A nonlinear interval number programming method for uncertain optimization problems

In this paper, a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints. Based on an order relation of interval number, the uncertain objective function is transformed into two determin...

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Veröffentlicht in:European journal of operational research Jg. 188; H. 1; S. 1 - 13
Hauptverfasser: Jiang, C., Han, X., Liu, G.R., Liu, G.P.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Amsterdam Elsevier B.V 01.07.2008
Elsevier
Elsevier Sequoia S.A
Schriftenreihe:European Journal of Operational Research
Schlagworte:
Applied sciences
Exact sciences and technology
Genetic algorithm
Genetic algorithms
Inequality
Interval number
Nonlinear programming
Operational research and scientific management
Operational research. Management science
Optimization
Studies
Uncertain optimization
Uncertainty
Uncertain optimization
Nonlinear programming
Genetic algorithm
Interval number
Probabilistic approach
Non linear programming
Penalty method
Non determinism
Constrained optimization
Penalty function
Uncertain system
Linear combination
Inequality constraint
Equality constraint
Robustness
Objective function
ISSN:0377-2217, 1872-6860
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Zusammenfassung:In this paper, a method is suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints. Based on an order relation of interval number, the uncertain objective function is transformed into two deterministic objective functions, in which the robustness of design is considered. Through a modified possibility degree, the uncertain inequality and equality constraints are changed to deterministic inequality constraints. The two objective functions are converted into a single-objective problem through the linear combination method, and the deterministic inequality constraints are treated with the penalty function method. The intergeneration projection genetic algorithm is employed to solve the finally obtained deterministic and non-constraint optimization problem. Two numerical examples are investigated to demonstrate the effectiveness of the present method.
Bibliographie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2007.03.031