Genetic tabu search for the fuzzy flexible job shop problem

Abstract

This paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its components but it is also quite competitive with the state-of-the-art when solving both crisp and fuzzy instances, providing new best-known solutions for a number of these test instances. Genetic Tabu AbstractThis paper tackles the flexible job-shop scheduling problem with uncertain processing times. The uncertainty in processing times is represented by means of fuzzy numbers, hence the name fuzzy flexible job-shop scheduling. We propose an effective genetic algorithm hybridised with tabu search and heuristic seeding to minimise the total time needed to complete all jobs, known as makespan. To build a high-quality and diverse set of initial solutions we introduce a heuristic method which benefits from the flexible nature of the problem. This initial population will be the starting point for the genetic algorithm, which then applies tabu search to every generated chromosome. The tabu search algorithm relies on a neighbourhood structure that is proposed and analysed in this paper; in particular, some interesting properties are proved, such as feasibility and connectivity. Additionally, we incorporate a filtering mechanism to reduce the neighbourhood size and a method that allows to speed-up the evaluation of new chromosomes. To assess the performance of the resulting method and compare it with the state-of-the-art, we present an extensive computational study on a benchmark with 205 instances, considering both deterministic and fuzzy instances to enhance the significance of the study. The results of these experiments clearly show that not only does the hybrid algorithm benefit from the synergy among its component...

A new genetic algorithm for flexible job-shop scheduling problems

“…The proposed new algorithm is compared to the following algorithms [17,20,29] The proposed NGA algorithm for FSJ problem was coded in Matlab and run on a 2.3 GHz PC with 4 GO memory with the following parameters: popsize =100, c P = 0.8, m P = 0.05, selection percentage = 30%. Table 2 summarizes the experimental results.…”

Benchmarks for fuzzy job shop problems

“…An alternative and increasingly popular approach is to use fuzzy sets in the setting of possibility theory [16,19,66], since they provide an acceptable trade-off between expressivity and computational difficulty. There are in fact numerous research papers where uncertain durations are represented as fuzzy numbers, mostly triangular fuzzy numbers, among others, for single machine scheduling [10], [32], parallel machine scheduling [4,49], flow shop scheduling [9,31], open shop scheduling [46], job shop scheduling [18,24,35,45,52,54,55,60,71] and [41], and for flexible job shop scheduling in [40,48,64,65] to mention but a few. Indeed, the recent review of metaheuristic algorithms to solve fuzzy job shop problems in [1] highlights the relevance of this topic.…”

Propagating Updates of Residential Areas in Multi-Representation Databases Using Constrained Delaunay Triangulations

“…In the Tabu Search algorithm, potential solutions are stored in the Tabu list, which are used to avoid repeating searches and to find the acceptable solution. The Tabu Search algorithm has a wide range of applications, such as job-shop scheduling, vehicle routing planning, and design of groundwater remediation systems [31][32][33]. Figure 3a illustrates the procedures to apply the Tabu Search algorithm for constructing the small-scale objects.…”