Balancing exploration and exploitation in differential evolution via variable scaling factors: An application to practical problems

Highlights: •We test differential evolution with variable scaling factors. •These factors balance the exploration and exploitation of the search space. •The two practical problems are highly multimodal. •One of them is an NP-hard combinatorial optimization problem. •The other is a reactor core design problem. -- Abstract: Some optimization problems in the field of nuclear engineering, as for example the incore nuclear fuel management and a nuclear reactor core design, are highly multimodal, requiring techniques that overcome local optima, exploring the search space and promoting the exploitation of its most promising areas. The differential evolution algorithm (DE) relies mainly on the mechanism of mutation, where an individual is perturbed using the weighted difference (with the so-called "scaling factor" F) between two randomly chosen individuals. DE's canonical version employs a constant value of F. However, this parameter should be variable in order to balance the exploration and exploitation of the search space. In this work, we test some variable scaling factors from the literature and present the novel exponential scaling factor. These methods are applied to two problems: the aforementioned core design and the turbine balancing problem, which is an NP-hard (i.e. intrinsically harder than those that can be solved in nondeterministic polynomial time) combinatorial optimization problem that can be used to assess the potential of an algorithm to be applied to fuel management optimization. DE with variable scaling factors perform well in both problems, showing potential to be used in other nuclear science and engineering optimization problems.