In this work we characterize different types of solutions of a vector optimization problem by means of a scalarization procedure. Usually different scalarizing functions are used in order to obtain the various solutions of the vector problem. Here we consider different kinds of solutions of the same scalarized problem. Our results allow us to establish a parallelism between the solutions of the...

In this paper, a method based on Nelder and Mead’s simplex search method, is developed for solving multi-objective optimization problems. Unlike other multi-objective optimization algorithms based on classical methods, this method does not require any a priori knowledge about the problem. Moreover, it does not need any pre-defined weights or additional constraints as it works without scalarizin...

A nadir point is constructed by the worst objective values of the solutions of the entire Pareto-optimal set. Along with the ideal point, the nadir point provides the range of objective values within which all Pareto-optimal solutions must lie. Thus, a nadir point is an important point to researchers and practitioners interested in multi-objective optimization. Besides, if the nadir point can b...

In this paper, we consider the problem of searching nondominated alternatives in a discrete multiple criteria problem. The search procedure is based on the use of a reference direction. A reference direction reflects the desire of the decision maker (DM) to specify a search direction. To find a set of given alternatives related somehow to the reference direction specified by the DM, the referen...

This paper describes a new Preference-based Interactive Evolutionary (PIE) algorithm for multi-objective optimization which exploits the advantages of both evolutionary algorithms andmultiple criteria decision making approaches. Our algorithm uses achievement scalarizing functions and the potential of population based evolutionary algorithms to help the decision maker to direct the search towar...

In this paper, we study the properties of Germeier’s scalarization applied for solving multicriteria games. The equilibria and equilibrium values such games, as a rule, make sets, problems parametrizing approximating these sets arise. Shapley proved that Nash matrix game can be found by two-parametric family scalar games obtained with help linear criteria vector. We show parametrizes using one-...

In this paper we systematically study the importance, i.e., the influence on performance, of the main design elements that differentiate scalarizing functions-based multiobjective evolutionary algorithms (MOEAs). This class of MOEAs includes Multiobjecitve Genetic Local Search (MOGLS) and Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D) and proved to be very successful in m...