Exact and Metaheuristic Algorithms for Variable Reduction

A variable reduction strategy (VRS) drives evolutionary algorithms (EAs) to evolve more effectively by simplifying optimization problems. To represent a decision space with the smallest set of variables via VRS, a variable reduction optimization problem (VROP) has been defined, which could be handled by a heuristic rule-based automatic variable reduction algorithm (HR-AVRA). However, HR-AVRA has limitations in identifying an optimal solution and is susceptible of getting trapped in local optimums. To handle these challenges, we propose to solve VROP with exact and metaheuristic algorithms. We construct a linear programming model of VROP for the first time. Then, Gurobi, an exact algorithm optimizer, is employed to seek and identify an optimal solution for it. Subsequently, we design two representative single-point-based and population-based metaheuristic algorithms, simulated annealing-based (SA-AVRA) and ant colony optimization-based (ACO-AVRA) methods, to solve VROP more effectively. These variable reduction algorithms can group variables of a continuous optimization problem into reduced and core variables, with the latter representing both reduced variables and the entire decision space. Extensive experiments verify that Gurobi can provide optimal solutions for small-scale VROPs, while SA/ACO-AVRA enables more reduced variables than other variable reduction methods. We also integrate various variable reduction algorithms with several competitive EAs to tackle equality-constrained optimization problems and nonlinear equations systems. Experiments show that EAs integrated with a variable reduction algorithm outperform both standard EAs and those with several other complexity reduction methods. Furthermore, integrating a variable reduction algorithm that introduces more reduced variables generally can lead to better performance of EAs.