A Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective ProgrammingReport as inadecuate




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In this paper, we present an algorithm to solve the inequality constrained multi-objective programming MP by using a penalty function with objective parameters and constraint penalty parameter. First, the penalty function with objective parameters and constraint penalty parameter for MP and the corresponding unconstraint penalty optimization problem UPOP is defined. Under some conditions, a Pareto efficient solution or a weakly-efficient solution to UPOP is proved to be a Pareto efficient solution or a weakly-efficient solution to MP. The penalty function is proved to be exact under a stable condition. Then, we design an algorithm to solve MP and prove its convergence. Finally, numerical examples show that the algorithm may help decision makers to find a satisfactory solution to MP.

KEYWORDS

Multi-Objective Programming, Penalty Function, Objective Parameters, Constraint Penalty Parameter, Pareto Weakly-Efficient Solution

Cite this paper

Meng, Z. , Shen, R. and Jiang, M. 2014 A Penalty Function Algorithm with Objective Parameters and Constraint Penalty Parameter for Multi-Objective Programming. American Journal of Operations Research, 4, 331-339. doi: 10.4236-ajor.2014.46032.





Author: Zhiqing Meng, Rui Shen, Min Jiang

Source: http://www.scirp.org/



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