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A non-dominated sorting based customized random-key genetic algorithm for the bi-objective traveling thief problem

Author

Listed:
  • Jonatas B. C. Chagas

    (Universidade Federal de Ouro Preto
    Universidade Federal de Viçosa)

  • Julian Blank

    (Michigan State University)

  • Markus Wagner

    (The University of Adelaide)

  • Marcone J. F. Souza

    (Universidade Federal de Ouro Preto)

  • Kalyanmoy Deb

    (Michigan State University)

Abstract

In this paper, we propose a method to solve a bi-objective variant of the well-studied traveling thief problem (TTP). The TTP is a multi-component problem that combines two classic combinatorial problems: traveling salesman problem and knapsack problem. We address the BI-TTP, a bi-objective version of the TTP, where the goal is to minimize the overall traveling time and to maximize the profit of the collected items. Our proposed method is based on a biased-random key genetic algorithm with customizations addressing problem-specific characteristics. We incorporate domain knowledge through a combination of near-optimal solutions of each subproblem in the initial population and use a custom repair operator to avoid the evaluation of infeasible solutions. The bi-objective aspect of the problem is addressed through an elite population extracted based on the non-dominated rank and crowding distance. Furthermore, we provide a comprehensive study showing the influence of each parameter on the performance. Finally, we discuss the results of the BI-TTP competitions at EMO-2019 and GECCO-2019 conferences where our method has won first and second places, respectively, thus proving its ability to find high-quality solutions consistently.

Suggested Citation

  • Jonatas B. C. Chagas & Julian Blank & Markus Wagner & Marcone J. F. Souza & Kalyanmoy Deb, 2021. "A non-dominated sorting based customized random-key genetic algorithm for the bi-objective traveling thief problem," Journal of Heuristics, Springer, vol. 27(3), pages 267-301, June.
    • Handle: RePEc:spr:joheur:v:27:y:2021:i:3:d:10.1007_s10732-020-09457-7
    DOI: 10.1007/s10732-020-09457-7
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    References listed on IDEAS

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    1. Markus Wagner & Marius Lindauer & Mustafa Mısır & Samadhi Nallaperuma & Frank Hutter, 2018. "A case study of algorithm selection for the traveling thief problem," Journal of Heuristics, Springer, vol. 24(3), pages 295-320, June.
    2. Wagner, Markus & Bringmann, Karl & Friedrich, Tobias & Neumann, Frank, 2015. "Efficient optimization of many objectives by approximation-guided evolution," European Journal of Operational Research, Elsevier, vol. 243(2), pages 465-479.
    3. Gonçalves, José Fernando & Resende, Mauricio G.C., 2015. "A biased random-key genetic algorithm for the unequal area facility layout problem," European Journal of Operational Research, Elsevier, vol. 246(1), pages 86-107.
    4. Mauricio Resende, 2012. "Biased random-key genetic algorithms with applications in telecommunications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(1), pages 130-153, April.
    5. Thiago Noronha & Mauricio Resende & Celso Ribeiro, 2011. "A biased random-key genetic algorithm for routing and wavelength assignment," Journal of Global Optimization, Springer, vol. 50(3), pages 503-518, July.
    6. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    7. Gonçalves, José Fernando & Resende, Mauricio G.C., 2013. "A biased random key genetic algorithm for 2D and 3D bin packing problems," International Journal of Production Economics, Elsevier, vol. 145(2), pages 500-510.
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    Cited by:

    1. Dalila B. M. M. Fontes & S. Mahdi Homayouni, 2023. "A bi-objective multi-population biased random key genetic algorithm for joint scheduling quay cranes and speed adjustable vehicles in container terminals," Flexible Services and Manufacturing Journal, Springer, vol. 35(1), pages 241-268, March.

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