Runtime Analysis of Evolutionary Diversity Maximization for OneMinMax

Diversity mechanisms are key to the working behaviour of evolutionary multi-objective algorithms. With this paper, we contribute to the theoretical understanding of such mechanisms by means of rigorous runtime analysis. We consider the OneMinMax problem for which it has been shown in [11] that a standard benchmark algorithm called SIBEA is not able to obtain a population with optimal hypervolume distribution in expected polynomial time if the population size is relatively small. We investigate the same setting as in [11] and show that SIBEA is able to achieve a good approximation of the optimal hypervolume distribution very efficiently. Furthermore, we study OneMinMax in the context of search-based diversity optimization and examine the time until SIBEA with a search-based diversity mechanism has obtained a population of maximal diversity covering the whole Pareto front.

[1]  Anne Auger,et al.  Theoretically Investigating Optimal µ-Distributions for the Hypervolume Indicator: First Results for Three Objectives , 2010, PPSN.

[2]  Benjamin Doerr,et al.  Multiplicative Drift Analysis , 2010, GECCO '10.

[3]  Markus Wagner,et al.  Fast and effective multi-objective optimisation of wind turbine placement , 2013, GECCO '13.

[4]  Anne Auger,et al.  Theory of Randomized Search Heuristics: Foundations and Recent Developments , 2011, Theory of Randomized Search Heuristics.

[5]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems (Genetic and Evolutionary Computation) , 2006 .

[6]  Carsten Witt,et al.  Bioinspired Computation in Combinatorial Optimization , 2010, Bioinspired Computation in Combinatorial Optimization.

[7]  Eckart Zitzler,et al.  Integrating decision space diversity into hypervolume-based multiobjective search , 2010, GECCO '10.

[8]  Angus R. Simpson,et al.  Improving the efficiency of multi-objective evolutionary algorithms through decomposition: An application to water distribution network design , 2015, Environ. Model. Softw..

[9]  Gary B. Lamont,et al.  Evolutionary Algorithms for Solving Multi-Objective Problems , 2002, Genetic Algorithms and Evolutionary Computation.

[10]  R. K. Ursem.  Multi-objective Optimization using Evolutionary Algorithms , 2009 .

[11]  Nicola Beume,et al.  SMS-EMOA: Multiobjective selection based on dominated hypervolume , 2007, Eur. J. Oper. Res..

[12]  Frank Neumann,et al.  Bioinspired computation in combinatorial optimization: algorithms and their computational complexity , 2010, GECCO '12.

[13]  Frank Neumann,et al.  Analyzing Hypervolume Indicator Based Algorithms , 2008, PPSN.

[14]  Wanru Gao,et al.  Runtime analysis for maximizing population diversity in single-objective optimization , 2014, GECCO.

[15]  Ofer M. Shir,et al.  Enhancing Decision Space Diversity in Evolutionary Multiobjective Algorithms , 2009, EMO.

[16]  Lothar Thiele,et al.  Defining and Optimizing Indicator-Based Diversity Measures in Multiobjective Search , 2010, PPSN.

[17]  Anne Auger,et al.  Theory of the hypervolume indicator: optimal μ-distributions and the choice of the reference point , 2009, FOGA '09.

[18]  Frank Neumann,et al.  Population size matters: rigorous runtime results for maximizing the hypervolume indicator , 2013, GECCO '13.

[19]  Frank Neumann,et al.  Population size matters: Rigorous runtime results for maximizing the hypervolume indicator , 2015, Theor. Comput. Sci..

[20]  Lothar Thiele,et al.  Maximizing population diversity in single-objective optimization , 2011, GECCO '11.