An Iterated Tabu Search Approach for the Clique Partitioning Problem

Abstract

Given an edge-weighted undirected graph with weights specifying dissimilarities between pairs of objects, represented by the vertices of the graph, the clique partitioning problem (CPP) is to partition the vertex set of the graph into mutually disjoint subsets such that the sum of the edge weights over all cliques induced by the subsets is as small as possible. We develop an iterated tabu search (ITS) algorithm for solving this problem. The proposed algorithm incorporates tabu search, local search, and solution perturbation procedures. We report computational results on CPP instances of size up to 2000 vertices. Performance comparisons of ITS against state-of-the-art methods from the literature demonstrate the competitiveness of our approach.

A three-phased local search approach for the clique partitioning problem

“…In previous studies on CPP like [4,6,8,28], selecting an appropriate move (u, G t ) requires the evaluation of all feasible neighboring solutions, i.e., by considering all reallocations of each vertex to each group including the empty one. Let s ⊕ move(u, G t ) designate the neighboring solution s obtained by applying move(u, G t ) to s, then this complete neighborhood N (s) is defined by:…”

“…We now discuss the major differences between CPP-P 3 and other local search algorithms for CPP. ITS [28] may be the closest approach for solving CPP as it also integrates a descent search, a tabu search and a perturbation procedure. However, there are three main differences between the two algorithms.…”

“…Different from previous local search algorithms, CPP-P 3 introduces a constrained Top Move neighborhood to make the search more focused and calls for a heap data structure to ensure a fast neighborhood examination. Computational experiments on four groups of graph instances (from 100 to 2000 vertices) show that CPP-P 3 competes favorably with the current best performing algorithms (including ITS [28] and SGVNS [3]) both in terms of solution quality and computational efficiency. We also carry out additional analysis to gain insights about the behavior of the proposed algorithm.…”

“…In [5,6], authors proposed a noising method which adds decreasing levels of noise to neighbor evaluations. More recently, two heuristic algorithms [28,3] were presented. The work of [28] focuses on an iterated tabu search with tuned parameters.…”

“…More recently, two heuristic algorithms [28,3] were presented. The work of [28] focuses on an iterated tabu search with tuned parameters. The approach of [3] uses a generalized VNS algorithm designed for the Maximally Diverse Grouping Problem to solve CPP.…”