Local search and genetic algorithm for the job shop scheduling problem with sequence dependent setup times

Abstract

The Job Shop Scheduling Problem (JSP) is an example of a combinatorial optimization problem that has interested researchers for several decades. In this paper we confront an extension of this problem called JSP with Sequence Dependent Setup Times (SDST-JSP). The approach extends a genetic algorithm and a local search method that demonstrated to be efficient in solving the JSP. For local search, we have formalized neighborhood structures that generalize three well-know structures defined for the JSP. We have conducted an experimental study across conventional benchmark instances showing that the genetic algorithm exploited in combination with the local search, considering all three neighborhoods at the same time, provides the best results. Moreover, this approach outperforms the current state-ofthe-art methods.

Weighted Tardiness Minimization in Job Shops with Setup Times by Hybrid Genetic Algorithm

“…Also, we have opted to consider a neighborhood structure that generates a small number of neighbors from each critical block. For this reason, we adapted the structure N S 1 proposed in [13] for SDST-JSP with makespan minimization, which is based on previous structures given in [8] and [12] for the standard JSP. This structure can be formalized for the SDST-JSP with weighted tardiness minimization from the disjunctive model defined in 2.1.…”

“…In [13] the authors define non-improving conditions for some reversals of critical arcs in makespan optimization that in principle can not be translated to the weighted tardiness case. Regarding feasibility, the next result gives a sufficient condition for an alternative path not existing after the reversal of a critical arc.…”

“…Incorporating sequence-dependent setup times changes the nature of scheduling problems, so well-known results and techniques for the JSP are not directly applicable to the SDST-JSP. Some extensions have been done for makespan minimization in [1,6,13].…”

“…The core of this algorithm is a variation of the neighborhood structure N S 1 introduced in [13] for the SDST-JSP with makespan minimization, which in its turn extends the structures proposed in [12] for the classical JSP. We define a disjunctive graph model for the SDST-JSP with weighted tardiness minimization to formalize this neigborhood.…”

Solving job shop scheduling with setup times through constraint-based iterative sampling: an experimental analysis

“…This is the case of the work by Brucker and Thiele (1996), for example, which relies on an earlier solutions introduced in Brucker et al (1994). Another example is the more recent work of Vela et al (2009) and González et al (2009a), which proposes effective heuristic procedures based on genetic algorithms and local search. The local search procedures that are introduced in these works extend a procedure originally proposed by Nowicki and Smutnicki (2005) for the classical job-shop scheduling problem to the setup times case by introducing a neighborhood structure that exhibits similar properties relatively to critical paths in the underlying disjunctive graph formulation of the problem.…”