Some New Ideas in TS for Job Shop Scheduling

Abstract

This paper deals with a classic job-shop scheduling problem with the makespan criterion. Some properties of the fast algorithm TSAB of Nowicki and Smutnicki, as well as properties of the solution space, have been discussed and examined. Next, by introducing the original method of diversification, TSAB has been embedded in more advanced algorithmic framework i-TSAB, which has far analogy to path relinking technique. Newly proposed algorithm is faster and has better accuracy than TSAB, runs within time of minutes on a PC and already in preliminary tests provides 23 new upper bounds among 35 unsolved yet common Taillard's benchmarks.

An Advanced Tabu Search Algorithm for the Job Shop Problem

“…The positive correlation between the distance among local extremes and the makespan value for all Taillard's instances has been detected (Nowicki and Smutnicki, 2001). This fact suggests the presence of big valley (BV) phenomenon in the solution space.…”

“…Other authors have evaluated neighbours by inexpensive lower bound, rather than by the makespan, see for example Taillard (1994) andTen Eikelder et al (1999). Unfortunately, it has been found in Nowicki and Smutnicki (2001) that the latter technique frequently deteriorates the quality of the algorithm. Therefore, we prefer a completely new approach heading towards the reduction of complexity O(o) stemmed from the standard method of makespan calculation.…”

“…We propose algorithm i -TSAB satisfying desired requirements; its general idea follows from our paper, Nowicki and Smutnicki (2001). Goal (1) is realized by the special generator of initial solutions, based on some elements of path relinking philosophy (Glover and Laguna, 1997).…”

“…Initial solutions have been found by algorithm INSA equipped with accelerator presented in Nowicki and Smutnicki (2001), which reduces running time from O(o 2 max k∈M m k ) to O(o 2 ). Made implementation applies Theorem 1 in NIS and TSAB (called at the lower level) for neighbourhoods N (π) and N * (π), respectively.…”

“…The problem has been known for years in the scheduling theory as a particularly hard combinatorial optimisation case. Although in the last three decades a lot of effort has been put into research in this area, good results have appeared quite recently, see state-of-the-art papers by Bl ażewicz, Domschke, and Pesch (1996), Vaessens, Aarts, and Lenstra (1996), and Jain and Meeran (1999), supplemented by a few recent studies (Jain, Rangaswamy, and Meeran, 2000;Pezella and Merelli, 2000;Nowicki and Smutnicki, 2001).…”