Parameter Tuning and Control: A Case Study on Differential Evolution With Polynomial Mutation

Abstract

Metaheuristics are known to be effective for solving a broad category of optimization problems. However, most heuristics require different parameter settings appropriately for a problem class or even for a specific problem. Researchers address this commonly by performing a parameter tuning study (also known as hyper-parameter optimization) or developing a parameter control mechanism that changes parameters dynamically. Whereas parameter tuning is computationally expensive and limits the parameter configuration to stay constant throughout the run, parameter control is also a challenging task because all dynamics induced by various operators must be learned to make an appropriate adaptation of parameters on the fly. This paper investigates parameter tuning and control for a well-known optimization method - differential evolution (DE). In contrast to most existing DE practices, an additional individualistic evolutionary operator called polynomial mutation is incorporated into the offspring creation. Results on test problems with up to 50 variables indicate that mutation can be helpful for multi-modal problems to escape from local optima. On the one hand, the effectiveness of parameter tuning for a specific problem becomes apparent; on the other hand, its generalization capabilities seem to be limited. Moreover, a generic coevolutionary approach for parameter control outperforms a random choice of parameters. Recognizing the importance of choosing a suitable parameter configuration to solve any optimization problem, we have incorporated a standard implementation of both tuning and control approaches into a single framework, providing a direction for the evolutionary computation and optimization researchers to use and further investigate the effects of parameters on DE and other metaheuristics-based algorithms.