author = "Chagas, Guilherme Oliveira and Lorena, Luiz Antonio Nogueira and 
                         Santos, Rafael Duarte Coelho dos",
          affiliation = "{Instituto Nacional de Pesquisas Espaciais (INPE)} and {Instituto 
                         Nacional de Pesquisas Espaciais (INPE)} and {Instituto Nacional de 
                         Pesquisas Espaciais (INPE)}",
                title = "A hybrid heuristic for the overlapping cluster editing problem",
              journal = "Applied Soft Computing",
                 year = "2019",
               volume = "81",
                pages = "105482",
             keywords = "Overlapping cluster editing, Cluster editing, Overlapping 
                         clustering, Hybrid heuristic.",
             abstract = "Clustering problems are applicable to several areas of science. 
                         Approaches and algorithms are as varied as the applications. From 
                         a graph theory perspective, clustering can be generated by 
                         partitioning an input graph into a vertex-disjoint union of 
                         cliques (clusters) through addition and deletion of edges. Finding 
                         the minimum number of edges additions and deletions required to 
                         cluster data that can be represented as graphs is a well-known 
                         problem in combinatorial optimization, often referred to as 
                         cluster editing problem. However, many real-world clustering 
                         applications are characterized by overlapping clusters, that is, 
                         clusters that are non-disjoint. In these situations cluster 
                         editing cannot be applied to these problems. Literature concerning 
                         a relaxation of the cluster editing, where clusters can overlap, 
                         is scarce. In this work, we propose the overlapping cluster 
                         editing problem, a variation of the cluster editing where the goal 
                         is to partition a graph, also by editing edges, into maximal 
                         cliques that are not necessarily disjoint. In addition, we also 
                         present three slightly different versions of a hybrid heuristic to 
                         solve this problem. Each hybrid heuristic is based on coupling two 
                         metaheuristicsthat, together, generate a set of clusters; and one 
                         of three mixed-integer linear programming models, also introduced 
                         in this paper, that uses these clusters as input. The objective 
                         with the metaheuristics is to limit the solution exploration space 
                         in the models resolution, therefore reducing its computational 
                         time. Tests results show that the all proposed hybrid heuristic 
                         versions are able to generate good-quality overlapping cluster 
                         editing solutions. In particular, one version of the hybrid 
                         heuristic achieved, at a low computational cost, the best results 
                         in 51 of 112 randomly-generated graphs. Although the other two 
                         hybrid heuristic versions have harder to solve models, they 
                         obtained reasonable results in medium-sized randomly-generated 
                         graphs. In addition, the hybrid heuristic achieved good results 
                         identifying labeled overlapping clusters in a supervised data set 
                         experiment. Furthermore, we also show that, with our new problem 
                         definition, clustering a vertex in more than one cluster can 
                         reduce the edges editing cost.",
                  doi = "10.1016/j.asoc.2019.105482",
                  url = "http://dx.doi.org/10.1016/j.asoc.2019.105482",
                 issn = "1568-4946",
                label = "lattes: 0096913881679975 3 ChagasLoreSant:2019:HyHeOv",
             language = "en",
           targetfile = "1-s2.0-S1568494619302522-main.pdf",
        urlaccessdate = "15 abr. 2021"