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- Multiobjective topology optimization of structures using genetic algorithms with chromosome repairingPublication . Madeira, JFA; Rodrigues, H. C.; Pina, H.In this work, a genetic algorithm (GA) for multiobjective topology optimization of linear elastic structures is developed. Its purpose is to evolve an evenly distributed group of solutions to determine the optimum Pareto set for a given problem. The GA determines a set of solutions to be sorted by its domination properties and a filter is defined to retain the Pareto solutions. As an equality constraint on volume has to be enforced, all chromosomes used in the genetic GA 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: (1) to define chromosomes satisfying this propriety and (2) to create corresponding crossover and mutation operators which preserve volume. Optimal solutions of each of the single-objective problems are introduced in the initial population to reduce computational effort and a repairing mechanism is developed to increase the number of admissible structures in the populations. Also, as the work of the external loads can be calculated independently for each individual, parallel processing was used in its evaluation. Numerical applications involving two and three objective functions in 2D and two objective functions in3Dare employed as tests for the computational model developed. Moreover, results obtained with and without chromosome repairing are compared.
- Multi-objective optimization of structures topology by genetic algorithmsPublication . Madeira, JFA; Rodrigues, H.; Pina, HeitorThis work develops a computational model for topology optimization of linear elastic structures for situations where more than one objective function is required, each one of them with a different optimal solution. The method is thus developed for multi-objective optimization problems and is based on Genetic Algorithms. Its purpose is to evolve an evenly distributed group of solutions (population) to obtain the optimum Pareto set for the given problem. To reduce computational effort, optimal solutions of each of the single-objective problems are introduced in the initial population. Two numerical examples are presented and discussed to assess the method.