Using the Min-Max Method to Solve Multiobjective Optimization Problems with Genetic Algorithms

In this paper, a new multiobjective optimization technique based on the genetic algorithm (GA) is introduced. This method is based in the concept of min-max optimum, taken from the Operations Research literature, and can produce the Pareto set and the best trade-off among the objectives. The results produced by this approach are compared to those produced with other mathematical programming techniques and GA-based approaches using a multiobjective optimization tool called MOSES (Multiobjective Optimization of Systems in the Engineering Sciences). The importance of representation is hinted in the example used, since it can be seen that reducing the chromosomic length of an individual tends to produce better results in the optimization process, even if it's at the expense of a higher cardinality alphabet.

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