This chapter has presented an experimental study on components of Multi-Objective Evolutionary Algorithms for clusterings. In Chapter 4, we described how a good
CHAPTER 6. COMPARISON OF CLUSTERING REPRESENTATIONS 126 configuration for a MOEA should lead to a set of diverse solutions that are close to the Pareto front. Using the techniques we described in Section 4.3, we evaluated the sets of solutions (or Pareto fronts) that were generated.
The experimental results show that CBRE and MBBE are superior clustering representations to LBIE as they generate better Pareto fronts and better individual solutions.
The CBRE representation is likely to produce a Pareto Front containing good clustering solutions. The results also show that this representation in-conjunction with the MOCA mutation operator can find good Pareto fronts, so it appears as a good compromise. Part of our motivation for this study was to assess how well our proposed implementation of a Multi-Objective Evolutionary Algorithm for cluster- ing, including the MOCA operators, worked in relation to other implementations. The results validate our approach.
We also found that in terms of mutation, operators such as Addition or MOCA that manipulate the values of the centroids provide good results. They outperform others such as the swap operator that only exchanges centroids. Furthermore, muta- tion operators that are very disruptive, that is to say change the solutions drastically, cause the algorithm to explore a larger area of the objective space and return better Pareto fronts. More constructive mutation operators that modify the solution with respect to the problem with little disruption such as: Addition, Swap or MOCA tend to produce clustering solutions that are more similar to the desired clustering solutions. Such information provides useful guidance to produce better mutation operators.
In terms of exploring the objective space and producing a good Pareto front, MBBE was better, particularly when the very disruptive Invert mutation operator was used. The Invert operator drastically changes the solution and may lead to solutions that are very different from the pre-existing population, hence why the space may be well explored. However, Invert mutation can lead to a great increase in the number of clusters, hence further research could be performed with mutation
operators that radically change the resulting clustering solutions without causing a large increase in the number of clusters.
In the results, we did not find that there was a clearly superior crossover operator for both producing high quality clustering solutions and investigating the objective space. This is an area that may require further investigation, for example, designing a crossover operator that attempts to improve the Pareto front and the clustering quality of the solutions in the population using a combination of disruptive and constructive techniques when appropriate.
In fact, future work on Multi-objective algorithms for clustering could focus upon medoid or centroid based representations of a clustering solution and should inves- tigate the effects of including an initial exploration phase with disruptive operators followed by a local search phase with more constructive operators. This may be key to investigating the space fully while also producing high quality clustering solutions. The LBIE performed poorly. This may be because it is difficult to randomly pro- duce solutions where the clusters are continuous shapes within the space. Clusters that are not continuous will obviously be of poor quality. This representation may still be worth considering as it allows the production of arbitrarily shaped clusters. This technique may show an improved performance if there was a stage of the algo- rithm that increased the quality of the clustering solutions that were found. Future work could also include enhancements that establish rules about clusters being con- tinuous. This could involve constraints using the K-nearest neighbours of objects as a method of forming clusters, which has been used previously by [62].
We observed that the Guided (Individual) mutation operator outperformed the Guided (Multiple) mutation operator for the LBIE. This was unusual as many pre- vious approaches to clustering change many cluster memberships at each iteration so we had not expected this bad result. Similarly, guided mutation operators for the other encodings should also be investigated.
Chapter 7
Experimental Comparison of New
Mutation Operators
7.1
Introduction
In this chapter we expand upon the experiment that we presented in Chapter 6. Previously we concluded that we had seen promising results using Centroid Based Real Encoding as the representation for a Multi-Objective Clustering Algorithm. We found that mutation operators that were very disruptive explored the objective space well and found good Pareto fronts but did not find the highest quality clustering solutions. We also found that mutation operators that manipulated the clustering solutions directly lead to highest quality clustering solutions but did not explore the Pareto front as well as the disruptive operators. We therefore suggested that further research on the performance of the operators used within the algorithm should be conducted. Here we will present an investigation into three mutation operators designed to emphasise these properties.
In this chapter we report on an investigation into the performance of three differ- ent mutation operators used in conjunction with CBRE. We first explain in section 7.2 the main configuration of the algorithm used: the representation, crossover op-
erator and MOEA.
In Section 7.2.3 we describe three mutation operators that attempt to promote different aspects of a solution: front quality, clustering solution quality and a hybrid combination of these. The mutation operator designed to promote front quality is a variation of the mutation operator that we proposed in Chapter 5. The mutation operator designed to promote the quality of the clustering solutions is loosely based upon the clustering algorithm k-means. The final choice is a combination of the two other mutation operators.
We present the experimental setup in section 7.3. The results are presented in section 7.4. Supporting figures have been placed in Appendix A.