Visualizing Mutually Nondominating Solution Sets in Many-Objective Optimization

Walker, David J.; Everson, Richard; Fieldsend, Jonathan E.

doi:10.1109/tevc.2012.2225064

Cited by 114 publications

(69 citation statements)

References 58 publications

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“…Walker et al [17] reviewed different methods (scatter plots, parallel coordinates and heat maps) to visualise solution sets for many-objective problems. They also proposed two techniques: a data mining visualisation tool to plot a convex graph, and a new similarity measure of solutions to plot them in a two-dimensional space.…”

Section: Related Workmentioning

confidence: 99%

Analysis of Objectives Relationships in Multiobjective Problems Using Trade-Off Region Maps

Pinheiro

Landa-Silva

Atkin

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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Understanding the relationships between objectives in manyobjective optimisation problems is desirable in order to develop more effective algorithms. We propose a technique for the analysis and visualisation of complex relationships between many (three or more) objectives. This technique looks at conflicting, harmonious and independent objectives relationships from different perspectives. To do that, it uses correlation, trade-off regions maps and scatter-plots in a four step approach. We apply the proposed technique to a set of instances of the well-known multiobjective multidimensional knapsack problem. The experimental results show that with the proposed technique we can identify local and complex relationships between objectives, trade-offs not derived from pairwise relationships, gaps in the fitness landscape, and regions of interest. Such information can be used to tailor the development of algorithms.

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Section: Related Workmentioning

confidence: 99%

Analysis of Objectives Relationships in Multiobjective Problems Using Trade-Off Region Maps

Pinheiro

Landa-Silva

Atkin

2015

Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation

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“…However, although popular across many application domains, both Neuroscale and PCA are oblivious to whether solutions dominate each other, or are mutually non-dominating in multi-objective populations, or what their Pareto shell is. We recently defined a new distance measure, the dominance distance, that captures the similarity of the dominance relations of solutions, and we have used this to project mutually non-dominating sets using multi-dimensional scaling [23,26] to points on the plane [25]. In the same work we also investigated the use of Radviz [13,14] for this mapping.…”

Section: Pareto Dominancementioning

confidence: 99%

“…The solution to the constrained problem can be found with linear algebra via the graph Laplacian [10,3] (further details on how to do this efficiently can be found in [17]). The similarity measure we choose to use here is the dominance similarity, which we have used previously for MDS visualisations of multi-objective sets [25,9].…”

Section: Visualisation Of Köppen and Yoshidamentioning

confidence: 99%

“…Visualisation of sets with more objectives is often more difficult to interpret via a single scatter plot, and a range of other approaches has been used to visualise these populations in the multi-objective optimisation literature (e.g. parallel coordinate plots [7,15,12] heatmaps [22,25], directed graphs [24], Chernoff faces [1], and self-organising maps [21,11]). Dominance relations and shells are not always apparent in these visualisations however (or are only presented between adjacent shells).…”

Section: Introductionmentioning

confidence: 99%

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Visualising High-Dimensional Pareto Relationships in Two-Dimensional Scatterplots

Fieldsend

Everson

2013

Lecture Notes in Computer Science

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Abstract. In this paper two novel methods for projecting high dimensional data into two dimensions for visualisation are introduced, which aim to limit the loss of dominance and Pareto shell relationships between solutions to multi-objective optimisation problems. It has already been shown that, in general, it is impossible to completely preserve the dominance relationship when mapping from a higher to a lower dimension -however, approaches that attempt this projection with minimal loss of dominance information are useful for a number of reasons. (1) They may represent the data to the user of a multi-objective optimisation problem in an intuitive fashion, (2) they may help provide insights into the relationships between solutions which are not immediately apparent through other visualisation methods, and (3) they may offer a useful visual medium for interactive optimisation. We are concerned here with examining (1) and (2), and developing relatively rapid methods to achieve visualisations, rather than generating an entirely new search/optimisation problem which has to be solved to achieve the visualisation-which may prove infeasible in an interactive environment for real time use. Results are presented on randomly generated data, and the search population of an optimiser as it progresses. Structural insights into the evolution of a set-based optimiser that can be derived from this visualisation are also discussed.

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“…Furthermore, the visualisation of candidate solutions becomes difficult, often resulting in the use of heat-maps or parallel-coordinate plots. This poses a difficulty to the DM as the selection of a final candidate solution may become non-intuitive [86].…”

Section: Introductionmentioning

confidence: 99%

Covariance matrix adaptation pareto archived evolution strategy with hypervolume-sorted adaptive grid algorithm

Rostami

Neri

2016

ICA

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Abstract. Real-world problems often involve the optimisation of multiple conflicting objectives. These problems, referred to as multi-objective optimisation problems, are especially challenging when more than three objectives are considered simultaneously. This paper proposes an algorithm to address this class of problems. The proposed algorithm is an evolutionary algorithm based on an evolution strategy framework, and more specifically, on the Covariance Matrix Adaptation Pareto Archived Evolution Strategy (CMA-PAES). A novel selection mechanism is introduced and integrated within the framework. This selection mechanism makes use of an adaptive grid to perform a local approximation of the hypervolume indicator which is then used as a selection criterion. The proposed implementation, named Covariance Matrix Adaptation Pareto Archived Evolution Strategy with Hypervolume-sorted Adaptive Grid Algorithm (CMA-PAES-HAGA), overcomes the limitation of CMA-PAES in handling more than two objectives and displays a remarkably good performance on a scalable test suite in five, seven, and ten-objective problems. The performance of CMA-PAES-HAGA has been compared with that of a competition winning meta-heuristic, representing the state-of-the-art in this sub-field of multi-objective optimisation.The proposed algorithm has been tested in a seven-objective real-world application, i.e. the design of an aircraft lateral control system. In this optimisation problem, CMA-PAES-HAGA greatly outperformed its competitors.

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Visualizing Mutually Nondominating Solution Sets in Many-Objective Optimization

Cited by 114 publications

References 58 publications

Analysis of Objectives Relationships in Multiobjective Problems Using Trade-Off Region Maps

Analysis of Objectives Relationships in Multiobjective Problems Using Trade-Off Region Maps

Visualising High-Dimensional Pareto Relationships in Two-Dimensional Scatterplots

Covariance matrix adaptation pareto archived evolution strategy with hypervolume-sorted adaptive grid algorithm

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