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.
Highlights
The interactive algorithm is very efficient in solving multi-objective optimization problems of many fields, while the penalty function is a very important method in solving optimization problems with constraints
The multi-objective programming (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
Numerical examples show that the algorithm can find a satisfactory solution to MP with objective weight value adjusted by decision maker
Summary
The interactive algorithm is very efficient in solving multi-objective optimization problems of many fields, while the penalty function is a very important method in solving optimization problems with constraints. In solving multi-objective optimization problems, the interactive algorithm provides a way to adjust objective weight value between the decision maker and computer, so that solution space is readily understood, which makes it easier in use and more convenient in operation. Such that all objective values are optimal, but this is obviously difficult in general. By using objective penalty functions as utility functions for MP, the paper obtains a satisfactory solution, when the decision maker is allowed, in the interactive algorithm, to choose another weight of objectives for some dissatisfactory objectives time and again. Numerical examples show that the proposed algorithm has good convergence and can control objective changes by changing objective weights
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