The paper describes a method for solving multi-objective optimization problems with box constraints. Unlike existing approaches, the proposed method not only constructs a finite approximation of Pareto frontier, but also proves its ϵ-optimality. The paper gives a detailed explanation of basic theoretical concepts behind the method and describes the algorithmic implementation. A practically important application of the proposed method to finding the working space of a robotic manipulator is presented.

The nonuniform covering method is applied to multicriteria optimization problems. The ɛ-Pareto set is defined, and its properties are examined. An algorithm for constructing an ɛ-Pareto set with...