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self-adjusting Evolutionary algorithms for Multimodal Optimization

ALGORITHMICA 2022年第6期84卷 1694-1723页

作者： Rajabi, Amirhossein Witt, Carsten Tech Univ Denmark Lyngby Denmark

Recent theoretical research has shown that self-adjusting and self-adaptive mechanisms can provably outperform static settings in evolutionary algorithms for binary search spaces. However, the vast majority of these studies focuses on unimodal functions which do not require the algorithm to flip several bits simultaneously to make progress. In fact, existing self-adjusting algorithms are not designed to detect local optima and do not have any obvious benefit to cross large Hamming gaps. We suggest a mechanism called stagnation detection that can be added as a module to existing evolutionary algorithms (both with and without prior self-adjusting schemes). Added to a simple (1+1) EA, we prove an expected runtime on the well-known JUMP benchmark that corresponds to an asymptotically optimal parameter setting and outperforms other mechanisms for multimodal optimization like heavy-tailed mutation. We also investigate the module in the context of a self-adjusting (1+lambda) EA. To explore the limitations of the approach, we additionally present an example where both self-adjusting mechanisms, including stagnation detection, do not help to find a beneficial setting of the mutation rate. Finally, we investigate our module for stagnation detection experimentally.

关键词： Randomized search heuristics self-adjusting algorithms Multimodal functions Runtime analysis

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self-adjusting Evolutionary algorithms for Multimodal Optimization

Self-Adjusting Evolutionary Algorithms for Multimodal Optimi...

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Genetic and Evolutionary Computation Conference (GECCO)

作者： Rajabi, Amirhossein Witt, Carsten Tech Univ Denmark Lyngby Denmark

ISBN: (纸本)9781450371285

Recent theoretical research has shown that self-adjusting and self-adaptive mechanisms can provably outperform static settings in evolutionary algorithms for binary search spaces. However, the vast majority of these studies focuses on unimodal functions which do not require the algorithm to flip several bits simultaneously to make progress. In fact, existing self-adjusting algorithms are not designed to detect local optima and do not have any obvious benefit to cross large Hamming gaps. We suggest a mechanism called stagnation detection that can be added as a module to existing evolutionary algorithms (both with and without prior self-adjusting schemes). Added to a simple (1+1) EA, we prove an expected runtime on the well-known Jump benchmark that corresponds to an asymptotically optimal parameter setting and outperforms other mechanisms for multimodal optimization like heavy-tailed mutation. We also investigate the module in the context of a self-adjusting (1+lambda) EA and show that it combines the previous benefits of this algorithm on unimodal problems with more efficient multimodal optimization. To explore the limitations of the approach, we additionally present an example where both self-adjusting mechanisms, including stagnation detection, do not help to find a beneficial setting of the mutation rate. Finally, we investigate our module for stagnation detection experimentally.

关键词： randomised search heuristics self-adjusting algorithms multimodal functions runtime analysis

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self-adjusting resilient control plane for virtual software-defined optical networks

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OPTICAL SWITCHING AND NETWORKING 2025年 55卷

作者： Mogyorosi, Ferenc Babarczi, Peter Pasic, Alija Budapest Univ Technol & Econ Fac Elect Engn & Informat Dept Telecommun & Media Informat Muegyetem Rkp 3 H-1111 Budapest Hungary

Optical networks must promptly respond to failures and efficiently handle dynamic traffic in order to fulfill their role as a critical infrastructure. Leveraging network softwarization and virtualization, virtual software- defined networks offer sufficient flexibility towards this goal by sharing the physical infrastructure among multiple tenants whose traffic must traverse the network hypervisor. Ina resilient optical control plane each switch must be assigned to a primary and backup hypervisor instance through short control paths, which challenge will be addressed in this paper. First, we propose an intelligent greedy hypervisor placement heuristic which maximizes acceptance ratio for current, and preparedness for future requests. Secondly, we introduce a graph neural network model that can be seamlessly integrated with either our integer linear program or heuristic method to yield high-quality placements insignificantly less time compared to our prior solutions. This enhancement renders our approach applicable to larger networks, significantly expanding its practical utility. Finally, we propose a self-adjusting hypervisor migration strategy, which continuously adapts the placement to the dynamically changing virtual network requests, thus, ensuring service continuity by avoiding frequent control plane reconfigurations. Through simulations we show that our hypervisor placement and migration strategies provide a balanced control load while they can handle a wide variety of changes.

关键词： Virtual software-defined optical networks Resilient hypervisor placement self-adjusting algorithms Machine learning

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Evolutionary algorithms with self-adjusting Asymmetric Mutation 16th

Evolutionary Algorithms with Self-adjusting Asymmetric Mutat...

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16th International Conference on Parallel Problem Solving from Nature (PPSN)

作者： Rajabi, Amirhossein Witt, Carsten Tech Univ Denmark Lyngby Denmark

ISBN: (纸本)9783030581114;9783030581121

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 OneMaxa describing the number of matching bits with a fixed target alpha is an element of{0, 1}(n).

关键词： Evolutionary algorithms Runtime analysis self-adjusting algorithms Parameter control Asymmetric mutations

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Stagnation Detection with Randomized Local Search

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EVOLUTIONARY COMPUTATION 2023年第1期31卷 1-29页

作者： Rajabi, Amirhossein Witt, Carsten Tech Univ Denmark DTU Compute Lyngby Denmark

Recently a mechanism called stagnation detection was proposed that automatically adjusts the mutation rate of evolutionary algorithms when they encounter local optima. The so-called SD-(1+1) EA introduced by Rajabi and Witt (2022) adds stagnation detection to the classical (1+1) EA with standard bit mutation. This algorithm flips each bit independently with some mutation rate, and stagnation detection raises the rate when the algorithm is likely to have encountered a local optimum. In this article, we investigate stagnation detection in the context of the k-bit flip operator of randomized local search that flips k bits chosen uniformly at random and let stagnation detection adjust the parameter k. We obtain improved runtime results compared with the SD-(1+1) EA amounting to a speedup of at least (1-o(1))root 2 pi m, where m is the so-called gap size, that is, the distance to the next improvement. Moreover, we propose additional schemes that prevent infinite optimization times even if the algorithm misses a working choice of k due to unlucky events. Finally, we present an example where standard bit mutation still outperforms the k-bit flip operator with stagnation detection.

关键词： Randomized search heuristics local search self-adjusting algorithms multimodal functions runtime analysis

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Stagnation Detection in Highly Multimodal Fitness Landscapes

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ALGORITHMICA 2024年第9期86卷 2929-2958页

作者： Rajabi, Amirhossein Witt, Carsten Tech Univ Denmark DTU Compute DK-2800 Kongens Lyngby Denmark

Stagnation detection has been proposed as a mechanism for randomized search heuristics to escape from local optima by automatically increasing the size of the neighborhood to find the so-called gap size, i. e., the distance to the next improvement. Its usefulness has mostly been considered in simple multimodal landscapes with few local optima that could be crossed one after another. In multimodal landscapes with a more complex location of optima of similar gap size, stagnation detection suffers from the fact that the neighborhood size is frequently reset to 1 without using gap sizes that were promising in the past. In this paper, we investigate a new mechanism called radius memory which can be added to stagnation detection to control the search radius more carefully by giving preference to values that were successful in the past. We implement this idea in an algorithm called SD-RLSm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>{\text {m}}$$\end{document} and show compared to previous variants of stagnation detection that it yields speed-ups for linear functions under uniform constraints and the minimum spanning tree problem. Moreover, its running time does not significantly deteriorate on unimodal functions and a generalization of the Jump benchmark. Finally, we present experimental results carried out to study SD-RLSm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$<^>{\text {m}}$$\end{document} and compare it with other algorithms.

关键词： Randomized search heuristics self-adjusting algorithms Multimodal functions Runtime analysis

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Stagnation Detection in Highly Multimodal Fitness Landscapes

Stagnation Detection in Highly Multimodal Fitness Landscapes

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2nd Genetic and Evolutionary Computation Conference (GECCO)

作者： Rajabi, Amirhossein Witt, Carsten Tech Univ Denmark Lyngby Denmark

ISBN: (纸本)9781450383509

Stagnation detection has been proposed as a mechanism for randomized search heuristics to escape from local optima by automatically increasing the size of the neighborhood to find the so-called gap size, i. e., the distance to the next improvement. Its usefulness has mostly been considered in simple multimodal landscapes with few local optima that could be crossed one after another. In multimodal landscapes with a more complex location of optima of similar gap size, stagnation detection suffers from the fact that the neighborhood size is frequently reset to 1 without using gap sizes that were promising in the past. In this paper, we investigate a new mechanism called radius memory which can be added to stagnation detection to control the search radius more carefully by giving preference to values that were successful in the past. We implement this idea in an algorithm called SD-RLSm and show compared to previous variants of stagnation detection that it yields speed-ups for linear functions under uniform constraints and the minimum spanning tree problem. Moreover, its running time does not significantly deteriorate on unimodal functions and a generalization of the JUMP benchmark. Finally, we present experimental results carried out to study SD-RLSm and compare it with other algorithms.

关键词： randomised search heuristics self-adjusting algorithms multimodal functions runtime analysis

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Stagnation Detection with Randomized Local Search 1

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21st European Conference on Evolutionary Computation in Combinatorial Optimization (EvoCOP)

作者： Rajabi, Amirhossein Witt, Carsten Tech Univ Denmark Lyngby Denmark

ISBN: (数字)9783030729042

ISBN: (纸本)9783030729035;9783030729042

Recently a mechanism called stagnation detection was proposed that automatically adjusts the mutation rate of evolutionary algorithms when they encounter local optima. The so-called SD-(1+1) EA introduced by Rajabi and Witt (GECCO 2020) adds stagnation detection to the classical (1+1) EA with standard bit mutation, which flips each bit independently with some mutation rate, and raises the mutation rate when the algorithm is likely to have encountered local optima. In this paper, we investigate stagnation detection in the context of the k-bit flip operator of randomized local search that flips k bits chosen uniformly at random and let stagnation detection adjust the parameter k. We obtain improved runtime results compared to the SD-(1+1) EA amounting to a speed-up of up to e = 2.71... Moreover, we propose additional schemes that prevent infinite optimization times even if the algorithm misses a working choice of k due to unlucky events. Finally, we present an example where standard bit mutation still outperforms the local k-bit flip with stagnation detection.

关键词： Randomized search heuristics Local search self-adjusting algorithms Multimodal functions Runtime analysis

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