We determine the power of weighted sum scalarization with respect to computation approximations for general multiobjective minimization and maximization problems. Additionally, we introduce a new multi-factor notion approximation that is specifically tailored case its inherent trade-offs between different objectives. For problems, provide an efficient algorithm computes problem by using exact o...

We characterize the class of (possibly incomplete) preference relations over lotteries that can be represented by a compact set of (continuous) expected utility functions which preserve both indifferences and strict preferences. This finding contrasts with the representation theorem of Dubra, Maccheroni and Ok (2004) which either delivers a noncompact set of utility functions, or at least one f...

Multi-objective integer or mixed-integer programming problems typically have disconnected feasible domains, making the task of constructing an approximation Pareto front challenging. The present article shows that certain algorithms were originally devised for continuous can be successfully adapted to approximate integer, and mixed-integer, multi-objective problems. Relationships amongst variou...

Multi-objective optimization is known as a useful mathematical model in order to investigate some real world problems with connicting objectives, arising from economics, engineering and human decision making. In this paper, a convex composite multi-objective optimization subject to a closed convex set constraint is studied. New rst-order optimality conditions of a weakly eecient solution for th...

A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version that pro...

A procedure to approximate the nondominated set for general (continuous) bi-criteria programs is proposed. The piecewise approximation is composed of quadratic curves, each of which is developed locally in a neighborhood of a nondominated point of interest and based on primal-dual relationships associated with the weighted-Tchebycheff scalarization of the original problem. The approximating qua...

where C ⊆ Rm is a closed convex and pointed cone with nonempty interior intC. (WVVI) was firstly introduced by Giannessi []. It has been shown to have many applications in vector optimization problems and traffic equilibrium problems (e.g., [, ]). Error bounds are to depict the distance from a feasible solution to the solution set, and have played an important role not only in sensitivity an...

Abstract Scalarization is a common technique to transform multiobjective optimization problem into scalar-valued problem. This article deals with the weighted Tchebycheff scalarization applied discrete problems. consists of minimizing maximum distance image feasible solution some desirable reference point. By choosing suitable weight, any Pareto optimal can be obtained. In this article, we prov...

In this paper, we consider the multiobjective linear programs where coefficients in the objective function belong to uncertainty sets. We introduce the concept of robust efficient solutions to uncertain multiobjective linear programming problems. By using two scalarization methods, the weighted sum method and the ϵ-constraint method, we obtain that the robust efficient solutions for uncertain m...

a concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $k$...