A genetic algorithm for the generalised assignment problem
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We consider the generalized assignment problem in which the objective is to find a minimum cost assignment of a set of jobs to a set of agents subject to resource constraints. The presented new approach is based on a previously published, successful hybrid genetic algorithm and includes as new features two alternative initialization heuristics, a modified selection and replacement scheme for handling infeasible solutions more appropriately, and a heuristic mutation operator. Tests are performed on standard test instances from the literature and on newly created, larger and more difficult instances. The presented genetic algorithm with its two initialization variants is compared to the previous genetic algorithm and to the commercial general purpose branch-and-cut system CPLEX. Results indicate that CPLEX is able to solve relatively large instances of the general assignment problem to provable optimality. For the largest and most difficult instances, however, the proposed genetic algorithm yields on average the best results in shortest time.