Extended launch pad method for the Pareto frontier approximation in multiextremal multiobjective optimization problems

For nonlinear nonconvex multiobjective optimization problems with multiextremal criteria, a new method for Pareto frontier approximation, i.e., the extended launch pad method, is proposed. Since the Pareto frontier is unstable in relation to perturbations of the parameters of a multiobjective optimization problem, instead of Pareto frontier approximation, the problem of approximating the Edgeworth–Pareto hull of a feasible objective set is solved. The proposed method is development of the launch pad method based on the preliminary construction of such subset of the set of feasible decisions that the gradient-based local optimization of functions of criteria starting from the points of the subset rather frequently lead to decisions close to efficient solutions of the multiobjective optimization problem. In addition to the procedures of the launch pad method, the extended launch pad method includes a genetic algorithm for Pareto frontier approximation. Experimentally it is shown that, in terms of quality of the constructed Edgeworth–Pareto hull approximation, the proposed method surpasses both the launch pad method and the earlier known optimum injection method. Experiments are performed with the problem of choosing rules for controlling the multistep system with criteria like reliability (frequency of fulfillment) of a priori requirements to the system.