Runtime Analysis of a Heavy-Tailed (1+(λ, λ)) Genetic Algorithm on Jump Functions

It was recently observed that the (1 + (λ, λ)) genetic algorithm can comparably easily escape the local optimum of the jump functions benchmark. Consequently, this algorithm can optimize the jump function with jump size k in an expected runtime of only n(k+1)/2k−k/2eO(k) fitness evaluations (Antipov, Doerr, Karavaev (GECCO 2020)). To obtain this performance, however, a nonstandard parameter setting depending on the jump size k was used. To overcome this difficulty, we propose to choose two parameters of the (1 + (λ, λ)) genetic algorithm randomly from a power-law distribution. Via a mathematical runtime analysis, we show that this

[1]  Duc-Cuong Dang,et al.  Self-adaptation of Mutation Rates in Non-elitist Populations , 2016, PPSN.

[2]  Aishwaryaprajna,et al.  The benefits and limitations of voting mechanisms in evolutionary optimisation , 2019, FOGA '19.

[3]  Benjamin Doerr,et al.  The (1+λ) evolutionary algorithm with self-adjusting mutation rate , 2017, GECCO.

[4]  Dirk Sudholt,et al.  Adaptive population models for offspring populations and parallel evolutionary algorithms , 2011, FOGA '11.

[5]  Benjamin Doerr,et al.  Fixed-Target Runtime Analysis , 2020, Algorithmica.

[6]  Benjamin Doerr,et al.  k-Bit Mutation with Self-Adjusting k Outperforms Standard Bit Mutation , 2016, PPSN.

[7]  Duc-Cuong Dang,et al.  Escaping Local Optima with Diversity Mechanisms and Crossover , 2016, GECCO.

[8]  Benjamin Doerr,et al.  Theory of Parameter Control for Discrete Black-Box Optimization: Provable Performance Gains Through Dynamic Parameter Choices , 2018, Theory of Evolutionary Computation.

[9]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[10]  Frank Neumann,et al.  Fast Building Block Assembly by Majority Vote Crossover , 2016, GECCO.

[11]  Benjamin Doerr,et al.  A tight runtime analysis for the (1 + (λ, λ)) GA on leadingones , 2019, FOGA '19.

[12]  Benjamin Doerr,et al.  The (1 + (λ,λ)) GA is even faster on multimodal problems , 2020, GECCO.

[13]  Maxim Buzdalov,et al.  Evaluation of heavy-tailed mutation operator on maximum flow test generation problem , 2017, GECCO.

[14]  Per Kristian Lehre,et al.  Escaping Local Optima Using Crossover With Emergent Diversity , 2018, IEEE Transactions on Evolutionary Computation.

[15]  Benjamin Doerr,et al.  Runtime Analysis for Self-adaptive Mutation Rates , 2018, Algorithmica.

[16]  Abraham Wald,et al.  Some Generalizations of the Theory of Cumulative Sums of Random Variables , 1945 .

[17]  Benjamin Doerr.  Does comma selection help to cope with local optima? , 2020, GECCO.

[18]  Thomas Jansen,et al.  The Analysis of Evolutionary Algorithms—A Proof That Crossover Really Can Help , 2002, Algorithmica.

[19]  William F. Punch,et al.  Parameter-less population pyramid , 2014, GECCO.

[20]  Benjamin Doerr,et al.  Static and Self-Adjusting Mutation Strengths for Multi-valued Decision Variables , 2018, Algorithmica.

[21]  Benjamin Doerr,et al.  From black-box complexity to designing new genetic algorithms , 2015, Theor. Comput. Sci..

[22]  Dirk Sudholt,et al.  Design and Analysis of Schemes for Adapting Migration Intervals in Parallel Evolutionary Algorithms , 2015, Evolutionary Computation.

[23]  Benjamin Doerr,et al.  Runtime analysis of the (1 + (λ, λ)) genetic algorithm on random satisfiable 3-CNF formulas , 2017, GECCO.

[24]  Benjamin Doerr,et al.  Fast genetic algorithms , 2017, GECCO.