An improved framework for solving NLIPs with signomial terms in the objective or constraints to global optimality

► We globally solve nonlinear integer programming problems with signomial terms. ► The original program is converted into a mixed-integer linear program. ► A logarithmic number of extra binary variables and constraints are used. ► The proposed method significantly enhances the computational efficien...

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Veröffentlicht in:Computers & chemical engineering Jg. 53; S. 44 - 54
Hauptverfasser: Tsai, Jung-Fa, Lin, Ming-Hua
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Kidlington Elsevier Ltd 11.06.2013
Elsevier
Schlagworte:
Applied sciences
Discrete global optimization
Exact sciences and technology
Integer programming
Mathematical programming
Nonlinear programming
Operational research and scientific management
Operational research. Management science
Integer programming
Discrete global optimization
Nonlinear programming
Logarithmic function
Constraint satisfaction
Global optimum
Linear programming
Mixed integer programming
Non linear programming
Experimental study
Modeling
Binary number
Global solution
Interval arithmetic
Constrained optimization
Problem solving
Discrete programming
Non linear effect
Signomial function
Linearization
Mathematical programming
ISSN:0098-1354, 1873-4375
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Zusammenfassung:► We globally solve nonlinear integer programming problems with signomial terms. ► The original program is converted into a mixed-integer linear program. ► A logarithmic number of extra binary variables and constraints are used. ► The proposed method significantly enhances the computational efficiency. Real application problems are often formulated as nonlinear integer programming problems or as discrete global optimization problems with signomial terms in the objective or constraints. Although various approaches have been proposed to solve the problems, they either utilize numerous extra binary variables and constraints to reconstruct the problems for finding a global solution or are unable to obtain globally optimized solutions. This study proposes a novel linearization method that employs a logarithmic number of extra binary variables and constraints to reformulate a signomial term with discrete variables. The original nonlinear integer program is therefore converted into a mixed-integer linear program solvable to obtain a global optimum. Several numerical experiments are presented to demonstrate the computational efficiency of the proposed methods in solving nonlinear integer problems, especially for treating signomial functions with large-interval variables or multiple variables.
ISSN:0098-1354
1873-4375
DOI:10.1016/j.compchemeng.2013.01.015