Arrow’s celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and nondictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about...

Recently, Gregório and Oliveira developed a proximal point scalarization method (applied to multiobjective optimization problems) for an abstract strict scalar representation with a variant of the logarithmic-quadratic function of Auslender et al. as regularization. In this work we propose a variation of this method, taking into account the regularization with logarithm and quasi-distance, wher...

Relative Nash welfarism is a solution to the problem of aggregating von NeumannMorgenstern preferences over a set of lotteries. It ranks such lotteries according to the product of any collection of 0—normalized von Neumann-Morgenstern utilities they generate. We show that this criterion is characterized by the Weak Pareto Principle, Anonymity, and Independence of Harmless Expansions: the social...

In this paper, a new evolutionary technique for detecting continuous Pareto optimal sets is proposed. The technique is designed for functions of one real variable but it can be extended for several variables functions. In this approach an individual (a solution) is either a closed interval or a point. Each solution in the final population corresponds to a decision region of Pareto optimal set. ...

This paper examines the problem of aggregating infinite utility streams with a social welfare function that respects the Hammond Equity and Weak Pareto Axioms. The paper provides a complete characterization of domains (of the one period utilities) on which such an aggregation is possible. A social welfare function satisfying the Hammond Equity and Weak Pareto Axioms exists on precisely those do...

Most of the engineering problems are modeled as evolutionary multiobjective optimization problems, but they always ask for only one best solution, not a set of Pareto optimal solutions. The decision maker’s subjective information plays an important role in choosing the best solution from several Pareto optimal solutions. Generally, the decision-making processing is implemented after Pareto opti...

In [5] an evolutionary algorithm for detecting continuous Pareto optimal sets has been proposed. In this paper we propose a new evolutionary elitist approach combing a non-standard solution representation and an evolutionary optimization technique. The proposed method permits detection of continuous decision regions. In our approach an individual (a solution) is either a closed interval or a po...

In this paper we consider two-person games in strategic form in cases in which each player has only two moves. The related Nash competitive and cooperative solution and Nash equilibria are presented. Nash cooperative solution is the only solution such that the corresponding payoffs respect three properties (belonging to feasible set, Pareto optimality and symmetry) together with two technical a...

Abstract: In multi-objective optimization problems, the optimization target is to obtain a set of non-dominated solutions. Comparing solution sets is crucial in evaluating the performances of different optimization algorithms. The use of performance indicators is common in comparing those sets and, subsequently, optimization algorithms. A good solution set must be close to the Pareto-optimal fr...

In multi-objective problems, it is desirable to use a fast algorithm that gains coverage over large parts of the Pareto front. The simplest multi-objective method is a linear combination of objectives given to a single-objective optimizer. However, it is proven that this method cannot support solutions on the concave areas of the Pareto front: one of the points on the convex parts of the Pareto...