The optimization of multiple conflictive objectives at the same time is a hard problem. In most cases, a uniform distribution of solutions on the Pareto front is the main objective. We propose a novel evolutionary multi-objective algorithm that is based on the selection with regard to equidistant lines in the objective space. The so-called rakes can be computed efficiently in high dimensional o...

This paper presents a new search procedure to tackle multi-objective traveling salesman problem (TSP). This procedure constructs the solution attractor for each of the objectives respectively. Each attractor contains the best solutions found for the corresponding objective. Then, these attractors are merged to find the Pareto-optimal solutions. The goal of this procedure is not only to generate...

Conventional multi-objective Particle Swarm Optimization (PSO) algorithms aim to find a representative set of Pareto-optimal solutions from which the user may choose preferred solutions. For this purpose, most multi-objective PSO algorithms employ computationally expensive comparison procedures such as non-dominated sorting. The crucial task of choosing a single preferred solution from the obta...

A new algorithm is proposed to solve constrained multi-objective problems in this paper. The constraints of the MOPs are taken account of in determining Pareto dominance. As a result, the feasibility of solutions is not an issue. At the same time, it takes advantage of both the orthogonal design method to search evenly, and the statistical optimal method to speed up the computation. The output ...

In this paper we address the question of how many objective functions are really needed to decide whether a given point is Pareto optimal. We prove a reduction result for the case of quasi-convex objective functions and a convex feasible set. This result states that in order to decide whether a point x in the decision space is Pareto optimal it suuces to consider at most n + 1 objectives at a t...

Several problems in the engineering domain are multi-objective in nature. The solution to multi-objective optimization is a set of solutions rather than a single point solution. Such a set of non-dominated solutions are called Pareto optimal solutions or non-inferior solutions. In this paper, a new algorithm, Elitist-Multi-objective Differential Evolution (E-MODE) is proposed. The proposed algo...

A multiobjective optimization problem is considered in a general formulation. It is well known that the solution of the problem is not unique and represented in the objective space by a Pareto frontier. In an engineering design it can be important to provide a discrete representation of the entire Pareto surface. Meanwhile, the obtaining of a single Pareto solution may be time-consuming. Moreov...

In this paper we present a new interactive procedure for multiObjective optimization, which is based on the use of a set of value functions as a preference model built by an ordinal regression method. The procedure is composed of two alternating stages. In the first stage, a representative sample of solutions from the Pareto optimal set (or from its approximation) is generated. In the second st...

In this paper, a fuzzy multi-objective constrained optimization problem (FMCOP) is converted to a single-objective constrained optimization problem with equality and inequality constraints (SCOP) by using α−level set of the fuzzy vector and weighting approach. A trust-region algorithm for solving problem (SCOP) is introduced to obtain α−pareto optimal solutions of problem (FMCOP). An εα−stabili...

In the multi objective optimization, in the case when generated set of Pareto optimal solutions is large, occurs the problem to select of the best solution from this set. In this paper is suggested a method to order of Pareto set. Ordering the Pareto optimal set carried out in conformity with the introduced distance function between each solution and selected reference point, where the referenc...