Abstract
This paper presents an effective procedure for solving the job shop problem. Synergistically combining small and large neighborhood schemes, the procedure consists of four components, namely (i) a construction method for generating semi-active schedules by a forward-backward mechanism, (ii) a local search for manipulating a small neighborhood structure guided by a tabu list, (iii) a feedback-based mechanism for perturbing the solutions generated, and (iv) a very large-neighborhood local search guided by a forward-backward shifting bottleneck method. The combination of shifting bottleneck mechanism and tabu list is used as a means of the manipulation of neighborhood structures, and the perturbation mechanism employed diversifies the search. A feedback mechanism, called repeat-check, detects consequent repeats and ignites a perturbation when the total number of consecutive repeats for two identical makespan values reaches a given threshold. The results of extensive computational experiments on the benchmark instances indicate that the combination of these four components is synergetic, in the sense that they collectively make the procedure fast and robust.
Highlights
As an integrated component of computerized and flexible manufacturing systems, the Job-Shop Scheduling Problem (JSP) is encountered in many industrial contexts
A local search differs from a systematic tree search in that systematic tree search expands a graph of partial solutions, whereas a local search explores a virtual graph connecting each complete solution to its neighboring complete solutions
In 53.8%, 21/39, of cases, the SLENP has generated solutions with the same quality as those generated by the TSSA and in general the solutions generated by the TSSA are on average around 1.05% better than those generated by the SLENP
Summary
As an integrated component of computerized and flexible manufacturing systems, the Job-Shop Scheduling Problem (JSP) is encountered in many industrial contexts. Defining a proper neighborhood scheme for a local search is, involved with highly conflicting factors, in the sense that despite the fact that many neighborhood schemes seem to be only superficial variation of one another, they can demonstrate entirely different results The reason of this phenomenon has been partly described by the notion of fitness landscape (Forrest and Mitchell 1993), and it seems that successful neighborhood schemes have the capability of effectively managing a trade-off between computational time and the number of arcs in their virtual graphs. An evidence for its intractability is that finding the optimal solution of a relatively small problem instance presented in (Fisher and Thompson 1963), with the dimension of 10*10, despite the focus of intensive research on it, remained unsolved for 26 years until it was solved by the exact procedure developed in (Carlier and Pinson 1989) This celebrated instance, which in the literature is called ft, is still used by many researchers to test their algorithms. Denoting the completion time of the last completed job with makespan, the JSP can be formulated as follows: min fmakespanðΠÞg ð1Þ
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