A filter-and-fan algorithm for the capacitated minimum spanning tree problem

Authors:
César Rego;Frank Mathew
Affiliations:
School of Business Administration, University of Mississippi, University, MS 38677, USA;School of Business Administration, University of Mississippi, University, MS 38677, USA
Venue:
Computers and Industrial Engineering
Year:
2011

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Abstract

The capacitated minimum spanning tree (CMST) is a notoriously difficult problem in combinatorial optimization. Extensive investigation has been devoted to developing efficient algorithms to find optimal or near-optimal solutions. This paper proposes a new CMST heuristic algorithm that effectively combines the classical node-based and tree-based neighborhoods embodied in a filter-and-fan (F&F) approach, a local search procedure that generates compound moves in a tree search fashion. The overall algorithm is guided by a multi-level oscillation strategy used to trigger each type of neighborhood while allowing the search to cross feasibility boundaries. Computational results carried out on a standard set of 135 benchmark problems show that a simple F&F design competes effectively with prior CMST metaheuristics, rivaling the best methods, which are significantly more complex.