A note on heuristic approach based on UBQP formulation of the maximum diversity problem

The maximum diversity problem (MDP) is a challenging NP-hard problem with a wide range of real applications. Several researchers have pointed out close relationship between the MDP and unconstrained binary quadratic program (UBQP). In this paper, we provide procedures to solve MDP ideas from the UBQ...

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Bibliographic Details
Published in:The Journal of the Operational Research Society Vol. 68; no. 1; pp. 102 - 110
Main Authors: Alidaee, Bahram, Wang, Haibo
Format: Journal Article
Language:English
Published: London Taylor & Francis 01.01.2017
Taylor & Francis, Ltd
Palgrave Macmillan UK
Taylor & Francis Ltd
Subjects:
Business and Management
combinatorial optimization problem
diversification strategy
Heuristic methods
Management
maximum diversity problem
Operations Research/Decision Theory
r-flip local search
Tabu search
unconstrained binary quadratic programming
maximum diversity problem
diversification strategy
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local search
combinatorial optimization problem
unconstrained binary quadratic programming
ISSN:0160-5682, 1476-9360
Online Access:Get full text
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Summary:The maximum diversity problem (MDP) is a challenging NP-hard problem with a wide range of real applications. Several researchers have pointed out close relationship between the MDP and unconstrained binary quadratic program (UBQP). In this paper, we provide procedures to solve MDP ideas from the UBQP formulation of the problem. We first give some local optimality results for r-flip improvement procedures on MDP. Then, a set of highly effective diversification approaches based on sequential improvement steps for MDP are presented. Four versions of the approaches are used within a simple tabu search and applied to 140 benchmark MDP problems available on the Internet. The procedures solve all 80 small- to medium-sized problems instantly to the best known solutions. For 22 of the 60 large problems, the procedures improved by significant amounts the best known solutions in reasonably short CPU time.
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ISSN:0160-5682
1476-9360
DOI:10.1057/s41274-016-0031-4