Many decision making problems can be formulated as multi-objective optimization problems (MOP). There hardly exists the solution that optimizes all objective functions in MOP, and then the concept of Pareto optimal solution (or efficient solution) is introduced. Usually, there exist a lot of Pareto optimal solutions, which are considered as candidates of final decision making solution. It is an...

In two-sided matching markets, the concept of stability proposed by Gale and Shapley (1962) is one of the most important solution concepts. In this paper, we consider a problem related to the stability of a matching in a two-sided matching market with indifferences (i.e., ties). The introduction of ties into preference lists dramatically changes the properties of stable matchings. For example, ...

Pareto local search (PLS) methods are local search algorithms for multiobjective combinatorial optimization problems based on the Pareto dominance criterion. PLS explores the Pareto neighbourhood of a set of non-dominated solutions until it reaches a local optimal Pareto front. In this paper, we discuss and analyse three different Pareto neighbourhood exploration strategies: best, first, and ne...

The paper is devoted to applications of modern tools of variational analysis to equilibrium models of welfare economics involving nonconvex economies with infinite-dimensional commodity spaces. The main results relate to generalized/ extended second welfare theorems ensuring an equilibrium price support at Pareto optimal allocations. Based on advanced tools of generalized differentiation, we es...

This paper is concerned with the problem of finding a representative sample of Pareto-optimal points inmulti-objective optimization. The Normal Boundary Intersection algorithm is a scalarization scheme for generating a set of evenly spaced Efficient solutions. A drawback of this algorithm is that Pareto-optimality of solutions is not guaranteed. The contributions of this paper are two-fold. Fir...

In multicriteria optimization, a compromise solution is a feasible solution whose cost vector minimizes the distance to the ideal point w.r.t. a given norm. The coordinates of the ideal point are given by the optimal values for the single optimization problem for each criterion. We show that the concept of compromise solutions fits nicely into the existing notion of Pareto optimality: For a hug...

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...

This paper proposes a new algorithm for the solution of fully fuzzy Multi objective linear programming problems involving triangular fuzzy number without converting them to equivalent classical problems. Based on the fuzzy ideal and fuzzy negative ideal solution of each single fuzzy objective function we propose an algorithm which provides a fuzzy Pareto-optimal solution for the given fully fuz...

In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.

In the previous paper ([5]), we studied the ordinary multiobjective convex program on a locally convex linear topological space in the case that the objective functions and the constraint functions were continuous and convex, but not always Gateaux differ entiable. In the case, we showed that the generalized Kuhn-Tucker conditions given by a subdifferential formula were necessary and sufficient...