We present a method to capture decision maker’s preferences in multiobjective problems and we discuss its use as a base for a decision maker – multiobjective optimization model interface. We illustrate the idea on a small but illustrative numerical example of the airport gate assignment problem.

A mixed type dual for multiobjective variational problems is formulated. Several duality theorems are established relating properly efficient solutions of the primal and dual variational problems under generalized (F,ρ)-convexity. Static mixed type dual multiobjective problems are particular cases of these problems.  2004 Elsevier Inc. All rights reserved.

The purpose of this paper is to characterize the weak Pareto optimality for multiobjective pseudoconvex problem. In fact, it is a first order optimality characterization that generalize the Karush-Kuhn-Tucker condition. Moreover, this work is an extension of the single-objective case [6] to the multiobjective one with pseudoconvex continuous functions. Mathematics Subject Classification: 46N10,...

Many real-life problems have a natural representation in the framework of multiobjective optimization. Evolutionary algorithms are generally considered one of the most successful methods for solving the multiobjective optimization problems. In this paper we present state-of-the-art multiobjective evolutionary algorithms and briefly discuss their advantages and disadvantages. In the last section...

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]).

We apply a multi-color extension of the Beck-Fiala theorem to show that the multiobjective maximum traveling salesman problem is randomized 1/2-approximable on directed graphs and randomized 2/3-approximable on undirected graphs. Using the same technique we show that the multiobjective maximum satisfiabilty problem is 1/2-approximable. 1998 ACM Subject Classification F.2.2 Nonnumerical Algorith...

In this paper, we extend the notions of ( , ρ)-invexity and generalized ( , ρ)invexity to the continuous case and we use these concepts to establish sufficient optimality conditions for the considered class of nonconvexmultiobjective variational control problems. Further, multiobjective variational control mixed dual problem is given for the considered multiobjective variational control problem...

This paper deals with a nonlinear multiobjective semi-infinite programming problem involving generalized (C,α, ρ, d)-convex functions. We obtain sufficient optimality conditions and formulate the Mond-Weirtype dual model for the nonlinear multiobjective semi-infinite programming problem. We also establish weak, strong and strict converse duality theorems relating the problem and the dual problem.

In this paper, we consider nonsmooth multiobjective fractional programming problems involving locally Lipschitz functions. We introduce the property of generalized invexity for fractional function. We present necessary optimality conditions, sufficient optimality conditions and duality relations for nonsmooth multiobjective fractional programming problems, which is for a weakly efficient soluti...

We introduce multiobjective disk cover problems and study their approximability. We construct a polynomial-time approximation scheme (PTAS) for the multiobjective problem where k types of points (customers) in the plane have to be covered by disks (base stations) such that the number of disks is minimized and for each type of points, the number of covered points is maximized. Our approximation ...