A New Differential Evolution Based Metaheuristic for Discrete Optimization

Abstract

The Differential Evolution (DE) algorithm is an important and powerful evolutionary optimizer in the context of continuous numerical optimization. Recently, some authors have proposed adaptations of its differential mutation mechanism to deal with combinatorial optimization, in particular permutation-based integer combinatorial problems. In this paper, the authors propose a novel and general DE-based metaheuristic that preserves its interesting search mechanism for discrete domains by defining the difference between two candidate solutions as a list of movements in the search space. In this way, the authors produce a more meaningful and general differential mutation for the context of combinatorial optimization problems. The movements in the list can then be applied to other candidate solutions in the population as required by the differential mutation operator. This paper presents results on instances of the Travelling Salesman Problem (TSP) and the N-Queen Problem (NQP) that suggest the adequacy of the proposed approach for adapting the differential mutation to discrete optimization.

Differential evolution using ancestor tree for service restoration in power distribution systems

“…Here, we extend these ideas to describe a new approach for implementing the concept of list of movements, proposed in Prado et al [22], in a discrete differential evolution by using the ancestor tree to obtain the list of movements. With this definition, we can have a meaningful version of the differential mutation for reconfiguration problems in power distribution systems.…”

“…The general ideas in Prado et al [22] are briefly revisited here. In this new approach the operator difference between two candidate solutions is a list of movements in the search space defined as: Definition 1.…”

“…Following the initial development and success of DE for numerical optimization, some researchers have investigated its performance in combinatorial optimization problems [22,23,8,32,11]. In continuous problems, the differential mutation is easily implemented with the subtraction between vectors operation.…”

“…In [22], the authors present a general approach for DE in combinatorial optimization problems, where the operators difference, addition, and product by scalar in the differential mutation equation (Eq. (4)) are redefined for the domain of discrete variables so that they can be applied to a wide number of combinatorial problems.…”

“…The approach is based on a discrete version of the differential evolution (DE) algorithm, initially presented in Prado et al [22,23] and Guimarães et al [11] for permutation-based combinatorial optimization problems. We extend the ideas and general framework presented in Prado et al [22,23], by using the NDE presented in Santos et al [26] and a new ancestor tree presented here to implement DE for service restoration problems. The use of an ancestor tree is not only central to implement differential mutation in our algorithm but also can track the sequence of switching operations in the restoration of the system when the optimization process is finished.…”