RAMP for the capacitated minimum spanning tree problem

Abstract

This paper introduces dual and primal-dual RAMP algorithms for the solution of the capacitated minimum spanning tree problem (CMST). A surrogate constraint relaxation incorporating cutting planes is proposed to explore the dual solution space. In the dual RAMP approach, primal-feasible solutions are obtained by simple tabu searches that project dual solutions onto primal feasible space. A primal-dual approach is achieved by including a scatter search procedure that further exploits the adaptive memory framework. Computational results from applying the methods to a standard set of benchmark problems disclose that the dual RAMP algorithm finds high quality solutions very efficiently and that its primal-dual enhancement is still more effective.

On an effective approach for the coach trip with shuttle service problem of the VeRoLog solver challenge 2015

“…In a wider context, similar problem structures are found in capacitated shortest spanning tree problems and variants . We believe that such more general formulations may serve as an inspiration for the introduction of appropriate data structures for the CTSSP.…”

A biased random-key genetic algorithm for the capacitated minimum spanning tree problem

“…We close this section by comparing our results with those produced by other heuristics. For this comparison we chose: (i) the VLNS heuristic of Ahuja et al (2003) which, in our opinion, is the heuristic which has produced the best results, (ii) the ant colony heuristic (ACO) of Reimann and Laumanns (2006), (iii) the enhanced second-order algorithm (ESO) of Martins (2007), and (iv) the RAMP heuristic of Rego et al (2010). Tables 6 and 8 summarize the results of the compared methods, taken from the original papers.…”

“…This explains why heuristic methods, based on the greedy paradigm (Esau and Williams, 1966;Chow and Kershenbaum, 1974;Gavish and Altinkemer, 1986), neighborhood exploration (Amberg et al, 1996;Sharaiha et al, 1997;Ahuja et al, 2001;Souza et al, 2003), or dynamic programming (Gouveia and Paixão, 1991), have been widely used. More recent heuristics include the second-order algorithm of Martins (2007), in which subproblems of the original problem including a set of constraints are solved with the Essau Williams heuristic, the heuristic of Rego et al (2010), which projects dual solutions into the primal feasible space and obtains primal feasible solutions by simple tabu searches and metaheuristics such as the ant colony algorithm by Reimann and Laumanns (2006) or the filter-and-fan algorithm by Rego and Mathew (2011).…”

On a New Constraint Reduction Heuristic Using Improved Bisection Method for Mixed Integer Linear Programming

“…Choi and Choi [7] proposed a redundancy identification method that is based on surrogate constraints. The relaxation adaptive memory programming approach based on surrogate constraints was proposed for combinatorial optimization problems in [44] and for capacitated minimum spanning tree problems in [45]. To review the scatter search method which was conceived as an extension of surrogate constraint relaxation, see [34].…”