Multiobjective Optimization Design with Pareto Genetic Algorithm

This paper presents a constrained multiobjective (multicriterion, vector) optimization methodology by integrating a Pareto genetic algorithm (GA) and a fuzzy penalty function method. A Pareto GA generates a Pareto optimal subset from which a robust and compromise design can be selected. 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 optimization problem is constructed. A fuzzy-logic penalty function method is developed with a combination of deterministic, probabilistic, and vague environments that are consistent with GA operation theory based on randomness and probability. Using this penalty function method, a constrained multiobjective optimization problem is transformed into an unconstrained one. The functions of a point (string, individual) thus transformed contain information on a point's status (feasible or infeasible), position in a search space, and distance from a Pareto optimal set. Sample cases investigated in this work include a multiobjective integrated structural and control design of a truss, a 72-bar space truss with two criteria, and a four-bar truss with three criteria. Numerical experimental results demonstrate that the proposed method is highly efficient and robust.