A Convergent Interactive Cutting-Plane Algorithm for Multiobjective Optimization

G. V. Loganathan and Hanif D. Sherali
Additional contact information
G. V. Loganathan: Virginia Polytechnical Institute and State University, Blacksburg, Virginia
Hanif D. Sherali: Virginia Polytechnical Institute and State University, Blacksburg, Virginia

Operations Research, 1987, vol. 35, issue 3, 365-377

Abstract: This paper presents an interactive cutting-plane algorithm for determining a best-compromise solution to a multiobjective optimization problem in situations with an implicitly defined utility function. We derive cutting planes that are based on suitable pairwise trade-offs between the objective functions, as prescribed by the decision maker at each iterate generated by the algorithm. The proposed algorithm requires no line searches, and generates iterates that are all contained in the efficient frontier. This feature facilitates the preference judgment of the decision maker, and permits an analyst to terminate short of optimality with an efficient near-optimal solution. A convergence analysis establishes that any accumulation point generated by the algorithm is a best-compromise solution. We also conduct an error analysis to point out the effect of inconsistencies in trade-off information provided by the decision maker. The algorithm may be extended to situations involving nonconvex feasible regions, as well as nonconcave (for a max problem) objective functions. We offer remarks for such cases, and describe an application to an urban runoff control-design problem.

Keywords: 651 multiobjective optimization; 654 cutting plane algorithm (search for similar items in EconPapers)
Date: 1987
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.35.3.365 (application/pdf)

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:inm:oropre:v:35:y:1987:i:3:p:365-377

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().