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A GRASP heuristic for the multi-objective permutation flowshop scheduling problem

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Abstract

This paper presents a multi-objective greedy randomized adaptive search procedure (GRASP)-based heuristic for solving the permutation flowshop scheduling problem in order to minimize two and three objectives simultaneously: (1) makespan and maximum tardiness; (2) makespan, maximum tardiness, and total flowtime. GRASP is a competitive metaheuristic for solving combinatorial optimization problems. We have customized the basic concepts of GRASP algorithm to solve a multi-objective problem and a new algorithm named multi-objective GRASP algorithm is proposed. In order to find a variety of non-dominated solutions, the heuristic blends two typical approaches used in multi-objective optimization: scalarizing functions and Pareto dominance. For instances involving two machines, the heuristic is compared with a bi-objective branch-and-bound algorithm proposed in the literature. For instances involving up to 80 jobs and 20 machines, the non-dominated solutions obtained by the heuristic are compared with solutions obtained by multi-objective genetic algorithms from the literature. Computational results indicate that GRASP is a promising approach for multi-objective optimization.

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  1. Departamento de Informática, Universidade Federal de Viçosa, Campus Universitário, Viçosa, Minas Gerais, CEP 36570-000, Brazil

    José Elias Claudio Arroyo & Ana Amélia de Souza Pereira

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  1. José Elias Claudio Arroyo
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  2. Ana Amélia de Souza Pereira
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Correspondence to José Elias Claudio Arroyo.

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Arroyo, J.C., de Souza Pereira, A.A. A GRASP heuristic for the multi-objective permutation flowshop scheduling problem. Int J Adv Manuf Technol 55, 741–753 (2011). https://doi.org/10.1007/s00170-010-3100-x

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