Evaluation of Parallel Hierarchical Differential Evolution for Min-Max Optimization Problems Using SciPy

Abstract

When optimization is applied in real-world applications, optimal solutions that do not take into account uncertainty are of limited value, since changes or disturbances in the input data may reduce the quality of the solution. One way to find a robust solution and consider uncertainty is to formulate the problem as a min-max optimization problem. Min-max optimization aims to identify solutions which remain feasible and of good quality under even the worst possible scenarios, i.e., realizations of the uncertain data, formulating a nested problem. Employing hierarchical evolutionary algorithms to solve the problem requires numerous function evaluations. Nevertheless, Evolutionary Algorithms can be easily parallelized. This work investigates a parallel model for differential evolution using SciPy, to solve general unconstrained min-max problems. A differential evolution is applied for both the design and scenario space optimization. To reduce the computational cost, the design level optimization is parallelized. The performance of the algorithm is evaluated for a different number of cores and different dimensionality of four benchmark test functions. The results show that, when the right parameters of the algorithm are selected, the parallelization can be of high benefit to a nested differential evolution.