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A novel non-dominated sorting genetic algorithm for solving the triple objective project scheduling problem

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Abstract

Multi-objective project scheduling has attracted wide attention for approximately two decades. However, most of the existing research has focused on the double-objective project scheduling problem, while literature on project scheduling problems with more than two objectives is rather scarce. In this paper, the typical multi-mode resource-constrained project scheduling problem is extended to a new triple-objective multi-mode project scheduling problem (TOMPSP) with the objectives of minimizing the project duration, minimizing the resource investment and maximizing the robustness of the schedule. To solve the presented triple-objective problem, we resort to the latest version of the multi-objective genetic algorithm, the non-dominated sorting genetic algorithm III (NSGA-III). In the decoding process of the NSGA-III, a modified SSGS (serial schedule generation scheme), in which resource constraints are relaxed, is suggested by considering the delays of activities. Although the NSGA-III shows excellent performance in numerous multi-objective optimization problems with more than two objectives, it has a potential disadvantage in that it occasionally cannot find the intercept during the adaptive normalization process, and thus, the population cannot be normalized as expected. Since a case without an intercept is impossible in the NSGA-II, we adopt the NSGA-II normalization process rather than that of NSGA-III. The standard instances in PSPLib are modified to serve as the instances of the TOMPSP, and a computational experiment is conducted to test the algorithms. The results show that the presented algorithm not only greatly simplifies the implementation of the NSGA-III but also significantly improves the execution efficiency and calculation quality.

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Availability of data and materials

The datasets used is download from http://www.om-db.wi.tum.de/psplib/getdata_mm.html. All the experiment results of our work are available from the corresponding author on reasonable request.

Code availability

The custom code are available from the corresponding author on reasonable request.

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Acknowledgments

This research was funded by the National Natural Science Foundation of China under Grant Nos. 71671117, 71831006 and 71971173, and the Key R & D Program of Shandong under Grant No. 2019JZZY010122.

Funding

This research was funded by the National Natural Science Foundation of China under Grant Nos. 71671117, 71831006 and 71971173.

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Authors and Affiliations

  1. School of Economics and Management, Yantai University, Yantai, 264005, China

    Wuliang Peng, Liangwei Chen & Jiali Lin

  2. School of Electromechanical and Automotive Engineering, Yantai University, Yantai, 264005, China

    Jianhui Mu

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  1. Wuliang Peng
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  2. Jianhui Mu
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  3. Liangwei Chen
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  4. Jiali Lin
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Contributions

Wuliang Peng conceived and designed the study. Jianhui Mu and Liangwei Chen developed the algorithm, and Jiali Lin performed the experiments.

Corresponding authors

Correspondence to Wuliang Peng or Jianhui Mu.

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The authors declared that they have no conflicts of interest to this work.

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Peng, W., Mu, J., Chen, L. et al. A novel non-dominated sorting genetic algorithm for solving the triple objective project scheduling problem. Memetic Comp. 13, 271–284 (2021). https://doi.org/10.1007/s12293-021-00332-x

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