Interactive stability cutting-plane algorithm for multiobjective nonlinear programming problems

In this paper, we introduce an interactive stability cutting-plane algorithm for determining a best-compromise solution to a multiobjective nonlinear programming problems in situations with an implicitly defined utility function. The method is called “interactive stability cutting-plane compromise p...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 192; no. 2; pp. 446 - 456
Main Author: Kassem, Mohamed Abd El-Hady
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 15.09.2007
Elsevier
Subjects:
Best-compromise solution
Calculus of variations and optimal control
Cutting-plane algorithm
Exact sciences and technology
Mathematical analysis
Mathematics
Multiobjective nonlinear programming
Numerical analysis
Numerical analysis. Scientific computation
Sciences and techniques of general use
Stability
Trade-off method
Cutting-plane algorithm
Stability
Best-compromise solution
Multiobjective nonlinear programming
Trade-off method
Multiobjective programming
Nonlinear problems
Non linear programming
Search algorithm
Numerical analysis
Applied mathematics
Optimal solution
Numerical stability
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:In this paper, we introduce an interactive stability cutting-plane algorithm for determining a best-compromise solution to a multiobjective nonlinear programming problems in situations with an implicitly defined utility function. The method is called “interactive stability cutting-plane compromise programming (ISCPCP)”. The cutting-planes which I am going to derive, are based on suitable pairwise trade-offs between the objective functions, as prescribed by the decision maker (DM) at each iterate generated by the algorithm. This algorithm requires no line searches, and generates iterates that are all contained in the efficient frontier. This feature facilitates the preference judgment of the decision maker, and permits an analyst to terminate short of optimality with an efficient near-optimal solution. Also, we investigate the stability of its efficient solutions which are obtained by using this algorithm. An illustrating example is presented to clarify this algorithm.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2007.03.037