Real-valued evolutionary multi-modal multi-objective optimization by hill-valley clustering

In model-based evolutionary algorithms (EAs), the underlying search distribution is adapted to the problem at hand, for example based on dependencies between decision variables. Hill-valley clustering is an adaptive niching method in which a set of solutions is clustered such that each cluster corresponds to a single mode in the fitness landscape. This can be used to adapt the search distribution of an EA to the number of modes, exploring each mode separately. Especially in a black-box setting, where the number of modes is a priori unknown, an adaptive approach is essential for good performance. In this work, we introduce multi-objective hill-valley clustering and combine it with MAMaLGaM, a multi-objective EA, into the multi-objective hill-valley EA (MO-HillVallEA). We empirically show that MO-HillVallEA outperforms MAMaLGaM and other well-known multi-objective optimization algorithms on a set of benchmark functions. Furthermore, and perhaps most important, we show that MO-HillVallEA is capable of obtaining and maintaining multiple approximation sets simultaneously over time

Real-valued evolutionary multi-modal optimization driven by hill-valley clustering

Model-based evolutionary algorithms (EAs) adapt an underlying search model to features of the problem at hand, such as the linkage between problem variables. The performance of EAs often deteriorates as multiple modes in the fitness landscape are modelled with a unimodal search model. The number of modes is however often unknown a priori, especially in a black-box setting, which complicates adaptation of the search model. In this work, we focus on models that can adapt to the multi-modality of the fitness landscape. Specifically, we introduce Hill-Valley Clustering, a remarkably simple approach to adaptively cluster the search space in niches, such that a single mode resides in each niche. In each of the located niches, a core search algorithm is initialized to optimize that niche. Combined with an EA and a restart scheme, the resulting Hill-Valley EA (HillVallEA) is compared to current state-of-the-art niching methods on a standard benchmark suite for multi-modal optimization. Numerical results in terms of the detected number of global optima show that, in spite of its simplicity, HillVallEA is competitive within the limited budget of the benchmark suite, and shows superior performance in the long run

Real-valued evolutionary multi-modal optimization driven by hill-valley clustering

textabstractModel-based evolutionary algorithms (EAs) adapt an underlying search model to features of the problem at hand, such as the linkage between problem variables. The performance of EAs often deteriorates as multiple modes in the fitness landscape are modelled with a unimodal search model. The number of modes is however often unknown a priori, especially in a black-box setting, which complicates adaptation of the search model. In this work, we focus on models that can adapt to the multi-modality of the fitness landscape. Specifically, we introduce Hill-Valley Clustering, a remarkably simple approach to adaptively cluster the search space in niches, such that a single mode resides in each niche. In each of the located niches, a core search algorithm is initialized to optimize that niche. Combined with an EA and a restart scheme, the resulting Hill-Valley EA (HillVallEA) is compared to current state-of-the-art niching methods on a standard benchmark suite for multi-modal optimization. Numerical results in terms of the detected number of global optima show that, in spite of its simplicity, HillVallEA is competitive within the limited budget of the benchmark suite, and shows superior performance in the long run