Fast Evolutionary Algorithm for Flow Shop Scheduling Problems

Being complex and combinatorial optimization problems, Permutation Flow Shop Scheduling Problems (PFSSP) are difficult to be solved optimally. PFSSP occurs in many manufacturing systems i.e. automobile industry, glass industry, paper industry, appliances industry, and pharmaceutical industry, and the generation of the best schedule is very important for these manufacturing systems. Evolution Strategy (ES) is a subclass of Evolutionary algorithms and in this paper, we propose an Improved Evolution Strategy to reduce the makespan of PFSSP. Two variants of the Improved Evolution Strategy are proposed namely ES5 and ES10. The initial solution is generated using the shortest processing time rule. In ES5, four offsprings are generated from one parent while in ES10, nine offsprings are generated from one parent. The selection pool consists of both the parents and offsprings. Quad swap mutation operator has been proposed to minimize computational time and for the maximum search of solution space. Also, a variable mutation rate is used for the fine-tuning of results, with the increasing number of iterations the mutation rate is reduced. The performances of both ES variants were tested on two test domains. First, it is applied to benchmark the PFSSP of Carlier and Reeves. Computational results are matched with other well-known techniques available in the literature, and the results show the effectiveness and robustness of the proposed techniques. Secondly, ES is applied to the real-life problem for the manufacturing of batteries to demonstrate its effectiveness. Data was taken from Pakistan Accumulator for NS30-40 Plates battery, the company is daily producing 1400 units of NS30-40 Plates battery. ES is applied to different batch sizes i.e. 35, 140, 1120 & 1400. Our results show that a Min %GAP of 1.25 is found using ES10. Hence the company can increase monthly 450 units of NS30 batteries using the ES10 algorithm.