Satisficing solutions of multi-objective fuzzy optimization problems using genetic algorithm

In the present paper, a genetic algorithm for multi-objective optimization problems with max-product fuzzy relation equations as constraints is presented. Since the non-empty feasible domain of such problems is, in general, a non-convex set; the traditional optimization methods cannot be applied. Here, we are presenting a genetic algorithm (GA) to find “Pareto optimal solutions” for solving such problems observing the role of non-convexity of the feasible domain of decision problem. Solutions are kept within feasible region during the mutation as well as crossover operations. Test problems are developed to evaluate the performance of the proposed algorithm and to determine satisficing decisions. In case of two objectives, weighting method is also applied to find the locus of optimal solutions.

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► A multi-objective optimization problem with max-product fuzzy relation equations as constraints is presented.
► Pareto optimal solutions are obtained for solving such problems observing the role of non-convexity of the feasible domain of decision problem.
► Solutions are kept within feasible region during mutation and crossover operations.
► Test problems are developed for evaluating performance and determining satisficing decisions.
► In case of two objectives, weighting method is also applied to find the locus of optimal solutions.