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Bi-Objective Optimization for Interval Max-Plus Linear Systems

Author

Listed:
  • Cailu Wang

    (School of Electrical Engineering, Yanshan University, Qinhuangdao 066000, China)

  • Jiye Zhang

    (School of Electrical Engineering, Yanshan University, Qinhuangdao 066000, China)

  • Pengcheng Chen

    (School of Electrical Engineering, Yanshan University, Qinhuangdao 066000, China)

  • Haichao Zhao

    (Handan Institute of Environmental Protection, Handan 056001, China)

Abstract

This paper investigates the interval-valued-multi-objective-optimization problem, whose objective function is a vector-valued max-plus interval function and the constraint function is a real-affine function. The strong and weak solvabilities of the interval-valued-optimization problem are introduced, and the solvability criteria are established. A necessary and sufficient condition for the strong solvability of the multi-objective-optimization problem is provided. In particular, for the bi-objective-optimization problem, a necessary and sufficient condition of the weak solvability is provided, and all the solvable sub-problems are found out. The interval optimal solution is obtained by constructing the set of all optimal solutions of the solvable sub-problems. The optimal load distribution is used to demonstrate how the presented results work in real-life examples.

Suggested Citation

  • Cailu Wang & Jiye Zhang & Pengcheng Chen & Haichao Zhao, 2024. "Bi-Objective Optimization for Interval Max-Plus Linear Systems," Mathematics, MDPI, vol. 12(5), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:5:p:653-:d:1344595
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