Uma proposta de algoritmo baseado em cone de preferência para otimização com muitos objetivos e robusta

Abstract

The solution of a multi-objective optimization problem is a set characterized by the trade off of M objectives. In the case of the minimization problem F : R N → R M, these trade off solutions correspond to a minimal set according to a partial order relation in space R M. The search for solutions of smaller variation in the presence of noise in the variables x ∈ R N characterizes Robust Multiobjective Optimization. This work presents a co-evolutionary algorithm for Robust Optimization. The presented proposal uses the objective space decomposition/aggregation strategy in a competitive co-evolution algorithm. Along with this new technique, a new method of generating vectors of weight almost equally spaced in the objective space was developed. This new method of generating weight vectors is not limited in the number of weight vectors created neither to the norm of each vector, that can be located in the first orthant of the objective space to form a cone of vectors with vertex in the origin. The axis of this cone corresponds to a preference vector of the decision maker and its aperture defines the extension of the chosen region of interest. The quality of the weight vectors of weight produced by this new methodology was compared with the usual method of generation of weight vectors and the results were satisfactory. In addition, a new class of multi-objective optimization problems was developed, encompassing usual and robust optimization, with and without the presence of equality and inequality constraints. Following the structure used in the construction of the test functions, a new performance evaluation metric is also presented. The comparison of the results obtained between the proposed method and other techniques showed the superiority of the presented methods. A sample of the results obtained was used in the data visualization tool developed, showing the conclusions obtained.