An Effective Ensemble Framework for Multiobjective Optimization

Abstract

This paper proposes an effective ensemble framework for tackling multi-objective optimization problems, by combining the advantages of various evolutionary operators and selection criteria that are run on multiple populations. A simple ensemble algorithm is realized as a prototype to demonstrate our proposed framework. Two mechanisms, namely competition and cooperation, are employed to drive the running of the ensembles. Competition is designed by adaptively running different evolutionary operators on multiple populations. The operator that better fits the problem's characteristics will receive more computational resources, being rewarded by a decomposition-based credit assignment strategy. Cooperation is achieved by a cooperative selection of the offspring generated by different populations.In this way, the promising offspring from one population have chances to migrate into the other populations to enhance their convergence or diversity. Moreover, the population update information is further exploited to build an evolutionary potentiality model, which is used to guide the evolutionary process. Our experimental results show the superior performance of our proposed ensemble algorithms in solving most cases of a set of thirty-one test problems, which corroborates the advantages of our ensemble framework.

Evolutionary Learning for Soft Margin Problems: A Case Study on Practical Problems with Kernels

“…As the standard SVM cannot be solved by EA, we only use GM to solve (4) under (5). The dual SVM (7) under (8) is essentially equal to the standard SVM (4) under (5), thus we employ EA to solve (7) under (8). It should be noted that we should generate solution individual α under restriction (8), just as that used in solving (19) under (20) with C = ∞.…”

“…The dual SVM (7) under (8) is essentially equal to the standard SVM (4) under (5), thus we employ EA to solve (7) under (8). It should be noted that we should generate solution individual α under restriction (8), just as that used in solving (19) under (20) with C = ∞. In summary, totally we have carried out 12 experiments as shown in Table III, which basically contains three SVMs on three kernels solved by GM and EA.…”

“…Generally, researchers use gradient-based optimization methods [2], [5] to solve (7) and (8). However, there are two tough issues usually encountered in tacking practical problems: (A) Uncertainty over choice of kernel functions.…”

“…However, in this way, some of the kernels in the pre-set ensemble may be not so exact to approximate the ideal kernel. Therefore slack variables were introduced which could relax the hard constraints (5) to become softer constraints [8,10], so that the kernels used could be equally considered as the ideal unknown one. Of course, the introduced positive slack variables will form an additional objective to be minimized, thus choosing an appropriate weighting parameter for balancing the margin objective and slack objective will affect the final optimum [10,11].…”

“…In this research, aiming to tackle polymer and glass materials classification and prediction problems, both of the kernel and slack methods will be used to model the classifiers, and the evolutionary algorithm be carried out on the Ld model in (7) and (8). We will treat information such as properties and chemical compositions as problem features, and the types of polymer and glass materials as labels.…”