Heuristic search to the capacitated clustering problem

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.

HA-CCP: A Hybrid Algorithm for Solving Capacitated Clustering Problem

“…CM2 performs the solution construction process up to 10 times (Algorithm 3, lines 1-3). If the feasible solution is successfully constructed, it will jump out of the loop and return to the feasible solution (Algorithm 3, lines [30][31][32][33][34].…”

“…let the binary variable X ig � 1; otherwise, X ig � 0, i � 1, 2, ..., n; g � 1, 2, ..., p. e CCP based on G can be expressed as an optimization problem [29,32]:…”

“…e experimental results in the literature [32] show that SGVNS has the best performance. We believe this is mainly due to the extension of the search to other promising areas of the solution space by adding skewed acceptance criteria.…”

“…Lai X et al [31] proposed the neighborhood decomposition-driven variable neighborhood search (NDVNS) for capacitated clustering. In addition, a Tabu search designed specifically for CCP includes the TS (denoted as FITS) and the memetic algorithm (MA) proposed in the literature [32].…”

“…Even if the upper and lower boundaries of the cluster are very tight, CM2 can successfully build a feasible solution. It can construct feasible solutions in a wider range of CCP solutions to make the algorithm run correctly and perform better than the random construction method [29,31,32]. (2) A destructive method DM3 is designed to destruct partial solutions.…”