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Outcome-Based Branch and Bound Algorithm for Optimization over the Efficient Set and Its Application

  • Tran Ngoc ThangEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 341)

Abstract

The problem of optimizing a real function over the efficient set of a multiple objective programming problem arises in a variety of applications. Because of its interesting mathematical aspects as well as its wide range of applications, this problem has attracted the attention of many authors. In this article, we propose a branch and bound algorithm in outcome space for minimizing a function \(h(x)=\varphi (f(x))\) over the efficient set \(X_{E}\) of the bi-criteria convex programming problem \(\mathrm{{Vmin}}\{f(x)=(f_{1}(x),f_{2}(x))^{T}|x\in X\}\), where the function \(\varphi \) is a quasi-concave function defined on \(f(X)\). The convergence of the algorithm is established. Preliminary computational results are reported.

Keywords

Global optimization Optimization over the efficient set Outcome set Bicriteria convex programming Branch and bound 

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.School of Applied Mathematics and InformaticsHanoi University of Science and TechnologyHai Ba TrungVietnam

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