MAPLE code of the cubic algorithm for multiobjective optimization with box constraints

M. Delgado Pineda; E. A. Galperin; P. Jiménez Guerra

doi:10.3934/naco.2013.3.407

Article Contents

2013, Volume 3, Issue 3: 407-424. Doi: 10.3934/naco.2013.3.407

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MAPLE code of the cubic algorithm for multiobjective optimization with box constraints

1.
Departamento de Matemáticas Fundamentales, Facultad de Ciencias, Universidad Nacional de Educación a Distancia, UNED, c/ Senda del Rey 9, C.P. 28040 Madrid
2.
Département de mathématiques, Université du Québec à Montréal, C.P. 8888, Succ. Centre Ville, Montréal, Québec H3C 3P8

Received: November 30, 2011

Revised: January 31, 2013

Published: June 2013

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Abstract

A generalization of the cubic algorithm is presented for global optimization of nonconvex nonsmooth multiobjective optimization programs $\min f_{s}(x),\ s=1,\dots,k,$ with box constraints $x\in X=[a_{1},b_{1}]\times \dots\times\lbrack a_{n},b_{n}]$.
This monotonic set contraction algorithm converges onto the entire exact Pareto set, if nonempty, and yields its approximation with given precision in a finite number of iterations. Simultaneously, approximations for the ideal point and for the function values over Pareto set are obtained. The method is implemented by Maple code, and this code does not create ill-conditioned situations.
Results of numerical experiments are presented, with graphs, to illustrate the use of the code, and the solution set can be visualized in projections on coordinate planes. The code is ready for engineering and economic applications.

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Mathematics Subject Classification: Primary: 90C26; Secondary: 58E17.

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References

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