Title: Multi-step crossover genetic algorithm for bi-criteria parallel machine scheduling problems

Authors: Sameer Sharma; Mehak Chadha; Harpreet Kaur

Addresses: Department of Mathematics, D.A.V. College, Jalandhar, India ' Department of Mathematics, I.K. Gujral Technical University, Jalandhar, India ' Department of Mathematics, SHIMT, Goraya, Jalandhar, India

Abstract: This paper propounds the bi-criteria scheduling problem with identical parallel machines, volatile due dates and processing times. A robust and simple structured nature inspired approach has been applied for minimisation of maximum tardiness as the primary and the number of tardy jobs as the secondary criteria. The optimal values of both criteria are evaluated on the trot confined with a constraint that optimal value of secondary criteria does not infringe the primary criteria in the opposite sense of the requirement. To unfold such kind of NP hard optimisation problems, genetic algorithm (GA) has shown a great advantage in solving the combinatorial optimisation problems in view of its characteristic that has high efficiency and is the best fit for practical application. In this paper, a multi-step crossover fusion operator of genetic algorithms (MSXF) has been introduced and applied to a set of randomly generated problems of different sizes. The results obtained are correlated with the other crossover operators. Computational results show that MSXF operator outperforms all the most every time on randomly generated problems analogous to the parameter under consideration.

Keywords: bi-criteria; scheduling; tardiness; due dates; genetic algorithm.

DOI: 10.1504/IJMOR.2021.112275

International Journal of Mathematics in Operational Research, 2021 Vol.18 No.1, pp.71 - 84

Received: 28 Feb 2019
Accepted: 05 Aug 2019
Published online: 06 Jan 2021 *

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