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An NSGA-II-Based Memetic Algorithm for an Energy-Efficient Unrelated Parallel Machine Scheduling Problem with Machine-Sequence Dependent Setup Times and Learning Effect

  • Research Article-Systems Engineering
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Abstract

In this study, an energy-efficient unrelated parallel machine scheduling problem is discussed. The speed scaling mechanism has been taken into account as an energy-efficient strategy. Unrelated parallel machine scheduling with speed scaling is generalized by considering machine-sequence dependent setup times and learning effect features. A multiobjective mixed-integer linear programming (MILP) model has been proposed for the problem. Due to the NP-hard nature of the problem, a multiobjective evolutionary algorithm, the NSGA-II-based memetic algorithm, is proposed. An encoding scheme, decoding algorithm, and local search algorithms are proposed for the problem. Speed tuning heuristic and job-machine switch heuristic algorithms are proposed as local search algorithms. A restarting strategy has been applied to ensure the diversification of the algorithm. The classical NSGA-II algorithm and the proposed memetic algorithm were compared over the generated test problems. As a result, the proposed memetic algorithm is more successful according to performance metrics.

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Abbreviations

I :

Machine indices and \(i \in \{1,\dots ,m\}\)

h :

Position indices and \(h \in \{1,\dots ,n\}\)

k, j :

Job indices and \(k, j \in \{1,\dots ,n\}\)

o :

Speed indices and \(o \in \{1,\dots ,S\}\)

a :

Learning index

\({s}_{ijk}\) :

Setup time of job k processing after job j on machine i

\({P}_{ij}\) :

Normal processing time of job j on machine i

\({v}_{o}\) :

Alternative speed values

\({q}_{ijo}\) :

Energy consumption rate on the speed of for job j on machine i

M :

Very big number

\({C}_{j}\) :

Completion time of job j

\({C}_{\rm max}\) :

Maximum completion time (makespan)

E :

Total energy consumption

\({x}_{ijho}\) :

\(\left\{ {\begin{array}{*{20}c} {1;\quad {\text{If}}\,{\text{job}}\,{\text{j}}\,{\text{is}}\,{\text{processing}}\,{\text{on}}\,{\text{machine}}\,{\text{i}}\,{\text{with}}\,{\text{speed}}\,{\text{o}}\,{\text{and}}\,{\text{position}}\,{\text{h}}} \\ {0;\quad o.w.} \\ \end{array} } \right.\)

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This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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  1. Department of Industrial Engineering, Iskenderun Technical University, Hatay, Turkey

    Gulcin Bektur

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  1. Gulcin Bektur
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Correspondence to Gulcin Bektur.

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Bektur, G. An NSGA-II-Based Memetic Algorithm for an Energy-Efficient Unrelated Parallel Machine Scheduling Problem with Machine-Sequence Dependent Setup Times and Learning Effect. Arab J Sci Eng 47, 3773–3788 (2022). https://doi.org/10.1007/s13369-021-06114-4

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