A nonlinear interval number programming method for uncertain optimization problems

• Published in: European journal of operational research Vol. 188; no. 1; pp. 1 - 13
• Main Authors: Jiang, C., Han, X., Liu, G.R., Liu, G.P.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-07-2008; Elsevier; Elsevier Sequoia S.A
• Series: European Journal of Operational Research
• Subjects: 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
• DOI: 10.1016/j.ejor.2007.03.031

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.