Solving Extremum Problems with Linear Fractional Objective Functions on the Combinatorial Configuration of Permutations Under Multicriteriality

• Published in: Cybernetics and systems analysis Vol. 53; no. 4; pp. 590 - 599
• Main Authors: Koliechkina, L. M., Dvirna, O. A.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.07.2017; Springer Nature B.V
• Subjects: Algorithms; Artificial Intelligence; Block diagrams; Combinatorial analysis; Configurations; Control; Graph theory; Mathematics; Mathematics and Statistics; Multiple criterion; Optimization; Pareto optimum; Permutations; Processor Architectures; Software Engineering/Programming and Operating Systems; Systems Theory; multicriteriality condition; linear fractional function; search optimization; extremum problem; combinatorial configuration; modified coordinate method
• ISSN: 1060-0396; 1573-8337
• DOI: 10.1007/s10559-017-9961-3

The authors consider the extremum optimization problem with linear fractional objective functions on combinatorial configuration of permutations under multicriteria condition. Solution methods for linear fractional problems are analyzed to choose the approach to problem’s solution. A solution technique based on graph theory is proposed. The algorithm of the modified coordinate method’s subprogram with search optimization is described. It forms a set of points that satisfy additional constraints of the problem. The general solution algorithm without linearization of the objective function and it’s block diagram are proposed. Examples of the algorithm are described.