9 research outputs found
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
One PLOT to Show Them All: Visualization of Efficient Sets in Multi-Objective Landscapes
Visualization techniques for the decision space of continuous multi-objective
optimization problems (MOPs) are rather scarce in research. For long, all
techniques focused on global optimality and even for the few available
landscape visualizations, e.g., cost landscapes, globality is the main
criterion. In contrast, the recently proposed gradient field heatmaps (GFHs)
emphasize the location and attraction basins of local efficient sets, but
ignore the relation of sets in terms of solution quality.
In this paper, we propose a new and hybrid visualization technique, which
combines the advantages of both approaches in order to represent local and
global optimality together within a single visualization. Therefore, we build
on the GFH approach but apply a new technique for approximating the location of
locally efficient points and using the divergence of the multi-objective
gradient vector field as a robust second-order condition. Then, the relative
dominance relationship of the determined locally efficient points is used to
visualize the complete landscape of the MOP. Augmented by information on the
basins of attraction, this Plot of Landscapes with Optimal Trade-offs (PLOT)
becomes one of the most informative multi-objective landscape visualization
techniques available.Comment: This version has been accepted for publication at the 16th
International Conference on Parallel Problem Solving from Nature (PPSN XVI
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 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
Peeking beyond peaks:Challenges and research potentials of continuous multimodal multi-objective optimization
Multi-objective (MO) optimization, i.e., the simultaneous optimization of multiple conflicting objectives, is gaining more and more attention in various research areas, such as evolutionary computation, machine learning (e.g., (hyper-)parameter optimization), or logistics (e.g., vehicle routing). Many works in this domain mention the structural problem property of multimodality as a challenge from two classical perspectives: (1) finding all globally optimal solution sets, and (2) avoiding to get trapped in local optima. Interestingly, these streams seem to transfer many traditional concepts of single-objective (SO) optimization into claims, assumptions, or even terminology regarding the MO domain, but mostly neglect the understanding of the structural properties as well as the algorithmic search behavior on a problem's landscape. However, some recent works counteract this trend, by investigating the fundamentals and characteristics of MO problems using new visualization techniques and gaining surprising insights. Using these visual insights, this work proposes a step towards a unified terminology to capture multimodality and locality in a broader way than it is usually done. This enables us to investigate current research activities in multimodal continuous MO optimization and to highlight new implications and promising research directions for the design of benchmark suites, the discovery of MO landscape features, the development of new MO (or even SO) optimization algorithms, and performance indicators. For all these topics, we provide a review of ideas and methods but also an outlook on future challenges, research potential and perspectives that result from recent developments.</p
Peeking beyond peaks: challenges and research potentials of continuous multimodal multi-objective optimization
Computer Systems, Imagery and Medi