A Covariance Matrix Self-Adaptation Evolution Strategy for Optimization Under Linear Constraints Patrick Spettel, Hans-Georg Beyer, and Michael Hellwig
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AI, Robots, and Swarms: Issues, Questions, and Recommended Studies
AI, Robots, and Swarms Issues, Questions, and Recommended Studies Andrew Ilachinski January 2017 Approved for Public Release; Distribution Unlimited. This document contains the best opinion of CNA at the time of issue. It does not necessarily represent the opinion of the sponsor. Distribution Approved for Public Release; Distribution Unlimited. Specific authority: N00014-11-D-0323. Copies of this document can be obtained through the Defense Technical Information Center at www.dtic.mil or contact CNA Document Control and Distribution Section at 703-824-2123. Photography Credits: http://www.darpa.mil/DDM_Gallery/Small_Gremlins_Web.jpg; http://4810-presscdn-0-38.pagely.netdna-cdn.com/wp-content/uploads/2015/01/ Robotics.jpg; http://i.kinja-img.com/gawker-edia/image/upload/18kxb5jw3e01ujpg.jpg Approved by: January 2017 Dr. David A. Broyles Special Activities and Innovation Operations Evaluation Group Copyright © 2017 CNA Abstract The military is on the cusp of a major technological revolution, in which warfare is conducted by unmanned and increasingly autonomous weapon systems. However, unlike the last “sea change,” during the Cold War, when advanced technologies were developed primarily by the Department of Defense (DoD), the key technology enablers today are being developed mostly in the commercial world. This study looks at the state-of-the-art of AI, machine-learning, and robot technologies, and their potential future military implications for autonomous (and semi-autonomous) weapon systems. While no one can predict how AI will evolve or predict its impact on the development of military autonomous systems, it is possible to anticipate many of the conceptual, technical, and operational challenges that DoD will face as it increasingly turns to AI-based technologies. -
Redalyc.Assessing the Performance of a Differential Evolution Algorithm In
Red de Revistas Científicas de América Latina, el Caribe, España y Portugal Sistema de Información Científica Villalba-Morales, Jesús Daniel; Laier, José Elias Assessing the performance of a differential evolution algorithm in structural damage detection by varying the objective function Dyna, vol. 81, núm. 188, diciembre-, 2014, pp. 106-115 Universidad Nacional de Colombia Medellín, Colombia Available in: http://www.redalyc.org/articulo.oa?id=49632758014 Dyna, ISSN (Printed Version): 0012-7353 [email protected] Universidad Nacional de Colombia Colombia How to cite Complete issue More information about this article Journal's homepage www.redalyc.org Non-Profit Academic Project, developed under the Open Acces Initiative Assessing the performance of a differential evolution algorithm in structural damage detection by varying the objective function Jesús Daniel Villalba-Moralesa & José Elias Laier b a Facultad de Ingeniería, Pontificia Universidad Javeriana, Bogotá, Colombia. [email protected] b Escuela de Ingeniería de São Carlos, Universidad de São Paulo, São Paulo Brasil. [email protected] Received: December 9th, 2013. Received in revised form: March 11th, 2014. Accepted: November 10 th, 2014. Abstract Structural damage detection has become an important research topic in certain segments of the engineering community. These methodologies occasionally formulate an optimization problem by defining an objective function based on dynamic parameters, with metaheuristics used to find the solution. In this study, damage localization and quantification is performed by an Adaptive Differential Evolution algorithm, which solves the associated optimization problem. Furthermore, this paper looks at the proposed methodology’s performance when using different functions based on natural frequencies, mode shapes, modal flexibilities, modal strain energies and the residual force vector. -
DEPSO: Hybrid Particle Swarm with Differential Evolution Operator
DEPSO: Hybrid Particle Swarm with Differential Evolution Operator Wen-Jun Zhang, Xiao-Feng Xie* Institute of Microelectronics, Tsinghua University, Beijing 100084, P. R. China *Email: [email protected] Abstract - A hybrid particle swarm with differential the particles oscillate in different sinusoidal waves and evolution operator, termed DEPSO, which provide the converging quickly , sometimes prematurely , especially bell-shaped mutations with consensus on the population for PSO with small w[20] or constriction coefficient[3]. diversity along with the evolution, while keeps the self- The concept of a more -or-less permanent social organized particle swarm dynamics, is proposed. Then topology is fundamental to PSO [10, 12], which means it is applied to a set of benchmark functions, and the the pbest and gbest should not be too closed to make experimental results illustrate its efficiency. some particles inactively [8, 19, 20] in certain stage of evolution. The analysis can be restricted to a single Keywords: Particle swarm optimization, differential dimension without loss of generality. From equations evolution, numerical optimization. (1), vid can become small value, but if the |pid-xid| and |pgd-xid| are both small, it cannot back to large value and 1 Introduction lost exploration capability in some generations. Such case can be occured even at the early stage for the Particle swarm optimization (PSO) is a novel multi- particle to be the gbest, which the |pid-xid| and |pgd-xid| agent optimization system (MAOS) inspired by social are zero , and vid will be damped quickly with the ratio w. behavior metaphor [12]. Each agent, call particle, flies Of course, the lost of diversity for |pid-pgd| is typically in a D-dimensional space S according to the historical occured in the latter stage of evolution process. -
Natural Evolution Strategies
Natural Evolution Strategies Daan Wierstra, Tom Schaul, Jan Peters and Juergen Schmidhuber Abstract— This paper presents Natural Evolution Strategies be crucial to find the right domain-specific trade-off on issues (NES), a novel algorithm for performing real-valued ‘black such as convergence speed, expected quality of the solutions box’ function optimization: optimizing an unknown objective found and the algorithm’s sensitivity to local suboptima on function where algorithm-selected function measurements con- stitute the only information accessible to the method. Natu- the fitness landscape. ral Evolution Strategies search the fitness landscape using a A variety of algorithms has been developed within this multivariate normal distribution with a self-adapting mutation framework, including methods such as Simulated Anneal- matrix to generate correlated mutations in promising regions. ing [5], Simultaneous Perturbation Stochastic Optimiza- NES shares this property with Covariance Matrix Adaption tion [6], simple Hill Climbing, Particle Swarm Optimiza- (CMA), an Evolution Strategy (ES) which has been shown to perform well on a variety of high-precision optimization tion [7] and the class of Evolutionary Algorithms, of which tasks. The Natural Evolution Strategies algorithm, however, is Evolution Strategies (ES) [8], [9], [10] and in particular its simpler, less ad-hoc and more principled. Self-adaptation of the Covariance Matrix Adaption (CMA) instantiation [11] are of mutation matrix is derived using a Monte Carlo estimate of the great interest to us. natural gradient towards better expected fitness. By following Evolution Strategies, so named because of their inspira- the natural gradient instead of the ‘vanilla’ gradient, we can ensure efficient update steps while preventing early convergence tion from natural Darwinian evolution, generally produce due to overly greedy updates, resulting in reduced sensitivity consecutive generations of samples. -
Differential Evolution Particle Swarm Optimization for Digital Filter Design
Missouri University of Science and Technology Scholars' Mine Electrical and Computer Engineering Faculty Research & Creative Works Electrical and Computer Engineering 01 Jun 2008 Differential Evolution Particle Swarm Optimization for Digital Filter Design Bipul Luitel Ganesh K. Venayagamoorthy Missouri University of Science and Technology Follow this and additional works at: https://scholarsmine.mst.edu/ele_comeng_facwork Part of the Electrical and Computer Engineering Commons Recommended Citation B. Luitel and G. K. Venayagamoorthy, "Differential Evolution Particle Swarm Optimization for Digital Filter Design," Proceedings of the IEEE Congress on Evolutionary Computation, 2008. CEC 2008. (IEEE World Congress on Computational Intelligence), Institute of Electrical and Electronics Engineers (IEEE), Jun 2008. The definitive version is available at https://doi.org/10.1109/CEC.2008.4631335 This Article - Conference proceedings is brought to you for free and open access by Scholars' Mine. It has been accepted for inclusion in Electrical and Computer Engineering Faculty Research & Creative Works by an authorized administrator of Scholars' Mine. This work is protected by U. S. Copyright Law. Unauthorized use including reproduction for redistribution requires the permission of the copyright holder. For more information, please contact [email protected]. Differential Evolution Particle Swarm Optimization for Digital Filter Design Bipul Luitel, 6WXGHQW0HPEHU ,((( and Ganesh K. Venayagamoorthy, 6HQLRU0HPEHU,((( Abstract— In this paper, swarm and evolutionary algorithms approximate the ideal filter. Since population based have been applied for the design of digital filters. Particle stochastic search methods have proven to be effective in swarm optimization (PSO) and differential evolution particle multidimensional nonlinear environment, all of the swarm optimization (DEPSO) have been used here for the constraints of filter design can be effectively taken care of design of linear phase finite impulse response (FIR) filters. -
Differential Evolution with Deoptim
CONTRIBUTED RESEARCH ARTICLES 27 Differential Evolution with DEoptim An Application to Non-Convex Portfolio Optimiza- tween upper and lower bounds (defined by the user) tion or using values given by the user. Each generation involves creation of a new population from the cur- by David Ardia, Kris Boudt, Peter Carl, Katharine M. rent population members fxi ji = 1,. .,NPg, where Mullen and Brian G. Peterson i indexes the vectors that make up the population. This is accomplished using differential mutation of Abstract The R package DEoptim implements the population members. An initial mutant parame- the Differential Evolution algorithm. This al- ter vector vi is created by choosing three members of gorithm is an evolutionary technique similar to the population, xi1 , xi2 and xi3 , at random. Then vi is classic genetic algorithms that is useful for the generated as solution of global optimization problems. In this note we provide an introduction to the package . vi = xi + F · (xi − xi ), and demonstrate its utility for financial appli- 1 2 3 cations by solving a non-convex portfolio opti- where F is a positive scale factor, effective values for mization problem. which are typically less than one. After the first mu- tation operation, mutation is continued until d mu- tations have been made, with a crossover probability Introduction CR 2 [0,1]. The crossover probability CR controls the fraction of the parameter values that are copied from Differential Evolution (DE) is a search heuristic intro- the mutant. Mutation is applied in this way to each duced by Storn and Price(1997). Its remarkable per- member of the population. -
A Restart CMA Evolution Strategy with Increasing Population Size
1769 A Restart CMA Evolution Strategy With Increasing Population Size Anne Auger Nikolaus Hansen CoLab Computational Laboratory, CSE Lab, ETH Zurich, Switzerland ETH Zurich, Switzerland [email protected] [email protected] Abstract- In this paper we introduce a restart-CMA- 2 The restart CMA-ES evolution strategy, where the population size is increased for each restart (IPOP). By increasing the population The (,uw, )-CMA-ES In this paper we use the (,uw, )- size the search characteristic becomes more global af- CMA-ES thoroughly described in [3]. We sum up the gen- ter each restart. The IPOP-CMA-ES is evaluated on the eral principle of the algorithm in the following and refer to test suit of 25 functions designed for the special session [3] for the details. on real-parameter optimization of CEC 2005. Its perfor- For generation g + 1, offspring are sampled indepen- mance is compared to a local restart strategy with con- dently according to a multi-variate normal distribution stant small population size. On unimodal functions the ) fork=1,... performance is similar. On multi-modal functions the -(9+1) A-()(K ( (9))2C(g)) local restart strategy significantly outperforms IPOP in where denotes a normally distributed random 4 test cases whereas IPOP performs significantly better N(mr, C) in 29 out of 60 tested cases. vector with mean m' and covariance matrix C. The , best offspring are recombined into the new mean value (Y)(0+1) = Z wix(-+w), where the positive weights 1 Introduction w E JR sum to one. The equations for updating the re- The Covariance Matrix Adaptation Evolution Strategy maining parameters of the normal distribution are given in (CMA-ES) [5, 7, 4] is an evolution strategy that adapts [3]: Eqs. -
Neuroevolution Strategies for Episodic Reinforcement Learning ∗ Verena Heidrich-Meisner , Christian Igel
J. Algorithms 64 (2009) 152–168 Contents lists available at ScienceDirect Journal of Algorithms Cognition, Informatics and Logic www.elsevier.com/locate/jalgor Neuroevolution strategies for episodic reinforcement learning ∗ Verena Heidrich-Meisner , Christian Igel Institut für Neuroinformatik, Ruhr-Universität Bochum, 44780 Bochum, Germany article info abstract Article history: Because of their convincing performance, there is a growing interest in using evolutionary Received 30 April 2009 algorithms for reinforcement learning. We propose learning of neural network policies Available online 8 May 2009 by the covariance matrix adaptation evolution strategy (CMA-ES), a randomized variable- metric search algorithm for continuous optimization. We argue that this approach, Keywords: which we refer to as CMA Neuroevolution Strategy (CMA-NeuroES), is ideally suited for Reinforcement learning Evolution strategy reinforcement learning, in particular because it is based on ranking policies (and therefore Covariance matrix adaptation robust against noise), efficiently detects correlations between parameters, and infers a Partially observable Markov decision process search direction from scalar reinforcement signals. We evaluate the CMA-NeuroES on Direct policy search five different (Markovian and non-Markovian) variants of the common pole balancing problem. The results are compared to those described in a recent study covering several RL algorithms, and the CMA-NeuroES shows the overall best performance. © 2009 Elsevier Inc. All rights reserved. 1. Introduction Neuroevolution denotes the application of evolutionary algorithms to the design and learning of neural networks [54,11]. Accordingly, the term Neuroevolution Strategies (NeuroESs) refers to evolution strategies applied to neural networks. Evolution strategies are a major branch of evolutionary algorithms [35,40,8,2,7]. -
The Use of Differential Evolution Algorithm for Solving Chemical Engineering Problems
Rev Chem Eng 2016; 32(2): 149–180 Elena Niculina Dragoi and Silvia Curteanu* The use of differential evolution algorithm for solving chemical engineering problems DOI 10.1515/revce-2015-0042 become more available, and the industry is on the lookout Received July 10, 2015; accepted December 11, 2015; previously for increased productivity and minimization of by-product published online February 8, 2016 formation (Gujarathi and Babu 2009). In addition, there are many problems that involve a simultaneous optimiza- Abstract: Differential evolution (DE), belonging to the tion of many competing specifications and constraints, evolutionary algorithm class, is a simple and power- which are difficult to solve without powerful optimization ful optimizer with great potential for solving different techniques (Tan et al. 2008). In this context, researchers types of synthetic and real-life problems. Optimization have focused on finding improved approaches for opti- is an important aspect in the chemical engineering area, mizing different aspects of real-world problems, includ- especially when striving to obtain the best results with ing the ones encountered in the chemical engineering a minimum of consumed resources and a minimum of area. Optimizing real-world problems supposes two steps: additional by-products. From the optimization point of (i) constructing the model and (ii) solving the optimiza- view, DE seems to be an attractive approach for many tion model (Levy et al. 2009). researchers who are trying to improve existing systems or The model (which is usually represented by a math- to design new ones. In this context, here, a review of the ematical description of the system under consideration) most important approaches applying different versions has three main components: (i) variables, (ii) constraints, of DE (simple, modified, or hybridized) for solving spe- and (iii) objective function (Levy et al. -
Evolutionary Computation Evolution Strategies
Evolutionary computation Lecture Evolutionary Strategies CIS 412 Artificial Intelligence Umass, Dartmouth Evolution strategies Evolution strategies • Another approach to simulating natural • In 1963 two students of the Technical University of Berlin, Ingo Rechenberg and Hans-Paul Schwefel, evolution was proposed in Germany in the were working on the search for the optimal shapes of early 1960s. Unlike genetic algorithms, bodies in a flow. They decided to try random changes in this approach − called an evolution the parameters defining the shape following the example of natural mutation. As a result, the evolution strategy strategy − was designed to solve was born. technical optimization problems. • Evolution strategies were developed as an alternative to the engineer’s intuition. • Unlike GAs, evolution strategies use only a mutation operator. Basic evolution strategy Basic evolution strategy • In its simplest form, termed as a (1+1)- evolution • Step 2 - Randomly select an initial value for each strategy, one parent generates one offspring per parameter from the respective feasible range. The set of generation by applying normally distributed mutation. these parameters will constitute the initial population of The (1+1)-evolution strategy can be implemented as parent parameters: follows: • Step 1 - Choose the number of parameters N to represent the problem, and then determine a feasible range for each parameter: • Step 3 - Calculate the solution associated with the parent Define a standard deviation for each parameter and the parameters: function to be optimized. 1 Basic evolution strategy Basic evolution strategy • Step 4 - Create a new (offspring) parameter by adding a • Step 6 - Compare the solution associated with the normally distributed random variable a with mean zero offspring parameters with the one associated with the and pre-selected deviation δ to each parent parameter: parent parameters. -
Differential Evolution Based Feature Selection and Classifier Ensemble
Differential Evolution based Feature Selection and Classifier Ensemble for Named Entity Recognition Utpal Kumar Sikdar Asif Ekbal∗ Sriparna Saha∗ Department of Computer Science and Engineering Indian Institute of Technology Patna, Patna, India ßutpal.sikdar,asif,sriparna}@iitp.ac.in ABSTRACT In this paper, we propose a differential evolution (DE) based two-stage evolutionary approach for named entity recognition (NER). The first stage concerns with the problem of relevant feature selection for NER within the frameworks of two popular machine learning algorithms, namely Conditional Random Field (CRF) and Support Vector Machine (SVM). The solutions of the final best population provides different diverse set of classifiers; some are effective with respect to recall whereas some are effective with respect to precision. In the second stage we propose a novel technique for classifier ensemble for combining these classifiers. The approach is very general and can be applied for any classification problem. Currently we evaluate the pro- posed algorithm for NER in three popular Indian languages, namely Bengali, Hindi and Telugu. In order to maintain the domain-independence property the features are selected and developed mostly without using any deep domain knowledge and/or language dependent resources. Experi- mental results show that the proposed two stage technique attains the final F-measure values of 88.89%, 88.09% and 76.63% for Bengali, Hindi and Telugu, respectively. The key contribu- tions of this work are two-fold, viz. (i). proposal of differential evolution (DE) based feature selection and classifier ensemble methods that can be applied to any classification problem; and (ii). scope of the development of language independent NER systems in a resource-poor scenario. -
An Introduction to Differential Evolution
An Introduction to Differential Evolution Kelly Fleetwood Synopsis • Introduction • Basic Algorithm • Example • Performance • Applications The Basics of Differential Evolution • Stochastic, population-based optimisation algorithm • Introduced by Storn and Price in 1996 • Developed to optimise real parameter, real valued functions • General problem formulation is: D For an objective function f : X ⊆ R → R where the feasible region X 6= ∅, the minimisation problem is to find x∗ ∈ X such that f(x∗) ≤ f(x) ∀x ∈ X where: f(x∗) 6= −∞ Why use Differential Evolution? • Global optimisation is necessary in fields such as engineering, statistics and finance • But many practical problems have objective functions that are non- differentiable, non-continuous, non-linear, noisy, flat, multi-dimensional or have many local minima, constraints or stochasticity • Such problems are difficult if not impossible to solve analytically • DE can be used to find approximate solutions to such problems Evolutionary Algorithms • DE is an Evolutionary Algorithm • This class also includes Genetic Algorithms, Evolutionary Strategies and Evolutionary Programming Initialisation Mutation Recombination Selection Figure 1: General Evolutionary Algorithm Procedure Notation • Suppose we want to optimise a function with D real parameters • We must select the size of the population N (it must be at least 4) • The parameter vectors have the form: xi,G = [x1,i,G, x2,i,G, . xD,i,G] i = 1, 2, . , N. where G is the generation number. Initialisation Initialisation Mutation Recombination Selection