An Adaptive Control for Surrogate Assisted Multi-objective Evolutionary Algorithms

Abstract

Multi-objective problems (MOPs), a class of optimization problems in the real-world, have multiple conflicting objectives. Multi-objective evolutionary algorithms (MOEAs) are known as great potential algorithms to solve difficult MOPs. With MOEAs, based on the principle of population, we have a set of optimal solutions (feasible solution set) after the search. We often use the concept of dominance relationship in population, and it is not difficult to find out set of Pareto optimal solutions during generations. However, with expensive optimization problems in the real world, it has to use a lot of fitness function evaluations during the search. To avoid expensive physical experiments, we can use computer simulations methods to solve the difficult MOPs. In fact, this way often costs expensive in computation and times for the simulation. In these cases, researchers discussed on the usage of surrogate models for evolutionary algorithms, especially for MOEAs to minimize the number of fitness callings. There are a series of proposals which were introduced with the usage of RBF, PRS, Kriging, SVM models. With the concept of machine learning, these MOEAs can solve expensive MOPS effectively. However, with our analysis, we found that using a fixed ratio of fitness functions and surrogate functions may make the unbalance of exploitation and exploration of the evolutionary process. In this paper, we suggest to use an adaptive control to determine the effective ratio during the search. The proposal is confirmed though an experiment with standard measurements on well-known benchmark sets.