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A Genetic Algorithm to Minimize the Total Tardiness for M-Machine Permutation Flowshop Problems

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Chung C.-S., Flynn J., Rom W., Staliński P.
Journal of Entrepreneurship, Management and Innovation
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2012
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vol. 8
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issue 2
26-43
EN
The m-machine, n-job, permutation flowshop problem with the total tardiness objective is a common scheduling problem, known to be NP-hard. Branch and bound, the usual approach to finding an optimal solution, experiences difficulty when n exceeds 20. Here, we develop a genetic algorithm, GA, which can handle problems with larger n. We also undertake a numerical study comparing GA with an optimal branch and bound algorithm, and various heuristic algorithms including the well known NEH algorithm and a local search heuristic LH. Extensive computational experiments indicate that LH is an effective heuristic and GA can produce noticeable improvements over LH.
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