Abstract
Given a weighted graph, the capacitated clustering problem (CCP) is to partition a set of nodes into a given number of distinct clusters (or groups) with restricted capacities, while maximizing the sum of edge weights corresponding to two nodes from the same cluster. CCP is an NP-hard problem with many relevant applications. This paper proposes two effective algorithms for CCP: a Tabu Search (denoted as FITS) that alternates between exploration in feasible and infeasible search space regions, and a Memetic Algorithm (MA) that combines FITS with a dedicated cluster-based crossover. Extensive computational results on five sets of 183 benchmark instances from the literature indicate that the proposed FITS competes favorably with the state-of-the-art algorithms. Additionally, an experimental comparison between FITS and MA under an extended time limit demonstrates that further improvements in terms of the solution quality can be achieved with MA in most cases. We also analyze several essential components of the proposed algorithms to understand their importance to the success of these approaches.
Highlights
Given a weighted graph G = (V, E) where V is a set of n nodes and E is a set of edges, let wi ≥ 0 be the weight of node i ∈ V and let cij ({i, j} ∈ E) be the edge weight between nodes i and j
To evaluate the quality of a solution s ∈ Ω during Infeasible Local Search (InfLS), we employ a penaltybased evaluation function fp which is a linear combination of the basic eval10
While a number of existing heuristics for Capacitated Clustering Problem (CCP) including Tabu Search method (TS) [29], Iterated Variable Neighborhood Search (IVNS) [24], GVNS [7] and SGVNS [7] restrict their search to the feasible regions only, a key feature of FITS and several other heuristics like Greedy Randomized Adaptive Search Procedure (GRASP)-PR [10], Tabu Search with Strategic Oscillation (TS SO) [6], GevPR-Handover Minimization Problem (HMP) [31] and GQAP [31] is the consideration of infeasible solutions
Summary
In 2013, Moran-Mirabal et al [31] proposed three algorithms for the equivalent handover minimization problem: a GRASP with path-relinking (denoted as GQAP in the corresponding paper), a GRASP with evolutionary path-relinking (GevPR-HMP) and a population-based biased random-key genetic algorithm (BRKGA). According to their computational results, GevPRHMP exhibits the best performance among those three algorithms. We motivate the choice for the crossover used by MA, prior to conclusions drawn in the last section
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