A Discrete Differential Evolution Algorithm for a Military Fleet Modernization Problem

Abstract

Differential evolution has a long track record of successfully solving optimization problems in continuous domain due it its powerful Euclidean distance-based learning concept. Although this affects its suitability for solving several problems with permutation variables, several studies show that it can be applicable for effectively solving permutation-based problems. In this paper, an improved design of differential evolution is introduced to solve a military fleet modernization problem with discrete parameters. In this problem, several modernization oper-ations are required to transition a military force from an outdated fleet to a more modern one with the objective of maximizing the force's deployment at the minimum cost over a pre-determined planning period. The proposed differential evolution incorporates a new solution representation, a proposed repairing heuristic method, a modified mutation operator and mapping method for efficiently tackling the discrete characteristics of the targeted problem and is coupled with a simulation model to evaluate the fitness of the generated solutions. To judge its performance, the proposed algorithm has been implemented to solve a case study that addresses recent fleet modernization strategies of the Australian Army to recapitalize its forces over the next decade and in a continual process. The experimental results show that the proposed algorithm can provide more efficient fleet modernization schedules which are 29.32% and 51.43% better than those obtained by other two comparative algorithms.