One of the most common approaches for multiobjective optimization is to generate a solution set that well approximates the whole Pareto-optimal frontier to facilitate the later decision-making process. However, how to evaluate and compare the quality of different solution sets remains challenging. Existing measures typically require additional problem knowledge and information, such as a refere...

A new game theoretical solution concept for open spectrum sharing in cognitive radio (CR) environments is highlighted – the Lorenz equilibrium (LE). Both Nash and Pareto solution concepts have limitations when applied to real world problems. Nash equilibrium (NE) rarely ensures maximal payoff and it is frequently Pareto inefficient. The Pareto set is usually a large set of solutions, often too ...

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...

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...

The coupling of performance functions due to common design variables and uncertainties in an engineering design process will result in difficulties in optimization design problems, such as poor collaboration among design objectives and poor resolution of design conflicts. To handle these problems, a fuzzy interactive multi-objective optimization model is developed based on Pareto solutions, whe...

A new game theoretical solution concept for open spectrum sharing in cognitive radio (CR) environments is presented – the Lorenz equilibrium (LE). Both Nash and Pareto solution concepts have limitations when applied to real world problems. Nash equilibrium (NE) rarely ensures maximal payoff and it is frequently Pareto inefficient. The Pareto set is usually a large set of solutions, often too ha...