Hierarchical Population Game Models of Coevolution in Multi-Criteria Optimization Problems under Uncertainty

Abstract

The article develops hierarchical population game models of co-evolutionary algorithms for solving the problem of multi-criteria optimization under uncertainty. The principles of vector minimax and vector minimax risk are used as the basic principles of optimality for the problem of multi-criteria optimization under uncertainty. The concept of equilibrium of a hierarchical population game with the right of the first move is defined. The necessary conditions are formulated under which the equilibrium solution of a hierarchical population game is a discrete approximation of the set of optimal solutions to the multi-criteria optimization problem under uncertainty.