In this paper Standard Error of Mean (SEM), as a new technique, is used for transforming multi-objective linear programming problems (MOLPPs) to the single objective (SOLPPs). To end, an algorithm has been proposed and suggested solve MOLPPs, which have tested through numerical examples by employing Excel Solver. However, study compares results other techniques like (Chandra Sen, Optimal Averag...

The aim of our paper is to obtain efficient solutions the interval multi-objective linear programming (IMOLP) models. In this paper, we propose a new method determine in IMOLP models by using expected value and variance operators (EVV operators). First, define concepts value, variance, uncertainty distributions, present some properties EVV operators. Then, introduce model under these An consist...

A Geometric programming (GP) is a type of mathematical problem characterized by objective and constraint functions that have a special form. Many methods have been developed to solve large scale engineering design GP problems. In this paper GP technique has been used to solve multi-objective GP problem as a vector optimization problem. The duality theory for lexicographic geometric programming ...

We develop in this article a geometric approach to duality in Multiple Objective Linear Programming. This approach is based on a very old idea, the duality of polytopes, which can be traced back to the old Greeks. We show that there is an inclusion reversing one-to-one map between the minimal faces of the image of the primal objective and the maximal faces of the image of the dual objective map.

Quadratic Programming (QP) is the well-studied problem of maximizing over {−1, 1} values the quadratic form ∑ i6=j aijxixj . QP captures many known combinatorial optimization problems, and assuming the unique games conjecture, semidefinite programming techniques give optimal approximation algorithms. We extend this body of work by initiating the study of Quadratic Programming problems where the...

In multiple objective programs [MOP], application functions are established to measure the degree of fulfillment of the decision maker’s requirements (achievement of goals, nearness to an ideal point, satisfaction, etc.) about the objective functions (see e.g. [7, 24]) and are extensively used in the process of finding ”good compromise” solutions. In [6] we demonstrated that the use of interdep...

Visual analytics is a human-machine collaboration to data modeling where extraction of the most informative features plays an important role. Although feature extraction is a multi-objective task, the traditional algorithms either only consider one objective or aggregate the objectives into one scalar criterion to optimize. In this paper, we propose a Pareto-based multi-objective approach to fe...

Within the past ten years, more emphasis has been placed on generating discrete representations of the nondominated set which are truly representative of the nondominated set as a whole. This paper reviews measures for assessing the quality of discrete representations as well as exact solution methods that attempt to produce representations satisfying certain quality criteria. The measures are ...