Multicriteria optimization using a genetic algorithm for determining a Pareto set

Abstract

Most optimization problems consist in reconciling multiple objectives with each other, particularly in food processes. For example, it is necessary to optimize different parameters such as texture, flavour, and so on, in order to formulate a new product; before using bacteria or yeasts, it is very important to find an optimal culture medium for cell growth or end product synthesis, for instance. Traditionally, objectives were either combined lo form a scalar objective, through a linear combination of multiple attributes;, or else only one was optimized and the others were turned into constraints. As these techniques depended on the user's choice, they were not adapted to solve multiple-objective problems found in the food industry, where it is more satisfactory to obtain an optimal surface in which the user will be able to choose his own working conditions. Consequently, a method that incorporates the concept of Pareto's domination would be more interesting because it would permit more general use. This work presents a new algorithm that generates Pareto-optimal points for multicriteria optimization problems. This method is based on the use of a genetic algorithm (GA) which optimizes each system response. Multicriteria optimization is not really executed with GA but with a selection algorithm that sorts Pareto-effcient points. This new method is here illustrated with several examples