MULTIOBJECTIVE OPTIMIZATION DESIGN WITH PARETO GENETIC ALGORITHM

This paper presents a constrained multiobjective (multicriterion, vect or) optimization methodology by integrating a Pareto genetic algorithm (GA) and a fuzzy penalty function method. A Pareto GA generates a Par eto optimal subset from which a robust and compromise design can be se lected. This Pareto GA consists of five basic operators: reproduction, crossover, mutation, niche, and the Pareto-set filter. The niche and the Pareto-set filter are defined, and fitness for a multiobjective op timization problem is constructed. A fuzzy-logic penalty function meth od is developed with a combination of deterministic, probabilistic, an d vague environments that are consistent with GA operation theory base d on randomness and probability. Using this penalty function method, a constrained multiobjective optimization problem is transformed into a n unconstrained one, The functions of a point (string, individual) thu s transformed contain information on a point's status (feasible or inf easible), position in a search space, and distance from a Pareto optim al set. Sample cases investigated in this work include a multiobjectiv e integrated structural and control design of a truss, a 72-bar space truss with two criteria, and a four-bar truss with three criteria, Num erical experimental results demonstrate that the proposed method is hi ghly efficient and robust.