Greedy and Local Search Heuristics for Unconstrained Binary Quadratic Programming

In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP). These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms. Th...

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Bibliographic Details
Published in:Journal of heuristics Vol. 8; no. 2; pp. 197 - 213
Main Authors: Merz, Peter, Freisleben, Bernd
Format: Journal Article
Language:English
Published: Boston Springer Nature B.V 01.03.2002
Subjects:
Algorithms
Boolean
Capital budgeting
Genetic algorithms
Heuristic
Mathematical programming
Neighborhoods
Optimization
Quadratic programming
Searches
Studies
ISSN:1381-1231, 1572-9397
Online Access:Get full text
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Summary:In this paper, a greedy heuristic and two local search algorithms, 1-opt local search and k-opt local search, are proposed for the unconstrained binary quadratic programming problem (BQP). These heuristics are well suited for the incorporation into meta-heuristics such as evolutionary algorithms. Their performance is compared for 115 problem instances. All methods are capable of producing high quality solutions in short time. In particular, the greedy heuristic is able to find near optimum solutions a few percent below the best-known solutions, and the local search procedures are sufficient to find the best-known solutions of all problem instances with n < or = 100. The k-opt local searches even find the best-known solutions for all problems of size n < or = 250 and for 11 out of 15 instances of size n = 500 in all runs. For larger problems (n = 500, 1000, 2500), the heuristics appear to be capable of finding near optimum solutions quickly. Therefore, the proposed heuristics--especially the k-opt local search--offer a great potential for the incorporation in more sophisticated meta-heuristics. [PUBLICATION ABSTRACT]
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ISSN:1381-1231
1572-9397
DOI:10.1023/A:1017912624016