «Pareto set», which can be applied for the development of the forecasting models on the base of the strictly binary trees has been offered. It is suggested to use the affinity indicator based on the average forecasting error rate, and the tendencies discrepancy indicator in the role of the objective functions. The results of experimental studies which confirm the efficiency of the offered multiobjective clonal selection algorithm have been given.
In this paper, we propose an extension to Banksealer, one of the most recent and effective banking fraud detection systems. In particular, until now Banksealer was unable to exploit analyst feedback to self-tune and improve its performance. It also depended on a complex set of parameters that had to be tuned by hand before operations. To overcome both these limitations, we propose a supervised evolutionary wrapper approach, that considers analyst’s feedbacks on fraudulent transactions to automatically tune feature weighting and improve Banksealer’s detection performance. We do so by means of a multi-objective genetic algorithm. We deployed our solution in a real-world setting of a large national banking group and conducted an in-depth experimental evaluation. We show that the proposed system was able to detect sophisticated frauds, improving Banksealer’s performance of up to 35% in some cases.
In a political redistricting problem, the aim is to partition a territory into electoral districts or clusters, subject to some constraints. The most common of these constraints include contiguity, population equality, and compactness. We propose an algorithm to address this problem based on multi-objective optimization. The hybrid algorithm we propose combines the use of the well-known Pareto-based NSGA-II technique with a novel variable neighbourhood search strategy. A new ad-hoc initialization method is also proposed. Finally, new specific genetic operators that ensure the compliance of the contiguity constraint are introduced. The experimental results we present, which are performed considering five US states, clearly show the appropriateness of the proposed hybrid algorithm for the redistricting problem. We give evidence of the fact that our method produces better and more reliable solutions with respect to those returned by the state-of-the-art methods.
We propose a new particle swarm optimization algorithm for problems where objective functions are subject to zero-mean, independent, and identically distributed stochastic noise. While particle swarm optimization has been successfully applied to solve many complex deterministic nonlinear optimization problems, straightforward applications of particle swarm optimization to noisy optimization problems are subject to failure because the noise in objective function values can lead the algorithm to incorrectly identify positions as the global/personal best positions. Instead of having the entire swarm follow a global best position based on the sample average of objective function values, the proposed new algorithm works with a set of statistically global best positions that include one or more positions with objective function values that are statistically equivalent, which is achieved using a combination of statistical subset selection and clustering analysis. The new PSO algorithm can be seamlessly integrated with adaptive resampling procedures to enhance the capability of PSO to cope with noisy objective functions. Numerical experiments demonstrate that the new algorithm is able to consistently find better solutions than the canonical particle swarm optimization algorithm in the presence of stochastic noise in objective function values with different resampling procedures.
During the past few years, many variations of genetic algorithm (GA) have been proposed. These algorithms have been successfully used to solve problems in different disciplines such as engineering, business, science, and networking etc. Real world optimization problems are divided into two categories: (1) single objective, and (2) multi-objective. Genetic algorithms have key advantages over other optimization techniques to deal with multi-objective optimization problems. One of the most popular techniques of GA to obtain the Pareto-optimal set of solutions for multi-objective problems is the non-dominated sorting genetic algorithm- II (NSGA-II). In this paper, we propose a variant of NSGA-II that we call the comprehensive parent selection-based genetic algorithm (CPSGA). The proposed strategy uses the information of all the individuals to generate new offspring from the selected parents. This strategy ensures diversity to discourage premature convergence. CPSGA is tested using the standard ZDT benchmark problems and the performance metrics taken from the literature. Moreover, the results produced are compared with the original NSGA-II algorithm. The results show that the proposed approach is a viable alternative to solve multi-objective optimization problems.
This paper presents an optimized design of airfoil cross section using two different meta-heuristic schemes with micro-population. Geometrical coordinates of airfoil section are obtained for achieving the desired target pressure distribution and minimum lift-to-drag ratio. The flow solution for a given angle of attack and free-stream velocity is obtained by using XFOIL and with coupled panel–boundary layer (viscous–inviscid interaction) method. Two optimization schemes namely micro-genetic algorithms and micro-differential evolution with five basic airfoil configurations are employed to achieve required objectives with certain constraints in each case. In minimizing the computation time and effort, a surrogate model based on three-layer perceptron neural network is developed and the results are also reported. The optimized section is analysed finally using computational fluid dynamics solution to know the correctness of the optimized data.
An important problem in evolutionary multi-objective optimization is how to build non-dominated set efficiently. An algorithm is proposed for building non-dominated set. In the algorithm, the individuals are sorted based on normalized parameter, and all individuals can be ranked linearly in evolutionary colony. The correlation theory and proof are presented at the same time. On the basis of the proposed algorithm, every individual in evolutionary colony is only compared with those individuals that have been in the non-dominated set, and this comparison is single-direction. Thus the quantity of comparison among the individuals is cut down, and non-dominated set can be built efficiently. This is validated by theoretical analysis and several experiments. The results show that the approach is better than other approaches and exhibits good properties.
Three different supplier selection models have been developed in crisp and fuzzy environments. Here two objective functions have been considered, profit and risk. In this paper, profit has been maximized and risk has been minimized with some constraints. Each supplier has an limited capacity. The purchasing cost of each item from different supplier as well as associative risk is known. The total space and budget of a retailer are constant. In Model I, all the parameters are considered as crisp. In Model II, the demand has been considered as fuzzy. In Model III, the risk values and demand have been considered as fuzzy. To defuzzyfy the fuzzy constraints, necessity and possibility have been introduced. To defuzzyfy the fuzzy objective, two different methods, credibility measure and α-cut method have been introduced. All the models have been illustrated numerically using multi-objective genetic algorithm (MOGA). Also a sensitivity analysis has been done taking different sets of risk values and a comparison result has been shown for credibility measure and α-cut method for Model III.
This paper presents a novel configuration optimization method for multi degree-of-freedom modular reconfigurable robots (MRR) using a memetic algorithm (MA) that combines genetic algorithms (GAs) and a local search method. The proposed method generates multiple solutions to the inverse kinematics (IK) problem for any given spatial task and the MA chooses the most suitable configuration based on the search objectives. Since the dimension of each robotic link in this optimization is considered telescopic, the proposed method is able to find better solutions to the IK problem than GAs. The case study for a 3-DOF MRR shows that the MA finds solutions to the IK problem much faster than a GA with noticeably less reachability error. Additional case studies show that the proposed MA method can find multiple IK solutions in various scenarios and identify the fittest solution as a suboptimal configuration for the MRR.
The task of finding minimal elements of a partially ordered set is a generalization of the task of finding the global minimum of a real valued function or of finding pareto optimal points of a multicriteria optimization problem. It is shown that evolutionary algorithms are able to converge to the set of minimal elements in finite time with probability one, provided that the search space is finite, the time invariant variation operator is associated with a positive transition probability function and that the selection operator obeys the so called elite preservation strategy.
Although there are many versions of evolutionary algorithms that
are tailored to multi-criteria optimization, theoretical results are
apparently not yet available. In this paper, it is shown that results
known from the theory of evolutionary algorithms in case of
single-criterion optimization do not carry over to the multi-criterion
case. At first, three different step size rules are investigated
numerically for a selected problem with two conflicting objectives. The
empirical results obtained by these experiments lead to the observation
that only one of these step size rules may have the property to ensure
convergence to the Pareto set. A theoretical analysis finally shows that
a special version of an evolutionary algorithm with this step size rule
converges with probability one to the Pareto set for the test problem
under consideration
This paper provides conditions under which evolutionary algorithms
with an elitist selection rule will converge to the global optimum of
some function whose domain may be an arbitrary space. These results
generalize the previously developed convergence theory for binary and
Euclidean search spaces to general search spaces
If f is a real-valued function which is upper semicontinuous on a compact subset of a topological space, then it attains a maximal value. There are similar results for partial-order-valued functions. This paper assumes f to be quasi-order-valued. Semicontinuity will be defined via level sets of the form {xx | α ≤ f(x)} or {x X | f <α}. Two order-induced topologies will allow the semicontinuity of f to be formulated as continuity relative to these topologies. In addition to the question of the existence of maximal values of f, the following will be discussed: properties of the order-induced topologies; semicontinuity of the greatest lower bound of a family of semicontinuous functions; partial semicontinuity of functions of the form f: x×Y→z.
We consider the usage of evolutionary algorithms for multiobjective programming (MOP), i.e. for decision problems with alternatives taken from a real-valued vector space and evaluated according to a vector-valued objective function. Selection mechanisms, possibilities of temporary fitness deterioration, and problems of unreachable alternatives for such multiobjective evolutionary algorithms (MOEAs) are studied. Theoretical properties of MOEAs such as stochastic convergence with probability 1 are analyzed.
this article we define the choice function of a non-empty set family that does not contain ; as introduced in [6, pages 88--89]. We define order of a set as a relation being reflexive, antisymmetric and transitive in the set, partially ordered set as structure non-empty set and order of the set, chains, lower and upper cone of a subset, initial segments of element and subset of partially ordered set. Some theorems that belong rather to [5] or [14] are proved. MML Identifier: ORDERS1.