An Algorithmic Package for the Resolution and Analysis of Convex Multiple Objective Problems

  • Rafael Caballero
  • Lourdes Rey
  • Francisco Ruiz
  • Mercedes González
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 448)

Abstract

The aim of this paper is to describe an algorithmic package which allows us to cany out a complete treatment of a general multiple objective convex problem. It includes the generalisation of many of the algorithms used in the linear case, as well as some others developed specially for our problem. This treatment can be divided into two main blocks:
  • Generation of efficient solutions: both the weighting and the constraint method are developed, through an automatic generation of weights in the former, and of bounds in the latter.

  • Goal Programming: We include two versions of the traditional lexicographic algorithms, adapted to the convex case under study, and we also allow the possibility to generate the set of solutions which are satisfying and efficient at the same time. Finally, we also cany out a post-optimal analysis on the target values, so as to find whether they can be improved or not. This analysis, which takes the form of an interactive method, can even lead to an efficient, as well as satisfying, solution for the original problem.

Some computational results are presented, which show the behaviour of the algorithms, in terms of C.P.U. time, on some test problems with different number of variables and constraints. These algorithms have been implemented in FORTRAN language, on a VAX 8530 computer, and with the aid of the NAG subroutine library, mark 15.

Keywords

Assure 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Rafael Caballero
    • 1
  • Lourdes Rey
    • 1
  • Francisco Ruiz
    • 1
  • Mercedes González
    • 1
  1. 1.Departamento de Economía Aplicada (Matemáticas)Facultad de Ciencias Económicas y EmpresarialesMálagaSpain

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