SOLUTION OF MULTIPLE PARAMETER, BI-CRITERIA OPTIMIZATION PROBLEMS BASED ON REDUCTION OF PROBLEM DIMENSION AND SPLINE APPROXIMATIONS

Abstract

A new numerical method for solving optimization bicreteria multiextremal problems with constraints is proposed that approximates the Pareto set with a given accuracy. The functions of the criteria and constraints are defined by a set of points in which the values of functions in the multidimensional space are experimentally (numerical experiments) calculated. The method is based on the reduction of the dimensionality of the design space, the approximation of one-dimensional functions by modified Bezier curves (for which the deviation of the curve from all control points is minimised), and the information-statistical approach for global optimization. As an example application of the proposed method, the two-objective problem of optimizing the shape of the rail in the railway crossings considered. The mathematical model of the problem includes four design parameters that determine the dimensions of the two controlling cross-sections of the rail and two optimization criteria. The first criterion reflects the occurrence of fatigue defects in the rail, the second criterion reflects the rail wear.

Keywords: multicriteria optimization, optimal design, approximation of multidimensional function, global optimization, Pareto-optimal solutions, railway crossings.