SAM: A Meta-Heuristic Algorithm for Singlemachine Scheduling Problems

Abstract

The main contribution of this work is to investigate the hypothesis that the performance of the Simulated Annealing (SA) algorithm can be improved by combining it with other sampling methods in solving the single machine weighted earliness and tardiness scheduling problem. In this paper we present the formulation of our novel hybrid algorithm, SAM, and the main results. The algorithm SAM, which stands for Simulated Annealing with Metropolis-Hastings, is a two-step process. To initialise, the search space of possible feasible schedules is divided into a number of sections. In the first step Metropolis-Hastings sampling is performed over the sections in order to obtain characteristics of a likelihood function over the sections so that a section with a high likelihood of containing the optimal schedule is chosen for step two. In step two SA is run on the pruned search space to find a solution schedule. This relies on a novel way of visualising the search space in a geometric way as a wheel of indices. The results show that low deviation solutions can be obtained in significantly shorter runs with SAM than seen in the literature or required of the basic SA algorithm. We can achieve a 4.5 times reduction in required algorithm run time to achieve a less than 2% deviation from the optimum value. SAM even enables us to find the optimal solution in as few as 1000 iterations of SA in some cases.