Advancing local search approximations for multiobjective combinatorial optimization problems

Lakmali Weerasena ()
Additional contact information
Lakmali Weerasena: University of Tennessee at Chattanooga

Journal of Combinatorial Optimization, 2022, vol. 43, issue 3, No 5, 589-612

Abstract: Abstract This study proposes a theoretical framework for defining approximations of the Pareto sets of multiobjective combinatorial optimization (MOCO) problems. The concept of t-representation is proposed for modeling the approximation quality and describes a local search algorithm to produce a t-representation. Unlike the current local search algorithms found in the literature, the proposed algorithm yields a representation for the Pareto set with a mathematically proven error term (quality). The algorithm starts with an initial representation containing efficient solutions. The approximation quality is derived mathematically and is measured using a tolerance function that depends on the cost coefficients of the problem and the initial representation. The computational experiments are conducted using two types of MOCO problems (multiobjective set covering problem and multiobjective knapsack problem). The computational results demonstrate that this algorithm significantly outperforms the initial representation, obeys the theoretical bounds, and efficiently solves MOCO problems.

Keywords: Approximation algorithm; Combinatorial optimization; t-representation; Local search; Tolerance function (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10878-021-00795-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:jcomop:v:43:y:2022:i:3:d:10.1007_s10878-021-00795-1

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10878

DOI: 10.1007/s10878-021-00795-1

Access Statistics for this article

Journal of Combinatorial Optimization is currently edited by Thai, My T.

More articles in Journal of Combinatorial Optimization from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().