Evolutionary Algorithms with Self-adjusting Asymmetric Mutation

Evolutionary Algorithms (EAs) and other randomized search heuristics are often considered as unbiased algorithms that are invariant with respect to different transformations of the underlying search space. However, if a certain amount of domain knowledge is available the use of biased search operators in EAs becomes viable. We consider a simple (1+1) EA for binary search spaces and analyze an asymmetric mutation operator that can treat zero- and one-bits differently. This operator extends previous work by Jansen and Sudholt (ECJ 18(1), 2010) by allowing the operator asymmetry to vary according to the success rate of the algorithm. Using a self-adjusting scheme that learns an appropriate degree of asymmetry, we show improved runtime results on the class of functions OneMax$_a$ describing the number of matching bits with a fixed target $a\in\{0,1\}^n$.Comment: 16 pages. An extended abstract of this paper will be published in the proceedings of PPSN 202

On the Impact of Operators and Populations within Evolutionary Algorithms for the Dynamic Weighted Traveling Salesperson Problem

Evolutionary algorithms have been shown to obtain good solutions for complex optimization problems in static and dynamic environments. It is important to understand the behaviour of evolutionary algorithms for complex optimization problems that also involve dynamic and/or stochastic components in a systematic way in order to further increase their applicability to real-world problems. We investigate the node weighted traveling salesperson problem (W-TSP), which provides an abstraction of a wide range of weighted TSP problems, in dynamic settings. In the dynamic setting of the problem, items that have to be collected as part of a TSP tour change over time. We first present a dynamic setup for the dynamic W-TSP parameterized by different types of changes that are applied to the set of items to be collected when traversing the tour. Our first experimental investigations study the impact of such changes on resulting optimized tours in order to provide structural insights of optimization solutions. Afterwards, we investigate simple mutation-based evolutionary algorithms and study the impact of the mutation operators and the use of populations with dealing with the dynamic changes to the node weights of the problem

Self-Adjusting Population Sizes for Non-Elitist Evolutionary Algorithms: Why Success Rates Matter

Evolutionary algorithms (EAs) are general-purpose optimisers that come with several parameters like the sizes of parent and offspring populations or the mutation rate. It is well known that the performance of EAs may depend drastically on these parameters. Recent theoretical studies have shown that self-adjusting parameter control mechanisms that tune parameters during the algorithm run can provably outperform the best static parameters in EAs on discrete problems. However, the majority of these studies concerned elitist EAs and we do not have a clear answer on whether the same mechanisms can be applied for non-elitist EAs. We study one of the best-known parameter control mechanisms, the one-fifth success rule, to control the offspring population size $\lambda$ in the non-elitist $(1,\lambda)$ EA. It is known that the $(1,\lambda)$ EA has a sharp threshold with respect to the choice of $\lambda$ where the expected runtime on the benchmark function OneMax changes from polynomial to exponential time. Hence, it is not clear whether parameter control mechanisms are able to find and maintain suitable values of $\lambda$. For OneMax we show that the answer crucially depends on the success rate $s$ (i.e. a one-$(s+1)$-th success rule). We prove that, if the success rate is appropriately small, the self-adjusting $(1,\lambda)$ EA optimises OneMax in $O(n)$ expected generations and $O(n \log n)$ expected evaluations, the best possible runtime for any unary unbiased black-box algorithm. A small success rate is crucial: we also show that if the success rate is too large, the algorithm has an exponential runtime on OneMax and other functions with similar characteristics.Comment: This is an extended version of a paper that appeared in the Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2021

On the Robustness of Evolutionary Algorithms to Noise: Refined Results and an Example Where Noise Helps

We present reined results for the expected optimisation time of the (1+1) EA and the (1+λ) EA on LeadingOnes in the prior noise model, where in each itness evaluation the search point is altered before evaluation with probability p. Previous work showed that the (1+1) EA runs in polynomial time if p = O((logn)/n 2 ) and needs superpolynomial time if p = Ω((logn)/n), leaving a huge gap for which no results were known. We close this gap by showing that the expected optimisation time is Θ(n 2 ) · exp(Θ(pn2 )), allowing for the irst time to locate the threshold between polynomial and superpolynomial expected times at p = Θ((logn)/n 2 ). Hence the (1+1) EA on LeadingOnes is much more sensitive to noise than previously thought. We also show that ofspring populations of size λ ≥ 3.42 logn can efectively deal with much higher noise than known before. Finally, we present an example of a rugged landscape where prior noise can help to escape from local optima by blurring the landscape and allowing a hill climber to see the underlying gradient

Self-adjusting offspring population sizes outperform fixed parameters on the cliff function

In the discrete domain, self-adjusting parameters of evolutionary algorithms (EAs) has emerged as a fruitful research area with many runtime analyses showing that self-adjusting parameters can out-perform the best fixed parameters. Most existing runtime analyses focus on elitist EAs on simple problems, for which moderate performance gains were shown. Here we consider a much more challenging scenario: the multimodal function Cliff, defined as an example where a (1, λ) EA is effective, and for which the best known upper runtime bound for standard EAs is O(n25).We prove that a (1, λ) EA self-adjusting the offspring population size λ using success-based rules optimises Cliff in O(n) expected generations and O(n log n) expected evaluations. Along the way, we prove tight upper and lower bounds on the runtime for fixed λ (up to a logarithmic factor) and identify the runtime for the best fixed λ as nη for η ≈ 3.9767 (up to sub-polynomial factors). Hence, the self-adjusting (1, λ) EA outperforms the best fixed parameter by a factor of at least n2.9767 (up to sub-polynomial factors)