Complexity Reduction in the Use of Evolutionary Algorithms to Function Optimization: A Variable Reduction Strategy

Discovering and utilizing problem domain knowledge is a promising direction towards improving the efficiency of evolutionary algorithms (EAs) when solving optimization problems. We propose a knowledge-based variable reduction strategy (VRS) that can be integrated into EAs to solve unconstrained and first-order derivative optimization functions more efficiently. VRS originates from the knowledge that, in an unconstrained and first-order derivative optimization function, the optimal solution locates in a local extreme point at which the partial derivative over each variable equals zero. Through this collective of partial derivative equations, some quantitative relations among different variables can be obtained. These variable relations have to be satisfied in the optimal solution. With the use of such relations, VRS could reduce the number of variables and shrink the solution space when using EAs to deal with the optimization function, thus improving the optimizing speed and quality. When we apply VRS to optimization problems, we just need to modify the calculation approach of the objective function. Therefore, practically, it can be integrated with any EA. In this study, VRS is combined with particle swarm optimization variants and tested on several benchmark optimization functions and a real-world optimization problem. Computational results and comparative study demonstrate the effectiveness of VRS.