A Non - Uniform Neighbourhood Relation for Job Shop Schedulingby Simulated

In this paper, we present a non-uniform neighbourhood relation which has been developed to solve job shop scheduling by simulated annealing-based algorithms. Using this neighbourhood relation combined with a speciically designed cooling schedule, we could improve ve upper bounds for the large unsolved benchmark problems YN1, YN4, SWV12, SWV13 and SWV15. The maximum improvement has been achieved for SWV13 and shortens the gap between the lower and the former upper bound by about 57%. To represent the job shop scheduling problem we employ the model of disjunctive graphs. In our approach, we analyze an extension of the neighbourhood function introduced by Van Laarhoven et al. in 19]. The neighbourhood involves a non-uniform generation probability, as opposed to the commonly used uniform probability. To obtain the neighbours of a schedule, we reverse more than a single arc of longest paths and perform a control on the increase of the makespan. The selection of the arcs depends on the number of longest paths to which a particular arc belongs. Furthermore, we have designed two cooling schedules which employ a detailed analysis of the objective function. The expected run-times can be either O ? n 3+" =m for the rst cooling schedule or O ? n 7=2 + " =m 1=2 for the second cooling schedule, where n is the number of tasks, m the number of machines and " represents O(ln ln n= ln n). Our computational experiments have shown that within short series of consecutive trials relatively stable results equal or close to optimal solutions are repeatedly obtained. Approximations within 0.6% and 2% of the upper bounds on YN1-YN4, SWV11-SWV13, and SWV15 were achieved in a relatively short run-time.