Analysis of solution space-dependent performance of simulated annealing: the case of the multi-level capacitated lot sizing problem

Abstract

This study describes an analysis of different neighbourhood transition schemes and their effects on the performance of a general purpose simulated annealing (SA) procedure in solving the dynamic multi-level capacitated lot sizing problem (MLCLSP) with general product structures. The proposed neighbourhood transition schemes are based on relaxing different types of constraints, each of which defines a different solution space. The experiments assess the influence of expanding the search space which includes infeasibilities arising from the elimination of different model restrictions. The results indicate that the performance of SA is highly dependent on the definition and the tightness of the search space. Furthermore, the increase in the number of search moves carried out by SA is shown to significantly improve the results with linearly increasing computational times. Scope and purpose Simulated annealing (SA) is a popular solution technique used in the field of combinatorial optimiziation. Due to its global search capability and the simplicity of its implementation, SA is used by many researchers and practitioners in solving difficult problems. Although the performance of SA depends on the generation of neighbours and neighbourhood transition schemes, this feature has not been studied adequately in literature for production planning problems. Here, various neighbourhood transition schemes are analysed within the context of a SA procedure designed for the multi-item multi-level capacitated lot sizing problem (MLCLSP) encountered frequently in industry and especially in material requirements planning (MRP) applications. In this problem, capacity availability and inventory feasibility should be considered simultaneously in order to avoid sub-optimal solutions. Considering these two major constraints, different neighbourhood transition schemes which define different search spaces evolve in developing the general purpose SA procedure, and their effects are observed on the quality of solutions resulting from SA. This study provides valuable guidance for selecting an appropriate solution space in the design of SA or other global/local search algorithms developed for production planning problems.