Some New Results on Tabu Search Algorithm Applied to the Job-Shop Scheduling Problem

The Job-Shop Scheduling Problem (JSSP) with the makespan criterion comes from the manufacturing industry and has excellent practical applications. The problem can be briefly described as follows. There are a set of jobs and a set of machines. Each job consists of a sequence of operations, and each of the operations uses one of the machines for a fixed duration. Each machine processes at most one operation at one time. Once the operation started, no preemption is permitted. A scheduling is an assignment of operations to time intervals on the machines. The objective of the problem is to find a schedule which minimizes the makespan (Cmax), that is, the finish time of the last operation completed. The JSSP is widely acknowledged as one of the most difficult NP-complete problems (Garey et al., 1976). This is illustrated by the fact that a relatively small instance with 10 jobs and 10 machines, proposed by Muth & Thompson (1963), remained unsolved for more than a quarter of a century, and until now no problems are solved to optimality for the 20×20 instances. Since it is an important practical problem, the JSSP has captured the interest of a significant number of researchers during the past three decades, and many optimization algorithms and approximation algorithms have been proposed. The optimization algorithms, which are primarily based on the B&B scheme (Carlier & Pinson, 1989; Brucker et al., 1994), have been successfully applied to solving small instances. However, they cannot accomplish optimal schedules in a reasonable time for instances larger than 250 operations with reached the limit. On the other hand, approximation algorithms, which include priority dispatch, shifting bottleneck approach, meta-heuristic methods and so on, provide a quite good alternative for the JSSP. Approximation algorithms were firstly developed on the basis of dispatching rules (Giffler & Thompson, 1960), which are very fast, but the quality of solutions that they provide usually leaves plenty of room for improvement. A more elaborate algorithm, which could produce considerably better approximations at a higher computational cost, is the shifting bottleneck approach proposed by Adams et al. (Adams et al., 1988). More recently, the meta-heuristic methods, such as tabu search (TS) (Taillard, 1994; Nowicki & Smutnicki, 1996), simulated annealing (SA) (Van Laarhoven et al., 1992), genetic algorithm (GA) (Croce et al., 1995), could provide the good solutions for a large scale problem and have captured the attention of many researchers. Moreover, most recent studies indicate that a single technique cannot solve this stubborn