This paper deals with the utilizing of the Bayesian optimization algorithm (BOA) for the niultiobjective optimization of combinatorial problems. Three probabilistic models used in the Estimation Distribution Algorithms (EDA), such as UMDA, BMDA and BOA which allow one to search effectively on the promising areas of the combinatorial search space, are discussed. The main attention is focused on the incorporation of Pareto optimality concept into classical structure of the BOA algorithm. We have modified the standard algorithm BOA for one criterion optimization utilizing the known niching techniques to find the Pareto optimal set. The experiments are focused on tree classes of the combinatorial problems: artificial problem with known Pareto set, multiple 0/1 knapsack problém and the bisectioning of hypergraphs as well.
This paper deals with a multiobjective control problem for nonlinear discrete time systems. The problem consists of finding a control strategy which minimizes a number of performance indexes subject to state and control constraints. A solution to this problem through the Receding Horizon approach is proposed. Under standard assumptions, it is shown that the resulting control law guarantees closed-loop stability. The proposed method is also used to provide a robustly stabilizing solution to the problem of simultaneously minimizing a set of H∞ cost functions for a class of systems subject to bounded disturbances and/or parameter uncertainties. Numeric examples are reported to highlight the stabilizing action of the proposed control laws.