A dynamic tabu search for large-scale generalised assignment problems

Abstract

A new tabu search (TS) for application to very large-scale generalised assignment and other combinatorial optimisation problems is presented in this paper. The new TS applies dynamic oscillation of feasible verses infeasible search and neighbourhood sample sizes that vary throughout the solution process. The dynamic oscillation and neighbourhood sample sizes are controlled by the success of the search as the solution progresses, to allow a faster increase in solution quality per unit time. Application of the TS to three types of randomly generated very large-scale generalised assignment problem instances was performed for sizes of up to 50 000 jobs and 40 agents. The new TS gave superior solutions to existing versions on all nearly occasions, given a fixed CPU time. For a fixed solution quality, the best of the existing versions required 1.5–3 times as much CPU time. Scope and purpose Very large-scale generalised assignment problems of several thousand jobs have important real-life applications such as vehicle routing, project planning, computer network design and sugar cane supply management. Existing heuristic techniques for the NP-hard problem are designed for medium-size problem instances of a few 100 jobs, since CPU time or search space significantly increases with problem size. This paper puts forward a new version of tabu search designed for very large generalised assignment and other large combinatorial optimisation problems. The new tabu search incorporates dynamic oscillation and neighbourhood sample sizes. These are controlled by the success of the search as the solution progresses, to allow a faster increase in solution quality per unit time. The results reported in the paper for problem sizes of up to 50 000 jobs and 40 agents, show a considerable reduction in CPU time over existing versions of tabu search to reach a desired solution quality.