Two novel approaches for many-objective optimization

Garza-Fabre, Mario; Toscano-Pulido, Gregorio; Coello, Carlos A. Coello

doi:10.1109/cec.2010.5585930

Cited by 21 publications

(16 citation statements)

References 19 publications

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“…We postulate that this is because as the objective number increases the distribution of points on the edge of the front also increases. Since AR only takes into account the ordering and not the geometric location of solutions it will then give greater and greater preference towards the edge in comparison with SR (as it prefers solutions that are in the centre of its ordering, rather than the geometric centre [12]). …”

Section: Analysis Of Resultsmentioning

confidence: 99%

On the effect of selection and archiving operators in many-objective particle swarm optimisation

Woolard

Fieldsend

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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The particle swarm optimisation (PSO) heuristic has been used for a number of years now to perform multi-objective optimisation, however its performance on many-objective optimisation (problems with four or more competing objectives) has been less well examined. Many-objective optimisation is well-known to cause problems for Pareto-based evolutionary optimisers, so it is of interest to see how well PSO copes in this domain, and how non-Pareto quality measures perform when integrated into PSO. Here we compare and contrast the performance of canonical PSO, using a wide range of many-objective quality measures, on a number of different parametrised test functions for up to 20 competing objectives. We examine the use of eight quality measures as selection operators for guides when truncated nondominated archives of guides are maintained, and as maintenance operators, for choosing which solutions should be maintained as guides from one generation to the next. We find that the Controlling Dominance Area of Solutions approach performs exceptionally well as a quality measure to determine archive membership for global and local guides. As a selection operator, the Average Rank and Sum of Ratios measures are found to generally provide the best performance.

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Section: Analysis Of Resultsmentioning

confidence: 99%

On the effect of selection and archiving operators in many-objective particle swarm optimisation

Woolard

Fieldsend

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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“…13(a) shows 500 3-objective DTLZ6 solutions projected onto the principal two eigenvectors of F. As before solutions are coloured by their average rank. Also marked are the best and worst solutions for each objective and the edges of the axis-parallel bounding box which contains the solutions which meet at the global best point [70], namely (min k (y k1 ), min k (y k2 ), . .…”

Section: Dominance Distance For Multidimensional Scalingmentioning

confidence: 99%

Visualizing Mutually Nondominating Solution Sets in Many-Objective Optimization

Walker

Everson

Fieldsend

2013

IEEE Trans. Evol. Computat.

114

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Abstract-As many-objective optimisation algorithms mature the problem owner is faced with visualising and understanding a set of mutually non-dominating solutions in a high dimensional space. We review existing methods and present new techniques to address this problem.We address a common problem with the well known heatmap visualisation, that the often arbitrary ordering of rows and columns renders the heatmap unclear, by using spectral seriation to rearrange the solutions and objectives and thus enhance the clarity of the heatmap. A multi-objective evolutionary optimiser is used to further enhance the simultaneous visualisation of solutions in objective and parameter space.Two methods for visualising multi-objective solution objectives in the plane are introduced. First, we use RadViz and exploit interpretations of barycentric coordinates for convex polygons and simplices to map a mutually non-dominating set to the interior of a regular convex polygon in the plane, providing an intuitive representation of the solutions and objectives.Second, we introduce a new measure of the similarity of solutions-the dominance distance-which captures the order relations between solutions. This metric provides an embedding in Euclidean space, which is shown to yield coherent visualisations in two dimensions.The methods are illustrated on standard test problems and data from a benchmark many-objective problem.

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“…As a consequence, the dominance criterion can not impose preferences among solutions, and this mitigates the guidance capability of the nondominated solutions during the search process. The diminution in the dominance differentiation capability weakens the evolutionary pressure to the Pareto front for many objectives and, as a consequence, the convergence performance is mitigated [24,18]. In some cases, these algorithms can even present a behavior equal or worse than random search [30,27,18,24].…”

Section: Introductionmentioning

confidence: 96%