Topographical clearing differential evolution: A new method to solve multimodal optimization problems

• We introduce a new niching method based on the clearing paradigm.
• The topographical heuristic may be applied in several approaches.
• The two practical problems are highly multimodal.
• One of them is an NP-hard combinatorial optimization problem.

Some optimization problems in the field of nuclear engineering, as for example incore nuclear fuel management and a nuclear reactor core design, are highly multimodal, requiring techniques that overcome local optima, which can be done using niching methods. In order to do so, we present a new niching method based on the clearing paradigm, Topographical Clearing, which employs a topographical heuristic introduced in the early nineties, as part of a global optimization method. This niching method is applied to differential evolution, but it can be used in other evolutionary or swarm-based methods, such as the genetic algorithm and particle swarm optimization. The new algorithm, called TopoClearing-DE, is favorably compared against the canonical version of differential evolution in two test problems: the aforementioned core design and the turbine balancing problem, which is an NP-hard combinatorial optimization problem that can be used to assess the potential of an algorithm to be applied to fuel management optimization. As the problems attacked are quite challenging, the results show that Topographical Clearing can be applied to populational optimization methods in order to solve nuclear science and engineering problems.