General variable neighbourhood search for cyclic bandwidth sum minimization problem

Abstract

In this paper we apply a general variable neighbourhood search (GVNS) to the cyclic bandwidth sum problem (CBSP). In CBSP the vertices of a graph must be laid out in a circle in such a way that the sum of the distances between pairs of vertices connected by an edge is minimized. GVNS uses different neighbourhood operations for its shaking phase and local search phase. Also the initial solution is improved using random variable neighbourhood search. Extensive experiments were carried out on classes of graphs with known results for which optimal values of cyclic bandwidth sum was achieved. On other classes of graphs, values less than known upper bounds were achieved. Index Terms--Cyclic bandwidth sum minimization problem, graph layout problem, variable neighbourhood search

Dynamic Multi-Armed Bandit Algorithm for the Cyclic Bandwidth Sum Problem

“…Although in a general sense the MA versions improved the results of previous works such as MACH [18] and GVNS [17], they had problems to reach the known optimal Cbs value for some instances, particularly those of the path, cycle, and wheel topologies. It was intuited in [15] that premature convergence was responsible for this behaviour, due to an excessive selective pressure introduced by the (µ + λ) survival strategy.…”

“…Only recently the CBSP has received more attention in the optimization and operation research communities where the following approaches have been proposed: a local search based approach [17], a constructive greedy heuristic [18], hybrid metaheuristic algorithms [15], and a reformulation of the evaluation function [19].…”

“…The first metaheuristic approach based in local search was a General Variable Neighborhood Search (GVNS) [17]. This algorithm starts from a lexicographical embedding which is improved using a Reduced Variable Neighborhood Search (RVNS).…”

“…The instances set includes 40 representative, topologically diverse graphs that have been often used in the GEP or CBSP literature [17]- [19]. The set includes 6 Cartesian products of graphs, 24 sparse matrices from the Harwell-Boeing collection, 2 paths, 2 cycles, 2 wheels, and 4 k-th powers of cycle (k ∈ {2, 10}).…”

“…For each instance being solved by a particular algorithm, we computed the relative root mean square error (RMSE) for 31 independent executions. The tested algorithms included our MA versions, as well as GVNS [17] and MACH [18]. The RMSE metric for a certain test instance t is defined as:…”