Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning

Lizhen Shao () and Matthias Ehrgott ()

Mathematical Methods of Operations Research, 2008, vol. 68, issue 2, 257-276

Abstract: In this paper, we propose a modification of Benson’s algorithm for solving multiobjective linear programmes in objective space in order to approximate the true nondominated set. We first summarize Benson’s original algorithm and propose some small changes to improve computational performance. We then introduce our approximation version of the algorithm, which computes an inner and an outer approximation of the nondominated set. We prove that the inner approximation provides a set of $${\varepsilon}$$ -nondominated points. This work is motivated by an application, the beam intensity optimization problem of radiotherapy treatment planning. This problem can be formulated as a multiobjective linear programme with three objectives. The constraint matrix of the problem relies on the calculation of dose deposited in tissue. Since this calculation is always imprecise solving the MOLP exactly is not necessary in practice. With our algorithm we solve the problem approximately within a specified accuracy in objective space. We present results on four clinical cancer cases that clearly illustrate the advantages of our method. Copyright Springer-Verlag 2008

Keywords: Multiobjective linear programming; Radiotherapy treatment planning; $${\varepsilon}$$ -efficient solution (search for similar items in EconPapers)
Date: 2008
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (22)

Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-008-0220-2 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:mathme:v:68:y:2008:i:2:p:257-276

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s00186-008-0220-2

Access Statistics for this article

Mathematical Methods of Operations Research is currently edited by Oliver Stein

More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().