Automatic Variable Reduction

A variable reduction strategy (VRS) is an effective method to accelerate the optimization process of evolutionary algorithms (EAs) by simplifying the corresponding optimization problems. Unfortunately, the VRS is manually realized in a trial-and-error manner currently. To boost the efficiency of VRS and enable a more extensive application, we propose a variable reduction optimization problem (VROP) to represent a decision space with the smallest sets of variables. Thereafter, a heuristic rule-based automatic variable reduction algorithm (AVRA) is designed to address the VROP. AVRA sequentially reduces variables by considering several sophisticated designed heuristic rules, which search for a variable that can be utilized to represent as many variables as possible and that can be represented by the smallest set of variables possible. With AVRA, the decision variables of an optimization problem can be automatically grouped into reduced variables and core variables, where core variables can represent reduced variables and the entire decision space. During the optimization process, we only need to search the core variables to optimize the problem. Therefore, the dimensionality of the decision space can be reduced by AVRA, subsequently, simplifying the complexity of the problem and improving the search efficiency of EAs. To testify the effectiveness of AVRA, we blend AVRA with several promising EAs to solve two types of challenging problems: 1) continuous equality-constrained optimization problems and 2) nonlinear equations systems. Extensive experiments verify that an EA with AVRA outperforms the standard EA.