Evolutionary multi-objective optimisation (EMO) boasts a proliferation algorithms and benchmark problems. principled compare performance of different EMO algorithms, is plicated the result EMO a single scalar value, a collection of vectors forming a non-dominated Various metrics non-dominated suggested. compare several, using framework of `outperformance relations' (Hansen Jaszkiewicz [4]). This enables criticise contrast a variety of published metrics, leading some recommendations which useful practice.

Many modern multiobjective evolutionary algorithms (MOEAs) store the points discovered during optimization in an external archive, separate from the main population, as a source of innovation and/or for presentation at the end of a run. Maintaining a bound on the size of the archive may be desirable or necessary for several reasons, but choosing which points to discard and which to keep in the archive, as they are discovered, is not trivial. In this paper we briefly review the state-of-the-art in bounded archiving, and present a new method based on locally maximizing the hypervolume dominated by the archive. The new archiver is shown to outperform existing methods, on several problem instances, with respect to the quality of the archive obtained when judged using three distinct quality measures.

Clustering is a core problem in data-mining with innumerable applications spanning many fields. A key di#culty of e#ective clustering is that for unlabelled data a `good' solution is a somewhat ill-defined concept, and hence a plethora of valid measures of cluster quality have been devised. Most clustering algorithms optimize just one such objective (often implicitly) and are thus limited in their scope of application. In this paper, we investigate whether an EA optimizing a number of di#erent clustering quality measures simultaneously can find better solutions. Using problems where the correct classes are known, our results show a clear advantage to the multiobjective approach: it exhibits a far more robust level of performance than the classic k-means and average-link agglomerative clustering algorithms over a diverse suite of 15 real and synthetic data sets, sometimes outperforming them substantially.

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Abstract- In previous work, we have introduced a novel and highly effective approach to data clustering, based on the explicit optimization of a partitioning with respect to two complementary clustering objectives [4, 5, 6]. In this paper, we make three modifications to the algorithm that improve its scalability to large data sets with high dimensionality and large numbers of clusters. Specifically, we introduce new initialization and mutation schemes that enable a more efficient exploration of the search space, and modify the null data model that is used as a basis for selecting the most significant solution from the Pareto front. The high performance of the resulting algorithm is demonstrated on a newly developed clustering test suite. 1

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Abstract- The large majority of existing clustering algorithms are centered around the notion of a feature, that is, individual data items are represented by their intrinsic properties, which are summarized by (usually numeric) feature vectors. However, certain applications require the clustering of data items that are defined by exclusively extrinsic properties: only the relationships between individual data items are known (that is, their similarities or dissimilarities). This paper develops a straightforward and efficient adaptation of our existing multiobjective clustering algorithm to such a scenario. The resulting algorithm is demonstrated on a range of data sets, including a dissimilarity matrix derived from real, non-feature-based data. 1 Similarity-based pattern recognition

Abstract- The issue of obtaining a well-converged and well-distributed set of Pareto optimal solutions efficiently and automatically is crucial in multi-objective evolutionary algorithms (MOEAs). Many studies have proposed different evolutionary algorithms that can progress towards Pareto optimal sets with a wide-spread distribution of solutions. However, most mathematically convergent MOEAs desire certain prior knowledge about the objective space in order to efficiently maintain widespread solutions. In this paper, we propose, based on our novel E-dominance concept, an Adaptive Rectangle Archiving (ARA) strategy that overcomes this important problem. The MOEA with this archiving technique provably converges to well-distributed Pareto optimal solutions without prior knowledge. ARA complements the existing archiving techniques, and is useful to both researchers and practitioners. 1

The paper analyzes the scalability of multiobjective estimation of distribution algorithms (MOEDAs) on a class of boundedly-difficult additively-separable multiobjective optimization problems. The paper illustrates that even if the linkage is correctly identified, massive multimodality of the search problems can easily overwhelm the nicher and lead to exponential scale-up. Facetwise models are subsequently used to propose a growth rate of the number of differing substructures between the two objectives to avoid the niching method from being overwhelmed and lead to polynomial scalability of MOEDAs. 1

In this chapter we present a brief analysis of the current research performed on evolutionary multiobjective optimization. After analyzing first and second generation multiobjective evolutionary algorithms, we address two important issues: the role of elitism in evolutionary multiobjective optimization and the way in which concepts from multiobjective optimization can be applied to constraint-handling techniques. We conclude with a discussion of some of the most promising research trends in the years to come.