Job-shop Neighbourhoods and Move Evaluation Strategies

The time complexity of a search depends on (1) the size of the neighbourhood and (2) the complexity in determining the cost of the moves. Therefore in order for the search to be effective and efficient, the neighbourhood must be highly constrained and it needs to be evaluated quickly, however without losing the ability to provide access to improved solutions. This paper investigates strategies that have an effect on both of these parameters and commences by investigating neighbourhood structures. This is done by documenting a historical sketch of job-shop neighbourhoods, which focuses attention on the approach of Nowicki and Smutnicki (1996) (NS), noted for proposing and implementing the most restrictive neighbourhood in the literature. Accordingly, the contribution of the method’s neighbourhood structure to its overall effectiveness is analysed. The findings show that if the NS neighbourhood is used in the search process, the choice of an initialisation procedure has an important influence on the best solution found. By contrast, alternative critical path generation methods have a negligible influence. Empirical testing further discloses that over 99.7 % of the moves evaluated in this neighbourhood (by the NS rules) are disimproving – regardless of the initial solution method or the critical path generation procedure employed. Furthermore, analysis of the solution space indicates that when the NS neighbourhood is used in the search process there is no clear pattern in the pursuit of an improved solution. The effect of neighbourhood evaluation strategies is investigated next. A procedure proposed by Ten Eikelder et al. (1997), that allows the neighbourhood search to be accelerated, is analysed and two new evaluation strategies are proposed. Empirical testing discloses that the acceleration method suggested by Ten Eikelder et al. (1997) is able to increase the search efficiency of various techniques between 30 and 40 %. The findings also show that the new evaluation strategy, which estimates the cost of a neighbour, is up to 87.5 % faster in evaluating moves in comparison to an evaluation technique that determines the cost of each neighbour exactly, with no material effect on solution quality. Similarly, the new approach which combines exact and estimation methods can improve the efficiency of the search by up to 64 % in comparison with an exact evaluation of the neighbourhood, guaranteeing no loss in solution quality. Finally, implications of these findings for developing new and more effective job-shop algorithms are discussed. page (2) Job-shop neighbourhoods and move evaluation strategies 03/10/98