Abstract
We describe an algorithm for solving the equicut problem on complete graphs. The core of the algorithm is a cutting-plane procedure that exploits a subset of the linear inequalities defining the convex hull of the incidence vectors of the edge sets that define an equicut. The cuts are generated by several separation procedures that will be described in the paper. Whenever the cutting-plane procedure does not terminate with an optimal solution, the algorithm uses a branch-and-cut strategy. We also describe the implementation of the algorithm and the interface with the LP solver. Finally, we report on computational results on dense instances with sizes up to 100 nodes.
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References
F. Barahona and A.R. Mahjoub, On the cut polytope,Mathematical Programming 36 (1986) 157–173.
F. Barahona, M. Grötschel, M. Jünger and G. Reinelt, An application of combinatorial optimization to statistical physics and circuit layout design,Operations Research 36 (1988) 493–513.
M. Conforti, M.R. Rao and A. Sassano, The equipartition polytope I: Formulations, dimension and basic facets,Mathematical Programming 49 (1990) 49–70.
M. Conforti, M.R. Rao and A. Sassano, The equipartition polytope II: Valid inequalities and facets,Mathematical Programming 49 (1990) 71–90.
CPLEX, Using the CPLEX Callable Library and CPLEX Mixed Integer Library, CPLEX Optimization Inc. (1992).
C. De Simone and G. Rinaldi, A cutting-plane algorithm for the max-cut problem,Optimization Methods and Software 3 (1994) 195–214.
C.C. De Souza and M. Laurent, Some new classes of facets for the equicut polytope, Working Paper, CORE (Louvain-la-Neuve, 1991).
J. Edmonds and E.L. Johnson, Matching: A well solved class of integer linear programs, in: R. Guy, ed.,Combinatorial Structures and Their Applications (Gordon and Breach, New York, 1970) 89–92.
A.V. Goldberg and R.E. Tarjan, A new approach to the maximum flow problem,Journal of ACM 35 (1988) 921–940.
D. Gusfield, Very simple algorithms and programs for all pairs network flow analysis, Research Report, University of California (Davis, California, 1987).
T.C. Hu, Multiterminal maximal flows, in: T.C. Hu,Integer Programming And Network Flows (Addison-Wesley, Reading, MA, 1969) 129–142.
B.W. Kernighan and S. Lin, An efficient heuristic procedure for partitioning graphs,Bell Systems Technical Journal 49 (1970) 291–307.
M. Padberg and G. Rinaldi, Optimization of a 532-city symmetric traveling salesman problems,Operations Research Letters 6 (1987) 1–7.
M. Padberg and G. Rinaldi, Facet identification for the symmetric traveling salesman polytope,Mathematical Programming 47 (1990) 219–258.
M. Padberg and G. Rinaldi, A branch-and-cut algorithm for the resolution of large-scale symmetric traveling salesman problems,SIAM Review 33 (1991) 1–41.
M. Padberg and M.R. Rao, Odd minimum cut-set andb-matchings,Mathematics of Operation Research 7 (1982) 67–80.
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Brunetta, L., Conforti, M. & Rinaldi, G. A branch-and-cut algorithm for the equicut problem. Mathematical Programming 78, 243–263 (1997). https://doi.org/10.1007/BF02614373
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DOI: https://doi.org/10.1007/BF02614373