An Improved Evolution Strategy Hybridization With Simulated Annealing for Permutation Flow Shop Scheduling Problems

Abstract

Flow Shop Scheduling Problem (FSSP) has significant application in the industry, and therefore it has been extensively addressed in the literature using different optimization techniques. Current research investigates Permutation Flow Shop Scheduling Problem (PFSSP) to minimize makespan using the Hybrid Evolution Strategy (HES <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SA</sub> ). Initially, a global search of the solution space is performed using an Improved Evolution Strategy (I.E.S.), then the solution is improved by utilizing local search abilities of Simulated Annealing (S.A.). I.E.S. thoroughly exploits the solution space using the reproduction operator, in which four offsprings are generated from one parent. A double swap mutation is used to guide the search to more promising areas in less computational time. The mutation rate is also varied for the fine-tuning of results. The best solution of the I.E.S. acts as a seed for S.A., which further improved the results by exploring better neighborhood solutions. In S.A., insertion mutation is used, and the cooling parameter and acceptance-rejection criteria induce randomness in the algorithm. The proposed HES <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SA</sub> algorithm is tested on well-known NP-hard benchmark problems of Taillard (120 instances), and the performance of the proposed algorithm is compared with the famous techniques available in the literature. Experimental results indicate that the proposed HES <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">SA</sub> algorithm finds fifty-four upper bounds for Taillard instances, while thirty-eight results are further improved for the Taillard instances.