Population-based Tabu search with evolutionary strategies for permutation flow shop scheduling problems under effects of position-dependent learning and linear deterioration

Oğuzhan Ahmet Arık

doi:10.1007/s00500-020-05234-7

Abstract

This paper investigates permutation flow shop scheduling (PFSS) problems under the effects of position-dependent learning and linear deterioration. In a PFSS problem, there are n jobs and m machines in series. Jobs are separated into operations on m different machines in series, and jobs have to follow the same machine order with the same sequence. The PFSS problem under the effects of learning and deterioration is introduced with a mixed-integer nonlinear programming model. The time requirement for solving large-scale problems type of PFSS problem is exceedingly high. Therefore, well-known metaheuristic methods for the PFSS problem without learning and deterioration effects such as iterated greedy algorithms and discrete differential evolution algorithm are adapted for the problem with learning and deterioration effects in order to find a faster and near-optimal or optimal solution for the problem. Furthermore, this paper proposes a hybrid solution algorithm that is called population-based Tabu search algorithm (TSPOP) with evolutionary strategies such as crossover and mutation. The search algorithm is built on the basic structure of Tabu search and it searches for the best candidate from a solution population instead of improving the current best candidate at each iteration. Furthermore, the performances of these methods in view of solution quality are discussed in this paper by using test problems for 20, 50, and 100 jobs with 5, 10, 20 machines. Experimental results show that the proposed TSPOP algorithm outperforms the other existing algorithms in view of solution quality.

Highlights

In a permutation flow shop scheduling (PFSS) problem, there are n jobs having m different operations on m serial machines
The Tabu search algorithm was introduced by Glover (1989, 1990) to present a search strategy for solving combinatorial optimization problems whose applications range from graph theory and matroid settings to general pure and mixed-integer programming problems
For comparison of solution approaches, some of Taillard’s (1993) benchmark problems under the effects of learning and deterioration are solved with a commercial solver

Summary

Introduction

In a PFSS problem, there are n jobs having m different operations on m serial machines. The phenomenon of deterioration effect denotes an increase in initially determined processing times while jobs are waiting in the queue or are being processed on machines Both of these effects have been widely studied for more than 15 years in scheduling problems. Let S1⁄2r be starting time of the job at position r, P1⁄2r can be calculated as follows: P1⁄2r 1⁄4 Pr þ BS1⁄2r; ð2Þ where B is the linear deterioration effect coefficient for scheduling problems ð0\B\1Þ. These special cases in flow shop scheduling problem are increasing series of dominating machines, 2-machine environment, equal job processing times and a fixed job in the first position of the first machine Without these special cases, the complexity of the PFSS problem under the effects of learning and deterioration is still NP-Hard. We compare our proposed algorithm with some existing algorithms for PFSS problems

Literature review

Mathematical model

Population-based Tabu search with evolutionary strategies

Numerical examples

Conclusion

Compliance with ethical standards