Evaluation‐Number Constrained Optimization Problem and its Solution Strategy

Abstract

This paper addresses optimization problems subject to an objective function's evaluation‐number constraint arbitrarily given in advance. These problems are practical for black‐box objective functions which cost much money and/or time per evaluation because money and/or time constraints are typically applicable in real‐world projects. This paper suggests a new solution strategy that can be used to adapt metaheuristics to evaluation‐number constraints arbitrarily given in advance. The proposed strategy updates the setting parameters of a target metaheuristic algorithm for every generation by solving a fixed small‐size optimization problem related to the evaluation‐number constraint. It has the advantage of being insensitive to the effects of dimensionality increases in principle. The effectiveness of the proposed strategy is confirmed by numerical experiments with two well‐known metaheuristics, i.e., the particle swarm optimization algorithm and the differential evolution algorithm. © 2024 Institute of Electrical Engineer of Japan and Wiley Periodicals LLC.