Several Multi-Criteria-Decision-Making methodologies assume the existence of weights associated with the different criteria, reflecting their relative importance. One of the most popular ways to infer such weights is the Analytic Hierarchy Process, which constructs first a matrix of pairwise comparisons, from which weights are derived following one out of many existing procedures, such as the … Read more
This paper is concerned with the study of envelope theorems for finite choice sets. More specifically, we consider the problem of differentiability of the value function arising out of the maximization of a parametrized objective function, when the set of alternatives is non-empty and finite. The parameter is confined to the closed interval [0,1] and … Read more
In this paper we study the relationship between bilevel optimization and bicriteria optimization. Given a bilevel optimization problem, we introduce an order relation such that the optimal solutions of the bilevel problem are the nondominated points with respect to the order relation. In the case where the lower level problem of the bilevel optimization problem … Read more
The purpose of this paper is to obtain conditions on weak tournaments, which guarantee that every non-empty subset of alternatives admits a stable set. We show that every stable set always contains the core. We also show that there exists a unique stable set for each non-empty subset of alternatives which coincides with its core … Read more
The paper studies and designs an genetic algorithm (GA) of the bilevel linear programming problem (BLPP) by constructing the fitness function of the upper-level programming problem based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into … Read more
Based on near convexity, we introduce the concepts of nearly convexlike set-valued maps and nearly semiconvexlike set-valued maps, give some charaterizations of them, and investigate the relationships between them. Then a Farkas-Minkowski type alternative theorem is shown under the assumption of near semiconvexlikeness. By using the alternative theorem and some other lemmas, we establish necessary … Read more
In multicriteria optimization, several objective functions have to be minimized simultaneously. For this kind of problem, no single solution can adequately represent the whole set of optimal points. We propose a new efficient method for approximating the solution set of a convex quadratic multiobjective programming problem. The method is based on a warm-start interior point … Read more
Weighted sum based approaches to multiobjective optimization is computationally very efficient. However,they have two main weakness: 1) Only one Pareto solution can be obtained in one run 2) The solutions in the concave part of the Pareto front cannot be obtained. This paper proposes a new theory on multiobjective optimization using weighted aggregation approach. Based … Read more
In this paper we address a general Goal Programming problem with linear objectives, convex constraints, and an arbitrary componentwise nondecreasing norm to aggregate deviations with respect to targets. In particular, classical Linear Goal Programming problems, as well as several models in Location and Regression Analysis are modeled within this framework. In spite of its generality, … Read more