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Measuring consistency and inconsistency of pair comparison systems

Jaroslav Ramík, Milan Vlach (2013)

Kybernetika

In this paper we deal with mathematical modeling of real processes that are based on preference relations in the sense that, for every pair of distinct alternatives, the processes are linked to a value of preference degree of one alternative over the other one. The use of preference relations is usual in decision making, psychology, economics, knowledge acquisition techniques for knowledge-based systems, social choice and many other social sciences. For designing useful mathematical models of such...

MEMOTS: a memetic algorithm integrating tabu search for combinatorial multiobjective optimization

Thibaut Lust, Jacques Teghem (2008)

RAIRO - Operations Research

We present in this paper a new multiobjective memetic algorithm scheme called MEMOX. In current multiobjective memetic algorithms, the parents used for recombination are randomly selected. We improve this approach by using a dynamic hypergrid which allows to select a parent located in a region of minimal density. The second parent selected is a solution close, in the objective space, to the first parent. A local search is then applied to the offspring. We experiment this scheme with a new multiobjective...

Multi-attribute evaluation with imprecise vector utility

Sixto Ríos-Insua, Alfonso Mateos (1996)

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales

We consider the multi-attribute decision making problem with incomplete information on the decision maker's preferences, given by an imprecise vector utility function. We introduce an approximation set to the utility efficient set which may be used to aid a decision maker in reaching a final compromise strategy. We provide sorne properties and an interactive procedure based on such approximation set.

Multicriteria scheduling problems : a survey

V. T'kindt, J.-C. Billaut (2001)

RAIRO - Operations Research - Recherche Opérationnelle

This paper presents a state-of-the-art survey on multicriteria scheduling and introduces a definition of a multicriteria scheduling problem. It provides a framework that allows to tackle multicriteria scheduling problems, according to Decision Aid concepts. This problem is decomposed into three different problems. The first problem is about obtaining a model. The second one is how to take criteria into account and the third one is about solving a scheduling problem. An extension to an existing notation...

Multicriteria scheduling problems: a survey

V. T'kindt, J.-C. Billaut (2010)

RAIRO - Operations Research

This paper presents a state-of-the-art survey on multicriteria scheduling and introduces a definition of a multicriteria scheduling problem. It provides a framework that allows to tackle multicriteria scheduling problems, according to Decision Aid concepts. This problem is decomposed into three different problems. The first problem is about obtaining a model. The second one is how to take criteria into account and the third one is about solving a scheduling problem. An extension to an existing...

Multiobjective De Novo Linear Programming

Petr Fiala (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Mathematical programming under multiple objectives has emerged as a powerful tool to assist in the process of searching for decisions which best satisfy a multitude of conflicting objectives. In multiobjective linear programming problems it is usually impossible to optimize all objectives in a given system. Trade-offs are properties of inadequately designed system a thus can be eliminated through designing better one. Multiobjective De Novo linear programming is problem for designing optimal system...

Multi-objective geometric programming problem with Karush−Kuhn−Tucker condition using ϵ-constraint method

A. K. Ojha, Rashmi Ranjan Ota (2014)

RAIRO - Operations Research - Recherche Opérationnelle

Optimization is an important tool widely used in formulation of the mathematical model and design of various decision making problems related to the science and engineering. Generally, the real world problems are occurring in the form of multi-criteria and multi-choice with certain constraints. There is no such single optimal solution exist which could optimize all the objective functions simultaneously. In this paper, ϵ-constraint method along with Karush−Kuhn−Tucker (KKT) condition has been used...

Multi-objective Optimization Problem with Bounded Parameters

Ajay Kumar Bhurjee, Geetanjali Panda (2014)

RAIRO - Operations Research - Recherche Opérationnelle

In this paper, we propose a nonlinear multi-objective optimization problem whose parameters in the objective functions and constraints vary in between some lower and upper bounds. Existence of the efficient solution of this model is studied and gradient based as well as gradient free optimality conditions are derived. The theoretical developments are illustrated through numerical examples.

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