Techniques for highly multiobjective optimisation: some nondominated points are better than others

By David Wolfe Corne, Joshua D. Knowles. Annual Conference on Genetic and Evolutionary Computation, 2007

314 citations recorded by the source corpus.

The research area of evolutionary multiobjective optimization (EMO) is reaching better understandings of the properties and capabilities of EMO algorithms, and accumulating much evidence of their worth in practical scenarios. An urgent emerging issue is that the favoured EMO algorithms scale poorly when problems have "many" (e.g. five or more) objectives. One of the chief reasons for this is believed to be that, in many-objective EMO search, populations are likely to be largely composed of nondominated solutions. In turn, this means that the commonly-used algorithms cannot distinguish between these for selective purposes. However, there are methods that can be used validly to rank points in a nondominated set, and may therefore usefully underpin selection in EMO search. Here we discuss and compare several such methods. Our main finding is that simple variants of the often-overlooked "Average Ranking" strategy usually outperform other methods tested, covering problems with 5-20 objectives and differing amounts of inter-objective correlation.

Subfields: Artificial Intelligence, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/d40684723feb2d1b682466667ddb155e2f6bc7be

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In Computational Theory and Mathematics

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Citations in the corpus

• Evolutionary many-objective optimization: A short review (2008, background): “For example, Corne and Knowles [16] reported that the best results were obtained from a simple average ranking method than more complicated ranking schemes.”
• A Knee Point-Driven Evolutionary Algorithm for Many-Objective Optimization (2015, background): “nondominated, although some of them may have a better ability to help the population to converge to the Pareto optimal front [19].”
• A Reference Vector Guided Evolutionary Algorithm for Many-Objective Optimization (2016, background): “verge toward the PF when dominance is adopted as a criterion for selecting individuals with a limited population size [7].”
• Many-Objective Evolutionary Algorithms (2015, methodology): “In the dominance resistance (DR) phenomenon [Fonseca and Fleming 1998; Purshouse and Fleming 2007; Knowles and Corne 2007], the incomparability of solutions caused by the enormously increasing proportion of nondominated solutions.”
• An Evolutionary Many-Objective Optimization Algorithm Based on Dominance and Decomposition (2015, background): “In the future, it is interesting to investigate the performance of MOEA/DD for a wider range of problems, such as problems with complicated PS shapes (see [40], [72], [73]), combinatorial optimization problems (see [18], [46], [74]), and problems in real-world with a large number of objectives.”
• PlatEMO: A MATLAB Platform for Evolutionary Multi-Objective Optimization [Educational Forum] (2017, unknown): “moTSP [83] 2007 mulTi-obJECTivE TRAvEling SAlESPERSon PRoblEm”
• A survey on multi-objective evolutionary algorithms for many-objective problems (2014, methodology): “…u m e [ 108 ] , M O E R S [ 42 ] [ 84 ] D TLZ 2 [ 25 ] 3 , 6 , 12 N S GA -II [ 24 ] P r ox i m it y i nd i ca t o r [ 83 ] , S p r ea d [ 22 ] 123 [ 19 ] w it h d i ff e r e n t r a nk i ng m e t hod s : t h e a v e r a g e a nd s u mm e d r a ti o r a nk i ng m e t hod s [ 9 ] , t h e f a vou r r…”
• Shift-Based Density Estimation for Pareto-Based Algorithms in Many-Objective Optimization (2014, methodology): “the search toward the desired direction [12], [43].”
• A Grid-Based Evolutionary Algorithm for Many-Objective Optimization (2013, unknown): “This seems to be more suitable for many-objective problems, considering the increase of selection pressure from the quantitative comparison of objective values among solutions [9], [31].”
• Preference-Inspired Coevolutionary Algorithms for Many-Objective Optimization (2013, methodology): “[33] demonstrated that an approach of this type is able to outperform NSGA-II, the average ranking method [14], and random search on many-objective problems.”