Differential Evolution Algorithms for the Generalized Assignment Problem

In this paper, differential evolution (DE) algorithms are presented to solve the generalized assignment problem (GAP), which is basically concerned with finding the minimum cost assignment of jobs to agents such that each job is assigned to exactly one agent, subject to capacity constraint of agents. The first algorithm is unique in terms of solving a discrete optimization problem on a continuous domain. The second one is a discrete/combinatorial variant of the traditional differential evolution algorithm working on a discrete domain. The objective is to present a continuous optimization algorithm dealing with discrete spaces hence to solve a discrete optimization problem. Both algorithms are hybridized with a "blind" variable neighborhood search (VNS) algorithm to further enhance the solution quality, especially to end up with feasible solutions. They are tested on a benchmark suite from OR Library. Computational results are promising for a continuous algorithm such that without employing any problem-specific heuristics and speed-up methods, the DE variant hybridized with a "blind" VNS local search was able to generate competitive results to its discrete counterpart.