Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control and Artificial Intelligence
Genetic Algorithms in Search, Optimization and Machine Learning
Genetic Algorithms in Search, Optimization and Machine Learning
Multi-Objective Optimization Using Evolutionary Algorithms
Multi-Objective Optimization Using Evolutionary Algorithms
Multiple Objective Optimization with Vector Evaluated Genetic Algorithms
Proceedings of the 1st International Conference on Genetic Algorithms
Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization
Proceedings of the 5th International Conference on Genetic Algorithms
Muiltiobjective optimization using nondominated sorting in genetic algorithms
Evolutionary Computation
Multiobjective evolutionary algorithms: a comparative case studyand the strength Pareto approach
IEEE Transactions on Evolutionary Computation
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The method is developed for multi-objective optimization problems. Its purpose is to evolve an evenly distributed group of solutions to determine the optimum Pareto set for a given problem. The algorithm determines a set of solutions (a population), this population being sorted by its domination properties and a filter is defined in order to retain the Pareto solutions. In most topology design problem volume is in general a constraint of the problem. Due to this constraint, all chromosomes used in the genetic algorithm must generate individuals with the same volume value; in the coding adopted this means that they must preserve the same number of ones and, implicitly, the same number of zeros, along the evolutionary process. It is thus necessary to define these chromosomes and to create corresponding operators of crossover and mutation which preserve volume. To reduce computational effort, optimal solutions of each of the single-objective problems are introduced in the initial population. Results obtained by the evolutionary and classical methods are compared.