We consider a setting where a coalition of individuals chooses one or several alternatives from each set in a collection of choice sets. We examine the computational complexity of Pareto rationalizability. Pareto rationalizability requires that we can endow each individual in the coalition with a preference relation such that the observed choices are Pareto efficient. We differentiate between t...

In this paper, we investigate the existence of Pareto and weak Pareto equilibria for multiobjective games without compactness. By employing an existence theorem of Pareto equilibria due to Yu and Yuan([10]), several existence theorems of Pareto and weak Pareto equilibria for the multiobjective games are established in a similar way to Flores-Bázan([4]).

In this article, we view the Pareto and weak solutions of multiobjective optimization by using an approximate version KKT type conditions. one our main results Ekeland’s variational principle for vector-valued maps plays a key role. We also focus on improved Geoffrion proper it’s approximation characterize them through saddle point

in this paper, a multi-objective reconfiguration problem has been solved simultaneously by a modified ant colony optimization algorithm. two objective functions, real power loss and energy not supplied index (ens), were utilized. multi-objective modified ant colony optimization algorithm has been generated by adding non-dominated sorting technique and changing the pheromone updating rule of ori...

Design is a multi-objective decision-making process considering manufacturing, cost, aesthetics, usability among many other product attributes. The set of optimal solutions, the Pareto set, indicates the tradeoffs between objectives. Decision-makers generally select their own optima from the Pareto set based on personal preferences or other judgements. However, uncertainties from manufacturing ...

Many practical optimization problems usually have several conflicting objectives. In those multi-objective optimization, no solution optimizing all objective functions simultaneously exists in general. Instead, Pareto optimal solutions, which are “efficient” in terms of all objective functions, are introduced. In general we have many Pareto optimal solutions. Therefore, we need to decide a fina...

In multidisciplinary optimization a designer solves a problem where there are different criteria usually contradicting each other. In general, the solution of such a problem is not unique. When seeking an optimal design, it is natural to exclude from the consideration any design solution which can be improved without deterioration of any discipline and violation of the constraints; in other wor...

In this paper, the concepts of Pareto H -eigenvalue and Pareto Z -eigenvalue are introduced for studying constrained minimization problem and the necessary and sufficient conditions of such eigenvalues are given. It is proved that a symmetric tensor has at least one Pareto H -eigenvalue (Pareto Z -eigenvalue). Furthermore, theminimumPareto H -eigenvalue (or Pareto Z -eigenvalue) of a symmetric ...

This paper deals with the problem of existence of compromise decisions and conditions for a compromise decision to be weakly Pareto-optimal, i.e., to be a weak Pareto-maximizer, Pareto-maximizer, or strong Pareto-maximizer. The concept of compromise decision is generalized by adopting triangular norms. Further, a concept of fuzzy interval is introduced. Suucient conditions for the existence of ...