This paper defines a new Moth-Flame optimization version withQuantum behaved moths, QMFO. The multi-objective version of QMFO (MOQMFO) is then applied to solve clustering problems. MOQMFO used three cluster validity criteria as objective functions (the I-index, Con-index and Sym-index) to establish the multi-objective clustering optimization. This paper details the proposal and the preliminary obtained results for clustering real-life datasets (including Iris, Cancer, Newthyroid, Wine, LiverDisorder and Glass) and artificial datasets (including Sph_5_2, Sph_4_3, Sph_6_2, Sph_10_2, Sph_9_2, Pat 1, Pat 2, Long 1, Sizes 5, Spiral, Square 1, Square 4, Twenty and Fourty). Compared with key multi-objectives clustering techniques, the proposal showed interesting results essentially for Iris, Newthyroid, Wine, LiverDisorder, Sph_4_3, Sph_6_2, Long 1, Sizes 5, Twenty and Fourty; and was able to provide the exact number of clusters for all datasets.

In this paper a new technique is integrated to Multi-Objective Particle Swarm Optimization (MOPSO) algorithm, named Pareto Neighborhood (PN) topology, to produce MOPSO-PN algorithm. This technique involves iteratively selecting a set of best solutions from the Pareto-Optimal-Fronts and trying to explore them in order to find better clustering results in the next iteration. MOPSO-PN was then used as a Multi?Objective Clustering Optimization (MOCO) Algorithm, it was tested on various datasets (real-life and artificial datasets). Two scenarios have been used to test the performances of MOPSO-PN for clustering: In the first scenario MOPSO-PN utilizes, as objective functions, two clusters validity index (Silhouette?Index and overall-cluster-deviation), three datasets for test, four algorithms for comparison and the average Minkowski Score as metric for evaluating the final clustering result; In the second scenario MOPSO-PN used, as objectives functions, three clusters validity index (I-index, Con-index and Sym?index), 20 datasets for test, ten algorithms for comparison and the F-Measure as metric for evaluating the final clustering result. In both scenarios, MOPSO-PN provided a competitive clustering results and a correct number of clusters for all datasets.