A Linearization to the Multi-objective Linear Plus Linear Fractional Program

The structure of the sum of linear plus linear ratio program is complex and 𝒩𝒫-completeness. In management science, game theory, and industry, there are problems such that their mathematical models can be represented as a multi-objective linear plus linear fractional programming problem (MOLLFPP). T...

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Veröffentlicht in:Operations Research Forum Jg. 4; H. 4; S. 82
Hauptverfasser: Borza, Mojtaba, Rambely, Azmin Sham, Edalatpanah, Seyed Ahmad
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.12.2023
Springer Nature B.V
Schlagworte:
Algorithms
Applications of Mathematics
Approximation
Business and Management
Game theory
Linear programming
Math Applications in Computer Science
Mathematical and Computational Engineering
Mathematical programming
Multiple objective analysis
Objectives
Operations Research/Decision Theory
Optimization
Original Research
Max–min technique
Pareto optimal solution
Genetic algorithm (GA)
Pareto front
Membership function
Weighted sum method
ISSN:2662-2556, 2662-2556
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Zusammenfassung:The structure of the sum of linear plus linear ratio program is complex and 𝒩𝒫-completeness. In management science, game theory, and industry, there are problems such that their mathematical models can be represented as a multi-objective linear plus linear fractional programming problem (MOLLFPP). The aim of this study is to introduce a method to address the MOLLFPP. The approach is designed in 2 phases. In phase 1, a method is created to reach the global optimal solution of the linear plus linear fractional programming problem (LLFPP) using suitable variable transformations. In fact, in this phase, the LLFPP is changed into a linear programming problem (LPP). In phase 2, taking into account the information of phase 1, the MOLLFPP is transformed into LPPs by applying the weighted sum and max–min techniques. Two examples are solved to illustrate the method and comparisons are made to show the accuracy.
Bibliographie:ObjectType-Article-1
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ISSN:2662-2556
2662-2556
DOI:10.1007/s43069-023-00256-x