Using variable reduction strategy to accelerate evolutionary optimization

Abstract In this study, we introduce a novel approach of variable reduction and integrate it into evolutionary algorithms in order to reduce the complexity of optimization problems. We develop reduction processes of variable reduction for derivative unconstrained optimization problems (DUOPs) and constrained optimization problems (COPs) with equality constraints and active inequality constraints. Variable reduction uses the problem domain knowledge implied when investigating optimal conditions existing in optimization problems. For DUOPs, equations involving derivatives are considered while for COPs, we discuss equations expressing the equality constraints. From the relationships formed in this way, we obtain relationships among the variables that have to be satisfied by optimal solutions. According to such relationships, we can utilize some variables (referred to as core variables) to express some other variables (referred to as reduced variables). We show that the essence of variable reduction is to produce a minimum collection of core variables and a maximum number of reduced variables based on a system of equations. We summarize some application-oriented situations of variable reduction and stress several important issues related to the further application and development of variable reduction. Essentially, variable reduction can reduce the number of variables and eliminate equality constraints, thus reducing the dimensionality of the solution space and improving the efficiency of evolutionary algorithms. The approach can be applied to unconstrained, constrained, continuous and discrete optimization problems only if there are explicit variable relationships to be satisfied in the optimal conditions. We test variable reduction on real-world and synthesized DUOPs and COPs. Experimental results and comparative studies point at the effectiveness of variable reduction.