Solving a Global-Mixed Integer Signomial Geometric Fractional Programming Problem

This article addresses mixed integer fractional signomial geometric programming (MIFSGP) problems, which have been widely used in industrial design. In this paper, first, we convert fractional signomial programming into a nonfractional problem so that it maintains its geometric structure. Then, conv...

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Veröffentlicht in:Neutrosophic sets and systems Jg. 81; S. 655 - 666
Hauptverfasser: Nejad, J. Shirin, Saraj, M
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Neutrosophic Sets and Systems 01.07.2025
University of New Mexico
Schlagworte:
Algorithms
fractional programming
geometric programming
Industrial design
mixed integer programming
non-convex functions
spatial branch and bound algorithm
ISSN:2331-6055, 2331-608X
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Abstract This article addresses mixed integer fractional signomial geometric programming (MIFSGP) problems, which have been widely used in industrial design. In this paper, first, we convert fractional signomial programming into a nonfractional problem so that it maintains its geometric structure. Then, convex relaxation is used to reach a mixed integer global solution. Although, in many cases, we obtain a better objective function value with this process, designers may still be dissatisfied with the rupture between the original objective function value and the relaxed value. Therefore, we apply a spatial branch and bound algorithm to decrease that distance to an acceptable extent and maintain the global solution. Finally, a real design problem is considered to evaluate the efficiency and accuracy of the proposed technique. Keywords: geometric programming, fractional programming, mixed integer programming, non-convex functions, spatial branch and bound algorithm.
AbstractList This article addresses mixed integer fractional signomial geometric programming (MIFSGP) problems, which have been widely used in industrial design. In this paper, first, we convert fractional signomial programming into a nonfractional problem so that it maintains its geometric structure. Then, convex relaxation is used to reach a mixed integer global solution. Although, in many cases, we obtain a better objective function value with this process, designers may still be dissatisfied with the rupture between the original objective function value and the relaxed value. Therefore, we apply a spatial branch and bound algorithm to decrease that distance to an acceptable extent and maintain the global solution. Finally, a real design problem is considered to evaluate the efficiency and accuracy of the proposed technique.
This article addresses mixed integer fractional signomial geometric programming (MIFSGP) problems, which have been widely used in industrial design. In this paper, first, we convert fractional signomial programming into a nonfractional problem so that it maintains its geometric structure. Then, convex relaxation is used to reach a mixed integer global solution. Although, in many cases, we obtain a better objective function value with this process, designers may still be dissatisfied with the rupture between the original objective function value and the relaxed value. Therefore, we apply a spatial branch and bound algorithm to decrease that distance to an acceptable extent and maintain the global solution. Finally, a real design problem is considered to evaluate the efficiency and accuracy of the proposed technique. Keywords: geometric programming, fractional programming, mixed integer programming, non-convex functions, spatial branch and bound algorithm.
Audience Academic
Author Nejad, J. Shirin
Saraj, M
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Snippet This article addresses mixed integer fractional signomial geometric programming (MIFSGP) problems, which have been widely used in industrial design. In this...
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SubjectTerms Algorithms
fractional programming
geometric programming
Industrial design
mixed integer programming
non-convex functions
spatial branch and bound algorithm
Title Solving a Global-Mixed Integer Signomial Geometric Fractional Programming Problem
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