Improved Differential Evolution Algorithm for Flexible Job Shop Scheduling Problems

Prasert Sriboonchandr,Nuchsara Kriengkorakot,Preecha Kriengkorakot

doi:10.3390/mca24030080

Prasert Sriboonchandr, Nuchsara Kriengkorakot + Show 1 more

Open Access

https://doi.org/10.3390/mca24030080

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Abstract

This research project aims to study and develop the differential evolution (DE) for use in solving the flexible job shop scheduling problem (FJSP). The development of algorithms were evaluated to find the solution and the best answer, and this was subsequently compared to the meta-heuristics from the literature review. For FJSP, by comparing the problem group with the makespan and the mean relative errors (MREs), it was found that for small-sized Kacem problems, value adjusting with “DE/rand/1” and exponential crossover at position 2. Moreover, value adjusting with “DE/best/2” and exponential crossover at position 2 gave an MRE of 3.25. For medium-sized Brandimarte problems, value adjusting with “DE/best/2” and exponential crossover at position 2 gave a mean relative error of 7.11. For large-sized Dauzere-Peres and Paulli problems, value adjusting with “DE/best/2” and exponential crossover at position 2 gave an MRE of 4.20. From the comparison of the DE results with other methods, it was found that the MRE was lower than that found by Girish and Jawahar with the particle swarm optimization (PSO) method (7.75), which the improved DE was 7.11. For large-sized problems, it was found that the MRE was lower than that found by Warisa (1ST-DE) method (5.08), for which the improved DE was 4.20. The results further showed that basic DE and improved DE with jump search are effective methods compared to the other meta-heuristic methods. Hence, they can be used to solve the FJSP.

Highlights

Nowadays, the goal of businesses and industry is to reduce costs, and this is affected by production scheduling
The results further showed that basic differential evolution (DE) and improved DE with jump search are effective methods compared to the other meta-heuristic methods
The sample problems of Kacem et al were used as examples of small-sized problems

Summary

Introduction

The goal of businesses and industry is to reduce costs, and this is affected by production scheduling. The issues of production scheduling concern the sequencing and machine assignment for each order. Owing to the requirement of the modern manufacturing processes for greater flexibility, the job shop scheduling problem (JSP) is an important type of production scheduling; the flexible job shop scheduling problem (FJSP) was developed from the classical JSP. It is possible to assign any job to more than one machine as per the machine’s capability and, constructing an environment that is similar to the actual industry [1]. FJSP is an NP-Hard problem of the combinatorial optimization type, which has a complex solution. Metaheuristics are developed to solve FJSP to find a near optimal production schedule and to shorten the time required to solve the problem

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