Bi-Objective Optimization for Interval Max-Plus Linear Systems

Cailu Wang, Jiye Zhang, Pengcheng Chen () and Haichao Zhao
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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

Mathematics, 2024, vol. 12, issue 5, 1-14

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.

Keywords: max-plus linear system; multi-objective optimization; interval-valued optimization; weak solvability; interval optimal solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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