Some methods for finding effective points of a multi-criteria optimization problem
Abstract
Thе paper describes numerous approaches to obtain Pareto-optimal points, based on the reduction of multi-criteria optimization problems to "scalarized" optimization problems with specific objective functions. The sequential optimization of the functions at the fixed values of criteria functions weights allows to select among the many effective solutions, those that satisfy the decision maker. The modification of the linearization method for solving multi-objective optimization problems was proposed. It is based on the discrete minimax problem, which is constructed using criteria and the weights. The original problem of finding the effective point is reduced to the successive solutions of quadratic programming problems. The results of numerical solutions of multiobjective optimization problems by different methods were presented. The performed analysis and comparison of the results of numerical experiments confirm the effectiveness of the proposed method.References
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