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.

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...

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 ...

Abstract Particle swarm optimization algorithm (PSO) is suggested to discover fractional order PID (FOPID) controller optimal variables for a better performance of induction motor. This PSO designed handle multiple issues, due its ease application. A Closed Loop Quadratic Boost Converter Multilevel Inverter Fed Induction Motor (QBCMLIIM) system simulated earn reduced switching losses and THD by...

We discuss two approaches to duality for multiple objective linear problems. The first approach is based on a duality relation between a set and its complement in the outcome space. It allows us to obtain a number of known duality constructions. The second approach utilizes polarity between a polyhedral set and the epigraph of its support function. It leads to a parametric dual problem which is...

In practical applications of mathematical programming it is frequently observed that the decision maker prefers apparently suboptimal solutions. A natural explanation for this phenomenon is that the applied mathematical model was not sufficiently realistic and did not fully represent all the decision makers criteria and constraints. Since multicriteria optimization approaches are specifically d...

The application of fuzzy approach models to forecast has been drawing a lot of attention. This study proposes a fuzzy approach to forecasting using a financial data set. The methodology used is multiple objective linear programming (MOLP). Selecting an individual forecast based upon a single objective may not make the best use of available information for a variety of reasons. Combined forecast...

This paper presents an improved lower bound and an approximation algorithm based on spectral decomposition for the binary constrained quadratic programming problem. To decompose spectrally the quadratic matrix in the objective function, we construct a low rank problem that provides a lower bound. Then an approximation algorithm for the binary quadratic programming problem together with a worst ...