Real-valued Evolutionary Multi-modal Multi-objective Optimization by Hill-Valley Clustering
This work addresses multi-modal optimization for evolutionary algorithms, which is incremental as it extends hill-valley clustering to multi-objective problems.
The paper tackled the problem of multi-modal multi-objective optimization in a black-box setting by introducing multi-objective hill-valley clustering combined with an evolutionary algorithm, resulting in MO-HillVallEA, which outperformed existing algorithms on benchmark functions and maintained multiple approximation sets simultaneously.
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.