Learning to recognize (un)promising simulated annealing runs: Efficient search procedures for job shop scheduling and vehicle routing

Simulated Annealing (SA) procedures can potentially yield nearoptimal solutions to many di cult combinatorial optimization problems, though often at the expense of intensive computational e orts. The single most signi cant source of ine ciency in SA search is the inherent stochasticity of the procedure, typically requiring that the procedure be rerun a large number of times before a near-optimal solution is found. This paper describes a mechanism that attempts to learn the structure of the search space over multiple SA runs on a given problem. Speci cally, probability distributions are dynamically updated over multiple runs to estimate at di erent checkpoints how promising a SA run appears to be. Based on this mechanism, two types of criteria are developed that aim at increasing search efciency: (1) a cuto criterion used to determine when to abandon unpromising runs and (2) restart criteria used to determine whether to start a fresh SA run or restart search in the middle of an earlier run. Experimental results obtained on a class of complex job shop scheduling problems show (1) that SA can produce high quality solutions for this class of problems, if run a large number of times, and (2) that our learning mechanism can signi cantly reduce the computation time required to nd high quality solutions to these problems. The results also indicate that, the closer one wants to be to the optimum, the larger the speedups. Similar results obtained on a smaller set of benchmark Vehicle Routing Problems with Time Windows (VRPTW) suggest that our learning mechanisms should help improve the e ciency of SA in a number of di erent domains.