On the Lexicographic Centre of Multiple Objective Optimization

• Published in: Journal of optimization theory and applications Vol. 168; no. 2; pp. 600 - 614
• Main Authors: Jiangao, Zhang, Yang, Shitao
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.02.2016; Springer Nature B.V
• Subjects: Algorithms; Applications of Mathematics; Calculus of Variations and Optimal Control; Optimization; Engineering; Functions (mathematics); Inequalities; Linear programming; Mathematical analysis; Mathematical models; Mathematics; Mathematics and Statistics; Multiple objective; Objectives; Operations Research/Decision Theory; Optimization; Programming; Simplex method; Studies; Theory of Computation; 65K05; Efficient solution; 90C47; Lexicographic order; Multiple objective programming; 49M29; 90C29; 90C05; Lexicographic centre; Image set
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-015-0810-0

We study the lexicographic centre of multiple objective optimization. Analysing the lexicographic-order properties yields the result that, if the multiple objective programming’s lexicographic centre is not empty, then it is a subset of all efficient solutions. It exists if the image set of multiple objective programming is bounded below and closed. The multiple objective linear programming’s lexicographic centre is nonempty if and only if there exists an efficient solution to the multiple objective linear programming. We propose a polynomial-time algorithm to determine whether there is an efficient solution to multiple objective linear programming, and we solve the multiple objective linear programming’s lexicographic centre by calculating at most the same number of dual linear programs as the number of objective functions and a system of linear inequalities.