Global optimization for generalized geometric programming problems with discrete variables

Generalized geometric programming (GGP) problems occur frequently in engineering design and management, but most existing methods for solving GGP actually only consider continuous variables. This article presents a new branch-and-bound algorithm for globally solving GGP problems with discrete variab...

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Vydáno v:Optimization Ročník 62; číslo 7; s. 895 - 917
Hlavní autoři: Shen, Pei-Ping, Bai, Xiao-Di
Médium: Journal Article
Jazyk:angličtina
Vydáno: Philadelphia Taylor & Francis Group 01.07.2013
Taylor & Francis LLC
Témata:
Algorithms
Branch & bound algorithms
Computation
discrete variable
Equivalence
generalized geometric programming
Geometry
global optimization
Linear programming
linearization technique
Lower bounds
Mathematical analysis
Mathematical models
Mathematical programming
Optimization
Optimization techniques
Programming
reduction cut
Studies
Variables
ISSN:0233-1934, 1029-4945
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Abstract Generalized geometric programming (GGP) problems occur frequently in engineering design and management, but most existing methods for solving GGP actually only consider continuous variables. This article presents a new branch-and-bound algorithm for globally solving GGP problems with discrete variables. For minimizing the problem, an equivalent monotonic optimization problem (P) with discrete variables is presented by exploiting the special structure of GGP. In the algorithm, the lower bounds are computed by solving ordinary linear programming problems that are derived via a linearization technique. In contrast to pure branch-and-bound methods, the algorithm can perform a domain reduction cut per iteration by using the monotonicity of problem (P), which can suppress the rapid growth of branching tree in the branch-and-bound search so that the performance of the algorithm is further improved. Computational results for several sample examples and small randomly generated problems are reported to vindicate our conclusions.
AbstractList Generalized geometric programming (GGP) problems occur frequently in engineering design and management, but most existing methods for solving GGP actually only consider continuous variables. This article presents a new branch-and-bound algorithm for globally solving GGP problems with discrete variables. For minimizing the problem, an equivalent monotonic optimization problem (P) with discrete variables is presented by exploiting the special structure of GGP. In the algorithm, the lower bounds are computed by solving ordinary linear programming problems that are derived via a linearization technique. In contrast to pure branch-and-bound methods, the algorithm can perform a domain reduction cut per iteration by using the monotonicity of problem (P), which can suppress the rapid growth of branching tree in the branch-and-bound search so that the performance of the algorithm is further improved. Computational results for several sample examples and small randomly generated problems are reported to vindicate our conclusions.
Generalized geometric programming (GGP) problems occur frequently in engineering design and management, but most existing methods for solving GGP actually only consider continuous variables. This article presents a new branch-and-bound algorithm for globally solving GGP problems with discrete variables. For minimizing the problem, an equivalent monotonic optimization problem (P) with discrete variables is presented by exploiting the special structure of GGP. In the algorithm, the lower bounds are computed by solving ordinary linear programming problems that are derived via a linearization technique. In contrast to pure branch-and-bound methods, the algorithm can perform a domain reduction cut per iteration by using the monotonicity of problem (P), which can suppress the rapid growth of branching tree in the branch-and-bound search so that the performance of the algorithm is further improved. Computational results for several sample examples and small randomly generated problems are reported to vindicate our conclusions. [PUBLICATION ABSTRACT]
Author Bai, Xiao-Di
Shen, Pei-Ping
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Snippet Generalized geometric programming (GGP) problems occur frequently in engineering design and management, but most existing methods for solving GGP actually only...
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SubjectTerms Algorithms
Branch & bound algorithms
Computation
discrete variable
Equivalence
generalized geometric programming
Geometry
global optimization
Linear programming
linearization technique
Lower bounds
Mathematical analysis
Mathematical models
Mathematical programming
Optimization
Optimization techniques
Programming
reduction cut
Studies
Variables
Title Global optimization for generalized geometric programming problems with discrete variables
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