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An Objective Penalty Functions Algorithm for Multiobjective Optimization Problem
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American Journal of Operations Research·Volume 01 (2011)·Pages 229–235·Published 21 December 2011·DOI10.4236/ajor.2011.14026
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Abstract
By using the penalty function method with objective parameters, the paper presents an interactive algorithm to solve the inequality constrained multi-objective programming (MP). The MP is transformed into a single objective optimal problem (SOOP) with inequality constrains; and it is proved that, under some conditions, an optimal solution to SOOP is a Pareto efficient solution to MP. Then, an interactive algorithm of MP is designed accordingly. Numerical examples show that the algorithm can find a satisfactory solution to MP with objective weight value adjusted by decision maker.
KeywordsMultiobjective Optimization ProblemObjective Penalty FunctionPareto Efficient SolutionInteractive Algorithm
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