A genetic algorithm for the generalised assignment problem

Abstract In this paper we present a genetic algorithm (GA)-based heuristic for solving the generalised assignment problem. The generalised assignment problem is the problem of finding the minimum cost assignment of n jobs to m agents such that each job is assigned to exactly one agent, subject to an agent's capacity. In addition to the standard GA procedures, our GA heuristic incorporates a problem-specific coding of a solution structure, a fitness-unfitness pair evaluation function and a local improvement procedure. The performance of our algorithm is evaluated on 84 standard test problems of various sizes ranging from 75 to 4000 decision variables. Computational results show that the genetic algorithm heuristic is able to find optimal and near optimal solutions that are on average less than 0.01 % from optimality. The performance of our heuristic also compares favourably to all other existing heuristic algorithms in terms of solution quality.