Engineering and Physical Sciences Research Council (EPSRC

Akman, O

Alyahya, K

Doherty, K

Fieldsend, JE

English

Open Research Exeter

Fieldsend et al./UQOP 2019UQOP 2019Uncertainty Quantification & Optimization Conference18-20 March, Paris, FranceRobust Optimisation usingVoronoi-Based Archive SamplingJonathan Fieldsend, Kevin Doherty, Khulood Alyahya, Ozgur AkmanUniversity of ExeterJ.E.Fieldsend@ex.ac.uk K.Doherty@ex.ac.ukK.Alyahya@ex.ac.ukO.E.Akman@ex.ac.ukKeywords: Robust optimisation, Voronoi, Fitness approximation, Uncertainty.ABSTRACTA key issue in tackling robust problems is the appropriate selection of solutions from theuncertainty set associated with a putative design, in order to estimate its robust quality andtherefore guide the search process. We consider here problems where the variation of performanceis due to some variability in the actual design realised (due to e.g. engineering tolerances), andthe uncertainty set is therefore some disturbance neighbourhood around a design. We outlinea framework, first reported in [Doherty et al., 2018], for online estimation solution quality in arobust optimisation setting by exploiting samples from the search history and using Monte Carlosampling to approximate a Voronoi tessellation of the design space. Voronoi tessellations (andtheir Euclidean dual graphs, Delaunay triangulations) have a wide range of applications acrossthe natural sciences [Aurenhammer, 1991]. The Voronoi tessellation of a set of discrete points in acontinuous space divides the space into a set of cells, one for each point, so that for each point, itscorresponding cell contains the volume of space that is closest to it. A useful feature of the Voronoitessellation is that the point that is furthest from all of the points used to generate the tessellationwill be a vertex of one of the cells. Therefore, a Voronoi tessellation provides us with a finite set ofcandidate points for the farthest point from all others. This is used to determine a new point inthe disturbance neighbourhood of a given solution such that — along with the relevant archivedpoints — they form a well-spread distribution. This approach is integrated within the widely usedCovariance Matrix Adaptation–Evolution Strategy (CMA-ES) [Hansen & Ostermeier, 2001]. It isalso used to weight the archive points to mitigate any selection bias in the neighbourhood history.We consider three robustness quality measures: the expected fitness with a uniform distur-bance (UD); the expected fitness with a Gaussian disturbance (GD); and the 95th percentile offitness values, with a uniform disturbance (PC). We assess the performance of our frameworkon benchmark problems with different properties and design dimensionality [Paenke et al., 2006,Branke & Fei, 2016] and compare the results with existing frameworks that incorporate thesearch history in the estimation of solution robustness [Tsutsui & Ghosh, 1997, Branke, 1998,Tsutsui, 1999, Tsutsui & Ghosh, 2003, Kruisselbrink et al., 2010, Branke & Fei, 2016, Fei et al., 2018].Our method performs competitively with these, and may be considered a new state-of-the-artapproach for optimising such problem types.1Fieldsend et al./UQOP 2019ACKNOWLEDGEMENTSThis work was supported by the Engineering and Physical Sciences Research Council [grantnumber EP/N017846/1].References[Aurenhammer, 1991] Aurenhammer, F (1991). Voronoi Diagrams — A Survey of a FundamentalGeometric Data Structure ACM Computing Surveys (CSUR), 23:3 345–405.[Branke, 1998] Branke, J. (1998). Creating robust solutions by means of evolutionary algorithmsParallel Problem Solving from Nature — PPSN V: 5th International Conference, 119–128.[Branke & Fei, 2016] Branke, J. and Fei, X. (2016). Efficient Sampling When Searching for RobustSolutions Parallel Problem Solving from Nature – PPSN XIV: 14th International Conference,237–246.[Doherty et al., 2018] Doherty, K and Alyahya, K and Fieldsend, J E and Akman, O E (2018).Voronoi-based archive sampling for robust optimisation Proceedings of the Genetic and Evolu-tionary Computation Conference Companion, 249–250.[Hansen & Ostermeier, 2001] Hansen, N. and Ostermeier, A. (2001). Completely DerandomizedSelf-Adaptation in Evolution Strategies Evolutionary Computation, 9:2 159–195[Fei et al., 2018] Fei, X. and Branke, J. and Gülpınar, N. (2018). New Sampling Strategieswhen Searching for Robust Solutions IEEE Transactions on Evolutionary Computation, doi:10.1109/TEVC.2018.2849331.[Kruisselbrink et al., 2010] Kruisselbrink, J. and Emmerich, M. and Bäck, T. (2010). An ArchiveMaintenance Scheme for Finding Robust Solutions Parallel Problem Solving from Nature, PPSNXI: 11th International Conference, 214–223.[Paenke et al., 2006] Paenke, I. and Branke, J. and Jin, Y. (2006). Efficient search for robustsolutions by means of evolutionary algorithms and fitness approximation IEEE Transactionson Evolutionary Computation, 10:4 405–420.[Tsutsui & Ghosh, 1997] Tsutsui, S. and Ghosh, A. (1997). Genetic Algorithms with a RobustSolution Searching Scheme IEEE Transactions on Evolutionary Computation, 1:3 201–208.[Tsutsui, 1999] Tsutsui, S. (1999). A comparative study on the effects of adding perturbations tophenotypic parameters in genetic algorithms with a robust solution searching scheme Systems,Man, and Cybernetics, 1999. IEEE SMC ’99 Conference Proceedings. 1999 IEEE InternationalConference on, 3 585–591.[Tsutsui & Ghosh, 2003] Tsutsui, S. and Ghosh, A. (2003). Effects of Adding Perturbations toPhenotypic Parameters in Genetic Algorithms for Searching Robust Solutions Advances inevolutionary computing, 203–365.2

Robust Optimisation using Voronoi-Based Archive Sampling

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Robust Optimisation using Voronoi-Based Archive Sampling

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