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.
['J. F. Aguilar Madeira', 'H. Rodrigues', 'Heitor Pina']
Genetic methods in multi-objective optimization of structures with an equality constraint on volume