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 algorithms). 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+$λ$) 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.
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…
We propose a new way to self-adjust the mutation rate in population-based evolutionary algorithms in discrete search spaces. Roughly speaking, it consists of creating half the offspring with a mutation rate that is twice the current mutation rate and the other half with half the current rate. The mutation rate is then updated to the rate used in that subpopulation which contains the best offspring. We analyze how the $(1+λ)$ evolutionary algorithm with this self-adjusting mutation rate optimizes the OneMax test function. We prove that this dynamic version of the $(1+λ)$ EA finds the optimum in…
We analyze the performance of the 2-rate $(1+λ)$ Evolutionary Algorithm (EA) with self-adjusting mutation rate control, its 3-rate counterpart, and a $(1+λ)$~EA variant using multiplicative update rules on the OneMax problem. We compare their efficiency for offspring population sizes ranging up to $λ=3,200$ and problem sizes up to $n=100,000$. Our empirical results show that the ranking of the algorithms is very consistent across all tested dimensions, but strongly depends on the population size. While for small values of $λ$ the 2-rate EA performs best, the multiplicative updates become super…
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 …
This report presents benchmarking results of the latest version of the Hill-Valley Evolutionary Algorithm (HillVallEA) on the CEC2013 niching benchmark suite. The benchmarking follows restrictions required by the GECCO 2018 competition on Niching methods for Multimodal Optimization. In particular, no problem dependent parameter tuning is performed. A number of adjustments have been made to original publication of HillVallEA that are discussed in this report.
This paper looks in detail at how an evolutionary algorithm attempts to solve instances from the multimodal problem generator. The paper shows that in order to consistently reach the global optimum, an evolutionary algorithm requires a population size that should grow at least linearly with the number of peaks. It is also shown a close relationship between the supply and decision making issues that have been identified previously in the context of population sizing models for additively decomposable problems. The most important result of the paper, however, is that solving an instance of the m…
The one-fifth success rule is one of the best-known and most widely accepted techniques to control the parameters of evolutionary algorithms. While it is often applied in the literal sense, a common interpretation sees the one-fifth success rule as a family of success-based updated rules that are determined by an update strength $F$ and a success rate. We analyze in this work how the performance of the (1+1) Evolutionary Algorithm on LeadingOnes depends on these two hyper-parameters. Our main result shows that the best performance is obtained for small update strengths $F=1+o(1)$ and success r…
An important challenge in reinforcement learning, including evolutionary robotics, is to solve multimodal problems, where agents have to act in qualitatively different ways depending on the circumstances. Because multimodal problems are often too difficult to solve directly, it is helpful to take advantage of staging, where a difficult task is divided into simpler subtasks that can serve as stepping stones for solving the overall problem. Unfortunately, choosing an effective ordering for these subtasks is difficult, and a poor ordering can reduce the speed and performance of the learning proce…
Clustering-based Transfer Learning for Dynamic Multimodal MultiObjective Evolutionary Algorithm
School of Automation and Electrical Engineering, Zhongyuan University of Technology（中原文理大学自动化与电气工程学院）；School of Electrical Engineering, Zhengzhou University（郑州大学电气工程学院）
Real world problems always have different multiple solutions. For instance, optical engineers need to tune the recording parameters to get as many optimal solutions as possible for multiple trials in the varied-line-spacing holographic grating design problem. Unfortunately, most traditional optimization techniques focus on solving for a single optimal solution. They need to be applied several times; yet all solutions are not guaranteed to be found. Thus the multimodal optimization problem was proposed. In that problem, we are interested in not only a single optimal point, but also the others. …
This paper investigates the performance of multistart next ascent hillclimbing and well-known evolutionary algorithms incorporating diversity preservation techniques on instances of the multimodal problem generator. This generator induces a class of problems in the bitstringdomain which is interesting to study from a theoretical perspective in the context of multimodal optimization, as it is a generalization of the classical OneMax and TwoMax functions for an arbitrary number of peaks. An average-case runtime analysis for multistart next ascent hill-climbing is presented for uniformly distribu…
In an evolutionary algorithm, the population has a very important role as its size has direct implications regarding solution quality, speed, and reliability. Theoretical studies have been done in the past to investigate the role of population sizing in evolutionary algorithms. In addition to those studies, several self-adjusting population sizing mechanisms have been proposed in the literature. This paper revisits the latter topic and pays special attention to the genetic algorithm with adaptive population size (APGA), for which several researchers have claimed to be very effective at autonom…
This report presents benchmarking results of the Hill-Valley Evolutionary Algorithm version 2019 (HillVallEA19) on the CEC2013 niching benchmark suite under the restrictions of the GECCO 2019 niching competition on multimodal optimization. Performance is compared to algorithms that participated in previous editions of the niching competition.
Calibration is a crucial step for the validation of computational models and a challenging task to accomplish. Dynamic Energy Budget (DEB) theory has experienced an exponential rise in the number of published papers, which in large part has been made possible by the DEBtool toolbox. Multimodal evolutionary optimisation could provide DEBtool with new capabilities, particularly relevant on the provisioning of equally optimal and diverse solutions. In this paper we present MultiCalib4DEB, a MATLAB toolbox directly integrated into the existing DEBtool toolbox, which uses multimodal evolutionary op…
Structure-Aware Cooperative Ensemble Evolutionary Optimization on Combinatorial Problems with Multimodal Large Language Models
School of Physical and Mathematical Sciences, Nanyang Technological University（南洋理工大学物理与数学科学学院）；College of Computing and Data Science, Nanyang Technological University（南洋理工大学计算与数据科学学院）
Online parameter controllers for evolutionary algorithms adjust values of parameters during the run of an evolutionary algorithm. Recently a new efficient parameter controller based on reinforcement learning was proposed by Karafotias et al. In this method ranges of parameters are discretized into several intervals before the run. However, performing adaptive discretization during the run may increase efficiency of an evolutionary algorithm. Aleti et al. proposed another efficient controller with adaptive discretization. In the present paper we propose a parameter controller based on reinforce…
In this article we provide a comprehensive review of the different evolutionary algorithm techniques used to address multimodal optimization problems, classifying them according to the nature of their approach. On the one hand there are algorithms that address the issue of the early convergence to a local optimum by differentiating the individuals of the population into groups and limiting their interaction, hence having each group evolve with a high degree of independence. On the other hand other approaches are based on directly addressing the lack of genetic diversity of the population by in…
The performance of deep neural networks, such as Deep Belief Networks formed by Restricted Boltzmann Machines (RBMs), strongly depends on their training, which is the process of adjusting their parameters. This process can be posed as an optimization problem over n dimensions. However, typical networks contain tens of thousands of parameters, making this a High-Dimensional Problem (HDP). Although different optimization methods have been employed for this goal, the use of most of the Evolutionary Algorithms (EAs) becomes prohibitive due to their inability to deal with HDPs. For instance, the Co…
First Mathematical Runtime Analyses of Evolutionary Multitask Multi-Objective Optimization
School of Computer Science and Technology, State Key Laboratory of Smart Farm Technologies and Systems, International Research Institute for Artificial Intelligence, Harbin Institute of Technology, Shenzhen, China（哈尔滨工业大学（深圳）计算机科学与技术学院、智慧农业技术与系统全国重点实验室、人工智能国际研究院）；Pengcheng Laboratory, Shenzhen, China（鹏城实验室）
Most of the real-world problems are multimodal in nature that consists of multiple optimum values. Multimodal optimization is defined as the process of finding multiple global and local optima (as opposed to a single solution) of a function. It enables a user to switch between different solutions as per the need while still maintaining the optimal system performance. Classical gradient-based methods fail for optimization problems in which the objective functions are either discontinuous or non-differentiable. Evolutionary Algorithms (EAs) are able to find multiple solutions within a population…
Recent works showed that simple success-based rules for self-adjusting parameters in evolutionary algorithms (EAs) can match or outperform the best fixed parameters on discrete problems. Non-elitism in a (1,$λ$) EA combined with a self-adjusting offspring population size $λ$ outperforms common EAs on the multimodal Cliff problem. However, it was shown that this only holds if the success rate $s$ that governs self-adjustment is small enough. Otherwise, even on OneMax, the self-adjusting (1,$λ$) EA stagnates on an easy slope, where frequent successes drive down the offspring population size. We …
The aim of global optimization is to find the global optimum of arbitrary classes of functions, possibly highly multimodal ones. In this paper we focus on the subproblem of global optimization for differentiable functions and we propose an Evolutionary Search-inspired solution where we model point search distributions via Generative Neural Networks. This approach enables us to model diverse and complex search distributions based on which we can efficiently explore complicated objective landscapes. In our experiments we show the practical superiority of our algorithm versus classical Evolutiona…
Multimodal multi-objective problems (MMOPs) commonly arise in real-world problems where distant solutions in decision space correspond to very similar objective values. To obtain all solutions for MMOPs, many multimodal multi-objective evolutionary algorithms (MMEAs) have been proposed. For now, few studies have encompassed most of the recently proposed representative MMEAs and made a comparative comparison. In this study, we first review the related works during the last two decades. Then, we choose 12 state-of-the-art algorithms that utilize different diversity-maintaining techniques and com…
Faculty of Electrical Engineering and Computer Science（电气与计算机科学学院）；VŠB-Technical University of Ostrava（俄斯特拉发VŠB技术大学）；Department of Computer Science and Engineering（计算机科学与工程系）；Shobhit University（肖布希特大学）
For many years, Evolutionary Algorithms (EAs) have been applied to improve Neural Networks (NNs) architectures. They have been used for solving different problems, such as training the networks (adjusting the weights), designing network topology, optimizing global parameters, and selecting features. Here, we provide a systematic brief survey about applications of the EAs on the specific domain of the recurrent NNs named Reservoir Computing (RC). At the beginning of the 2000s, the RC paradigm appeared as a good option for employing recurrent NNs without dealing with the inconveniences of the tr…
By default, the Linux network stack is not configured for highspeed large file transfer. The reason behind this is to save memory resources. It is possible to tune the Linux network stack by increasing the network buffers size for high-speed networks that connect server systems in order to handle more network packets. However, there are also several other TCP/IP parameters that can be tuned in an Operating System (OS). In this paper, we leverage Genetic Algorithms (GAs) to devise a system which learns from the history of the network traffic and uses this knowledge to optimize the current perfo…
A Modality-Aware Cooperative Co-Evolutionary Framework for Multimodal Graph Neural Architecture Search
Department of Computer Science and Information Technology, La Trobe University（计算机科学与信息技术系，拉特罗布大学）；Institute for Sustainable Industries and Liveable Cities, Victoria University（可持续产业与宜居城市研究所，维多利亚大学）
Surrogate assisted evolutionary algorithms (EA) are rapidly gaining popularity where applications of EA in complex real world problem domains are concerned. Although EAs are powerful global optimizers, finding optimal solution to complex high dimensional, multimodal problems often require very expensive fitness function evaluations. Needless to say, this could brand any population-based iterative optimization technique to be the most crippling choice to handle such problems. Use of approximate model or surrogates provides a much cheaper option. However, naturally this cheaper option comes with…
Wasserstein Evolution : Evolutionary Optimization as Phase Transition
University of Science and Technology of China（中国科学技术大学）；Nankai University（南开大学）；National University of Singapore（新加坡国立大学）；Northwestern University（西北大学）；Guizhou University（贵州大学）；Northeastern University（东北大学）；Hong Kong Baptist University（香港浸会大学）
Theoretical Analyses of Multiobjective Evolutionary Algorithms on Multimodal Objectives
School of Computer Science and Technology（计算机科学与技术学院）；International Research Institute for Artificial Intelligence（国际人工智能研究院）；Harbin Institute of Technology（哈尔滨工业大学）；Southern University of Science and Technology（南方科技大学）；Laboratoire d’Informatique (LIX)（信息学实验室）；École Polytechnique（巴黎综合理工学院）；CNRS（法国国家科学研究中心）；Institut Polytechnique de Paris（巴黎理工学院）
Estimate Hitting Time by Hitting Probability for Elitist Evolutionary Algorithms
Nottingham Trent University（诺丁汉特伦特大学）；Southern University of Science and Technology（南方科技大学）；University of Nottingham Ningbo China（诺丁汉大学宁波校区）；Lingnan University（岭南大学）
In this paper we propose a crossover operator for evolutionary algorithms with real values that is based on the statistical theory of population distributions. The operator is based on the theoretical distribution of the values of the genes of the best individuals in the population. The proposed operator takes into account the localization and dispersion features of the best individuals of the population with the objective that these features would be inherited by the offspring. Our aim is the optimization of the balance between exploration and exploitation in the search process. In order to t…
Dynamic and multimodal features are two important properties and widely existed in many real-world optimization problems. The former illustrates that the objectives and/or constraints of the problems change over time, while the latter means there is more than one optimal solution (sometimes including the accepted local solutions) in each environment. The dynamic multimodal optimization problems (DMMOPs) have both of these characteristics, which have been studied in the field of evolutionary computation and swarm intelligence for years, and attract more and more attention. Solving such problems…
A new method has been developed for the correction of the distortions and/or enhanced phase differentiation in Electron Backscatter Diffraction (EBSD) data. Using a multi-modal data approach, the method uses segmented images of the phase of interest (laths, precipitates, voids, inclusions) on images gathered by backscattered or secondary electrons of the same area as the EBSD map. The proposed approach then search for the best transformation to correct their relative distortions and recombines the data in a new EBSD file. Speckles of the features of interest are first segmented in both the EBS…
Despite significant empirical and theoretically supported evidence that non-static parameter choices can be strongly beneficial in evolutionary computation, the question how to best adjust parameter values plays only a marginal role in contemporary research on discrete black-box optimization. This has led to the unsatisfactory situation in which feedback-free parameter selection rules such as the cooling schedule of Simulated Annealing are predominant in state-of-the-art heuristics, while, at the same time, we understand very well that such time-dependent selection rules can only perform worse…
One of the most challenging types of ill-posedness in global optimization is the presence of insensitivity regions in design parameter space, so the identification of their shape will be crucial, if ill-posedness is irrecoverable. Such problems may be solved using global stochastic search followed by post-processing of a local sample and a local objective approximation. We propose a new approach of this type composed of Hierarchic Memetic Strategy (HMS) powered by the Covariance Matrix Adaptation Evolutionary Strategy (CMA-ES) well-known as an effective, self-adaptable stochastic optimization …
The $(1+(λ,λ))$ genetic algorithm, first proposed at GECCO 2013, showed a surprisingly good performance on so me optimization problems. The theoretical analysis so far was restricted to the OneMax test function, where this GA profited from the perfect fitness-distance correlation. In this work, we conduct a rigorous runtime analysis of this GA on random 3-SAT instances in the planted solution model having at least logarithmic average degree, which are known to have a weaker fitness distance correlation. We prove that this GA with fixed not too large population size again obtains runtimes bette…
Zuse Institute Berlin（柏林Zuse研究所）；Technical University of Berlin（柏林技术大学）；Hong Kong Baptist University（香港 Baptist大学）；RIKEN Center for Advanced Intelligence Project（RIKEN高级智能项目中心）
