Simple Efficient Hybridization of Classic Global Optimization and Genetic Algorithms for Multiobjective Optimization

Abstract

An efficient method combining classical (gradient-based) methods for global scalar optimization and genetic algorithms for multiobjective optimization (MOO) is proposed for approximating the Pareto frontier and the Edgeworth–Pareto hull (EPH) of the feasible objective set in complicated nonlinear MOO problems involving piecewise constant functions of criteria with numerous local extrema. An optima injection method is proposed in which the global optima of individual criteria are added to the population of a genetic algorithm. It is experimentally shown that the method is significantly superior to the original genetic algorithm in the order of convergence and the approximation accuracy. Experiments concerning EPH approximation are also performed for the problem of constructing control rules for a cascade of reservoirs with criteria reflecting the reliability with which the requirements imposed on the cascade are met.