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Hybrid GA for multi objective aerodynamic shape optimization
... a. Binh & Korn Function [10] b. Scaffer function N.1 [11] c. Poloni's two objective function [12] d. Zitzler-Deb-Thiele's function N. 1 [13] e. Zitzler-Deb-Thiele's function N. 2 [13] All except (d) in the list represent MOO problems with convex, connected Pareto fronts whereas (d) represents a problem with non-convex, disconnected Pareto front. ...
Optimization problems concern exploration of the best possible solutions to a given problem. The feasible solutions are termed good or bad based on the respective values of the objective function. For optimization problems involving more than one objective functions, absolute comparison among feasible solutions is not as straight forward as is the case with problems involving single objective functions. It can be shown that comparison among all the feasible solutions cannot be accomplished for problems involving more than one objective functions, due to lack of total order among the solutions. Scalarization is the process of transforming the multi-objective vector into a single scalar objective value. Scalarization is a popular approach for solving multi-objective optimization problems. The most prevalent scalarization technique is weighted sum method, which has been shown to be unsuitable for MOO problems having non-convex Pareto Front. It has been shown that non-convex optimization problems can be transformed into better structured problems through monotonic transformations of the objective functions. This work proposes Pairing Functions as an efficient scalarization method. Pairing functions are monotonic, bijective transformations from R2 → R. This makes pairing functions as strictly monotonic functions, which guarantee unique single-valued aggregated objective for unique combinations of the multiple objectives. The effectiveness of the pairing function based scalarization has been demonstrated on bench-mark MOO problems.
... A step towards aerodynamic shape optimisation was reported by Yamamoto [30] who apphed a Genetic Algorithm to a 2D wing section design for maximum Lift to Drag ratio (L/D) using a There has been significant activity within the literature over the past three years involving the couphng of Genetic Algorithms to CFD solvers. Poloni [3], P&iaux aZ. ...
p>Natural evolutionary systems exhibit a complex mapping between the genetic encoding carried by cells, to the body an form of a living species. The nature of this mapping facilitates the hereditary transfer of parental features to offspring through genes. Adaptation to this mapping occurs during the reproduction process, when parental chromosomes are blended together, and random mutations creep into this process.
Genetic Algorithms, which mimic evolutionary processes such as natural selection, reproduction , and survival of the fittest, can be applied to the problem of aerodynamic design, by breeding shapes together in the hope of finding better ones. Fixed chromosome structures are currently used to map the genetic encoding adapted by the Genetic Algorithm, to a geometric language that can be used to describe shapes such as airfoil sections or wings. To adequately encapsulate high quality aerodynamic shapes, large numbers of genes are required by this mapping at significant expense to the evolutionary process.
Suitable methods that reduce the computational time required to evolve aerodynamic shapes, may be sought by using an encoding that can add necessary detail to shapes, and adapting the complexity of its description.
In this thesis, the complexity and adaptation of shape encoding is explored. A distributed Genetic Algorithm has been created over clusters of networked PCs to perform aerodynamic optimisation. Different representations for describing shapes have been used to design airfoil sections. In order to reduce computational cost, meta-modelling techniques were successfully implemented to predict which newly created shapes will be useful to the Genetic Algorithm, repairing breeding errors to increase design survivability. An object orientated chromosome framework has been developed, to facilitate adaptation of both genes and chromosome structure by Genetic Algorithms. A new hierarchical crossover operator is explored on evolving simple curves from straight lines, by adapting the complexity of the chromosome mapping used by Genetic Algorithm. Finally, the new adaptive encoding is exploited to evolve aerofoil sections, resulting in improvements to design quality and performance costs.</p
... This issue can be tackled by employing surrogate models [13,14]. Expensive calculations are performed for only a handful of designs. ...
This paper presents the multi-objective optimisation of the MH114 high-lift airfoil. We seek the set of Pareto optimal solutions that maximise the airfoil lift and minimise the drag. The lift and drag forces are considered uncertain due to geometrical uncertainties. The uncertainty quantification of the probabilistic aerodynamic force values requires a large number of samples. However, the prediction of the aerodynamic forces is expensive due to the numerical solution of the Navier–Stokes equations. Therefore, a multi-fidelity surrogate assisted approach is employed to combine expensive RANS simulations with cheap potential flow calculations. The multi-fidelity surrogate-based approach allows us to economically optimise the aerodynamic design of the airfoil under uncertainty.
This study proposes a multi-objective, non-dominated, imperialist competitive algorithm (NSICA) to solve optimal feature selection problems. The NSICA is a multi-objective and discrete version of the original Imperialist Competitive Algorithm (ICA) that utilizes the competition between colonies and imperialists to solve optimization problems. This study focused on solving challenges such as discretization and elitism by modifying the original operations and using a non-dominated sorting approach. The proposed algorithm is independent of the application, and with customization, it could be employed to solve any feature selection problem. We evaluated the algorithm's efficiency using it as a feature selection system for diagnosing cardiac arrhythmias. The Pareto optimal selected features from NSICA were utilized to classify arrhythmias in binary and multi-class forms based on three essential objectives: accuracy, number of features, and false negativity. We applied NSICA to an ECG-based arrhythmia classification dataset from the UCI machine learning repository. The evaluation results indicate the efficiency of the proposed algorithm compared to other state-of-the-art algorithms.
This paper introduces the implementation of two new algorithms to solve a special class of optimization problems, called Mixed Pareto-Lexicographic Multi-Objective Optimization Problems (MPL-MOPs). The algorithms concern both problems in which the objective functions are divided in multiple priority levels and problems in which the objective functions are organized in priority chains. In particular: in Priority Levels (PL) problems a single level contains objective functions which have the same priority between them but each level is lex-icographically ordered by importance, instead in Priority Chains (PC) problems a priority chain is a sequence of objective functions lexicographycally ordered by importance but each chain have the same importance respect other chain. To represent these type of problems we exploit the Alpha Theory which is a new theory that allow us to handle the priority which is exploited in the PC and PL model, indeed with the use of the infinity and infinitesimal values, explained in Alpha theory, we are able to mimic the classical approach in which we used the weights to assign the priority to the objective functions. Moreover, thanks to the Alpha theory , we can overcame the limits of the classical approach. In particular the paper is focused on the implementation of the Priority Chain and Priority Level version of the well-known evolutionary genetic algorithm "Non-Dominated Sorting Genetic Algorithm-III" (NSGA-III) which is one of the first algorithms able to deal Many-Objectives problems, for this reason the implemented algorithms will be called PC-NSGA-III and PL-NSGA-III. After the explanation of the implementation of the algorithms, we illustrate the results, using some benchmark, that the algorithms provide us in multi-objective problems. The experiments show that the algorithms provide us good results.
This paper puts forward an improved multi-objective bacterial colony chemotaxis (MOBCC) algorithm based on Pareto dominance. A time-varying step size tactic is adopted to increase the global and local searching abilities of the improved MOBCC algorithm. An external archive is created to keep previously found Pareto optimal solutions. A non-dominated sorting method integrating crowding distance assignment is applied to enhance the time efficiency of the improved MOBCC algorithm. A hybrid method combining bacterial individual mutation, oriented mutation of bacterial colony and local search of external archive is applied to enhance the convergence of the algorithm and maintain the diversity of solution set. The framework of MOEAs based on Pareto dominance is integrated into the improved MOBCC algorithm properly through replacements of the bacterial individuals in the bacterial colony, archive operation, and updating of the bacterial colony. The improved MOBCC algorithm is compared with three common multi-objective optimization algorithms SPEA2, NSGA-II and MOEA/D on fifteen test problems and evolution of optimization, and the experimental results confirm the validity of the improved MOBCC algorithm. Furthermore, the effects of the improved MOBCC algorithm’s parameters on the performance of the improved MOBCC algorithm are analyzed.
The process of optimization is approached as a searching problem, where an optimization algorithm attempts to find the best possible solution to a given objective function within a permissible search domain. Such problems are complicated since we attempt to find the best possible solution to a given objective function. The problem becomes harder when there is more than one objective function that can be defined as multi-objective optimization problems. In such problems, the algorithm attempts to optimize more than one objective function. Furthermore, the problem becomes worse when these objectives are contradicting. Evolutionary algorithms are used to solve such problems including genetic algorithms (GAs). Hybridizing genetic algorithms is also utilized to overcome the sub optimal solution tendency of basic genetic algorithms. In this paper, an enhanced hybrid genetic algorithm is introduced with an advanced selection operator mechanism based on the K-means clustering algorithm that is also supported by the initial centroid selection optimization to ensure the best possible selection process. The proposed algorithm was tested against 4 benchmark multi-objective optimization algorithms where it succeeded to maximize the balance between search space exploration performed by the GA and search space exploitation performed by the PSO, that was reflected in the optimization ability of the algorithm. The enhanced ICSO/K-means selection operator also succeeded to enhance the optimization ability of the proposed algorithm by assuring fair distribution of the selected individuals from each generation.
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