DOCSLIB.ORG

Clever Algorithms Nature-Inspired Programming Recipes Ii

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Clever Algorithms Nature-Inspired Programming Recipes Ii Jason Brownlee Clever Algorithms Nature-Inspired Programming Recipes ii Jason Brownlee, PhD Jason Brownlee studied Applied Science at Swinburne University in Melbourne, Australia, going on to complete a Masters in Information Technology focusing on Niching Genetic Algorithms, and a PhD in the field of Artificial Immune Systems. Jason has worked for a number of years as a Consultant and Software Engineer for a range of Corporate and Government organizations. When not writing books, Jason likes to compete in Machine Learning competitions. Cover Image © Copyright 2011 Jason Brownlee. All Reserved. Clever Algorithms: Nature-Inspired Programming Recipes © Copyright 2011 Jason Brownlee. Some Rights Reserved. Revision 2. 16 June 2012 ISBN: 978-1-4467-8506-5 This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 2.5 Australia License. The full terms of the license are located online at http://creativecommons.org/licenses/by-nc-sa/2.5/au/legalcode Webpage Source code and additional resources can be downloaded from the books companion website online at http://www.CleverAlgorithms.com Contents Foreword vii Preface ix I Background1 1 Introduction3 1.1 What is AI.........................3 1.2 Problem Domains...................... 10 1.3 Unconventional Optimization............... 13 1.4 Book Organization..................... 17 1.5 How to Read this Book.................. 20 1.6 Further Reading...................... 21 1.7 Bibliography........................ 22 II Algorithms 27 2 Stochastic Algorithms 29 2.1 Overview.......................... 29 2.2 Random Search....................... 30 2.3 Adaptive Random Search................. 34 2.4 Stochastic Hill Climbing.................. 40 2.5 Iterated Local Search.................... 44 2.6 Guided Local Search.................... 50 2.7 Variable Neighborhood Search............... 57 2.8 Greedy Randomized Adaptive Search........... 63 2.9 Scatter Search....................... 69 2.10 Tabu Search......................... 76 2.11 Reactive Tabu Search................... 82 iii iv Contents 3 Evolutionary Algorithms 91 3.1 Overview.......................... 91 3.2 Genetic Algorithm..................... 96 3.3 Genetic Programming................... 103 3.4 Evolution Strategies.................... 113 3.5 Differential Evolution................... 119 3.6 Evolutionary Programming................ 125 3.7 Grammatical Evolution.................. 131 3.8 Gene Expression Programming.............. 139 3.9 Learning Classifier System................. 146 3.10 Non-dominated Sorting Genetic Algorithm........ 157 3.11 Strength Pareto Evolutionary Algorithm......... 165 4 Physical Algorithms 173 4.1 Overview.......................... 173 4.2 Simulated Annealing.................... 175 4.3 Extremal Optimization................... 181 4.4 Harmony Search...................... 188 4.5 Cultural Algorithm..................... 194 4.6 Memetic Algorithm..................... 200 5 Probabilistic Algorithms 207 5.1 Overview.......................... 207 5.2 Population-Based Incremental Learning......... 211 5.3 Univariate Marginal Distribution Algorithm....... 216 5.4 Compact Genetic Algorithm................ 220 5.5 Bayesian Optimization Algorithm............. 224 5.6 Cross-Entropy Method................... 232 6 Swarm Algorithms 237 6.1 Overview.......................... 237 6.2 Particle Swarm Optimization............... 241 6.3 Ant System......................... 247 6.4 Ant Colony System..................... 254 6.5 Bees Algorithm....................... 261 6.6 Bacterial Foraging Optimization Algorithm....... 266 7 Immune Algorithms 275 7.1 Overview.......................... 275 7.2 Clonal Selection Algorithm................ 280 7.3 Negative Selection Algorithm............... 288 7.4 Artificial Immune Recognition System.......... 295 7.5 Immune Network Algorithm................ 304 7.6 Dendritic Cell Algorithm.................. 312 v 8 Neural Algorithms 319 8.1 Overview.......................... 319 8.2 Perceptron......................... 323 8.3 Back-propagation...................... 328 8.4 Hopfield Network...................... 336 8.5 Learning Vector Quantization............... 342 8.6 Self-Organizing Map.................... 348 III Extensions 357 9 Advanced Topics 359 9.1 Programming Paradigms.................. 360 9.2 Devising New Algorithms................. 370 9.3 Testing Algorithms..................... 382 9.4 Visualizing Algorithms................... 389 9.5 Problem Solving Strategies................ 402 9.6 Benchmarking Algorithms................. 417 IV Appendix 427 A Ruby: Quick-Start Guide 429 A.1 Overview.......................... 429 A.2 Language Basics...................... 429 A.3 Ruby Idioms........................ 433 A.4 Bibliography........................ 435 Errata 437 Index 439 vi Contents Foreword I am delighted to write this foreword. This book, a reference where one can look up the details of most any algorithm to find a clear unambiguous description, has long been needed and here it finally is. A concise reference that has taken many hours to write but which has the capacity to save vast amounts of time previously spent digging out original papers. I have known the author for several years and have had experience of his amazing capacity for work and the sheer quality of his output, so this book comes as no surprise to me. But I hope it will be a surprise and delight to you, the reader for whom it has been written. But useful as this book is, it is only a beginning. There are so many algorithms that no one author could hope to cover them all. So if you know of an algorithm that is not yet here, how about contributing it using the same clear and lucid style? Professor Tim Hendtlass Complex Intelligent Systems Laboratory Faculty of Information and Communication Technologies Swinburne University of Technology Melbourne, Australia 2010 vii viii Foreword Preface About the book The need for this project was born of frustration while working to- wards my PhD. I was investigating optimization algorithms and was implementing a large number of them for a software platform called the Optimization Algorithm Toolkit (OAT)1. Each algorithm required considerable effort to locate the relevant source material (from books, papers, articles, and existing implementations), decipher and interpret the technique, and finally attempt to piece together a working imple- mentation. Taking a broader perspective, I realized that the communication of algorithmic techniques in the field of Artificial Intelligence was clearly a difficult and outstanding open problem. Generally, algorithm descrip- tions are: • Incomplete: many techniques are ambiguously described, partially described, or not described at all. • Inconsistent: a given technique may be described using a variety of formal and semi-formal methods that vary across different tech- niques, limiting the transferability of background skills an audience requires to read a technique (such as mathematics, pseudocode, program code, and narratives). An inconsistent representation for techniques means that the skills used to understand and internal- ize one technique may not be transferable to realizing different techniques or even extensions of the same technique. • Distributed: the description of data structures, operations, and parameterization of a given technique may span a collection of papers, articles, books, and source code published over a number of years, the access to which may be restricted and difficult to obtain. 1OAT located at http://optalgtoolkit.sourceforge.net ix x Preface For the practitioner, a badly described algorithm may be simply frustrating, where the gaps in available information are filled with intuition and `best guess'. At the other end of the spectrum, a badly described algorithm may be an example of bad science and the failure of the scientific method, where the inability to understand and implement a technique may prevent the replication of results, the application, or the investigation and extension of a technique. The software I produced provided a first step solution to this problem: a set of working algorithms implemented in a (somewhat) consistent way and downloaded from a single location (features likely provided by any library of artificial intelligence techniques). The next logical step needed to address this problem is to develop a methodology that anybody can follow. The strategy to address the open problem of poor algorithm communication is to present complete algorithm descriptions (rather than just implementations) in a consistent manner, and in a centralized location. This book is the outcome of developing such a strategy that not only provides a methodology for standardized algorithm descriptions, but provides a large corpus of complete and consistent algorithm descriptions in a single centralized location. The algorithms described in this work are practical, interesting, and fun, and the goal of this project was to promote these features by making algorithms from the field more accessible, usable, and understandable. This project was developed over a number years through a lot of writing, discussion, and revision. This book has been released under a permissive license that encourages the reader to explore new and creative ways of further communicating its message and content. I hope that this project has succeeded in some small way and that you too can enjoy applying, learning, and playing with Clever Algorithms. Jason Brownlee Melbourne, Australia 2011 Acknowledgments This book could not have been completed without
Load more

Recommended publications
  • Guided Local Search
    GUIDED LOCAL SEARCH Christos Voudouris, Edward P. K. Tsang and Abdullah Alsheddy Abstract Combinatorial explosion problem is a well known phenomenon that pre- vents complete algorithms from solving many real-life combinatorial optimization problems. In many situations, heuristic search methods are needed. This chapter de- scribes the principles of Guided Local Search (GLS) and Fast Local Search (FLS) and surveys their applications. GLS is a penalty-based meta-heuristic algorithm that sits on top of other local search algorithms, with the aim to improve their efficiency and robustness. FLS is a way of reducing the size of the neighbourhood to improve the efficiency of local search. The chapter also provides guidance for implement- ing and using GLS and FLS. Four problems, representative of general application categories, are examined with detailed information provided on how to build a GLS- based method in each case. Key words: Heuristic Search, Meta-Heuristics, Penalty-based Methods, Guided Local Search, Tabu Search, Constraint Satisfaction. 1 INTRODUCTION Many practical problems are NP-hard in nature, which means complete, construc- tive search is unlikely to satisfy our computational demand. For example, suppose Christos Voudouris Group Chief Technology Office, BT plc, Orion Building, mlb1/pp12, Marthlesham Heath, Ipswich, IP5 3RE, United Kingdom, e-mail: [email protected] Edward P. K. Tsang Department of Computer Science, Univeristy of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom, e-mail: [email protected] Abdullah Alsheddy Department of Computer Science, Univeristy of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom, e-mail: [email protected] 1 2 Christos Voudouris, Edward P.
    [Show full text]
  • (Stochastic) Local Search Algorithms
    DM841 DISCRETE OPTIMIZATION Part 2 – Heuristics (Stochastic) Local Search Algorithms Marco Chiarandini Department of Mathematics & Computer Science University of Southern Denmark Local Search Algorithms Basic Algorithms Outline Local Search Revisited 1. Local Search Algorithms 2. Basic Algorithms 3. Local Search Revisited Components 2 Local Search Algorithms Basic Algorithms Outline Local Search Revisited 1. Local Search Algorithms 2. Basic Algorithms 3. Local Search Revisited Components 3 Local Search Algorithms Basic Algorithms Local Search Algorithms Local Search Revisited Given a (combinatorial) optimization problem Π and one of its instances π: 1. search space S(π) I specified by the definition of (finite domain, integer) variables and their values handling implicit constraints I all together they determine the representation of candidate solutions I common solution representations are discrete structures such as: sequences, permutations, partitions, graphs (e.g., for SAT: array, sequence of truth assignments to propositional variables) Note: solution set S 0(π) ⊆ S(π) (e.g., for SAT: models of given formula) 4 Local Search Algorithms Basic Algorithms Local Search Algorithms (cntd) Local Search Revisited 2. evaluation function fπ : S(π) ! R I it handles the soft constraints and the objective function (e.g., for SAT: number of false clauses) S(π) 3. neighborhood function, Nπ : S ! 2 I defines for each solution s 2 S(π) a set of solutions N(s) ⊆ S(π) that are in some sense close to s. (e.g., for SAT: neighboring variable assignments differ in the truth value of exactly one variable) 5 Local Search Algorithms Basic Algorithms Local Search Algorithms (cntd) Local Search Revisited Further components [according to [HS]] 4.
    [Show full text]
  • Exploring High-Order Neighborhoods by Pattern Mining and Injection
    PILS: Exploring high-order neighborhoods by pattern mining and injection Florian Arnolda, ´Italo Santanab, Kenneth S¨orensena, Thibaut Vidalb∗ a University of Antwerp, Department of Engineering Management, Belgium fflorian.arnold,[email protected] bDepartamento de Inform´atica,Pontif´ıciaUniversidade Cat´olicado Rio de Janeiro (PUC-Rio) fisantana,[email protected] Abstract. We introduce pattern injection local search (PILS), an optimization strategy that uses pattern mining to explore high-order local-search neighborhoods, and illustrate its application on the vehicle routing problem. PILS operates by storing a limited number of frequent patterns from elite solutions. During the local search, each pattern is used to define one move in which 1) incompatible edges are disconnected, 2) the edges defined by the pattern are reconnected, and 3) the remaining solution fragments are optimally reconnected. Each such move is accepted only in case of solution improvement. As visible in our experiments, this strategy results in a new paradigm of local search, which complements and enhances classical search approaches in a controllable amount of computational time. We demonstrate that PILS identifies useful high-order moves (e.g., 9-opt and 10-opt) which would otherwise not be found by enumeration, and that it significantly improves the performance of state-of-the-art population-based and neighborhood-centered metaheuristics. Keywords. Local search, Pattern mining, Combinatorial optimization, Vehicle routing problem ∗ Corresponding author 1. Introduction Since the \no free lunch" theorem [46], it is known that no method can | on average | perform arXiv:1912.11462v1 [cs.AI] 24 Dec 2019 better than any other method on all possible problems.
    [Show full text]
  • On the Design of (Meta)Heuristics
    On the design of (meta)heuristics Tony Wauters CODeS Research group, KU Leuven, Belgium There are two types of people • Those who use heuristics • And those who don’t ☺ 2 Tony Wauters, Department of Computer Science, CODeS research group Heuristics Origin: Ancient Greek: εὑρίσκω, "find" or "discover" Oxford Dictionary: Proceeding to a solution by trial and error or by rules that are only loosely defined. Tony Wauters, Department of Computer Science, CODeS research group 3 Properties of heuristics + Fast* + Scalable* + High quality solutions* + Solve any type of problem (complex constraints, non-linear, …) - Problem specific (but usually transferable to other problems) - Cannot guarantee optimallity * if well designed 4 Tony Wauters, Department of Computer Science, CODeS research group Heuristic types • Constructive heuristics • Metaheuristics • Hybrid heuristics • Matheuristics: hybrid of Metaheuristics and Mathematical Programming • Other hybrids: Machine Learning, Constraint Programming,… • Hyperheuristics 5 Tony Wauters, Department of Computer Science, CODeS research group Constructive heuristics • Incrementally construct a solution from scratch. • Easy to understand and implement • Usually very fast • Reasonably good solutions 6 Tony Wauters, Department of Computer Science, CODeS research group Metaheuristics A Metaheuristic is a high-level problem independent algorithmic framework that provides a set of guidelines or strategies to develop heuristic optimization algorithms. Instead of reinventing the wheel when developing a heuristic
    [Show full text]
  • A Novel LP-Based Local Search Technique – Fast and Quite Good –
    A Novel LP-based Local Search Technique – Fast and Quite Good – Vom Fachbereich Informatik der Technische Universit¨at Darmstadt zur Erlangung des akademischen Grades eines Dr. rer. nat. genehmigte Dissertation von Herrn Alaubek Avdil (M.Sc.) aus der Ulaanbaatar, Mongolei Referent: Professor Dr. Karsten Weihe Korreferent: Professor Dr. Matthias M¨uller-Hannemann Tag der Einreichung: 04. Juni 2009 Tag der m¨undlichen Pr¨ufung: 17. Juli 2009 Darmstadt 2009 D 17 ii Acknowledgments I want to express my deep and sincere gratitude to my supervisor Prof. Karsten Weihe for enabling my doctoral study, inspiring with scientific work and motivating and providing me pleasant research and work atmosphere. Without his trust and encouragement my research would not be done and this theses would not exist. I am extremely grateful to Prof. Matthias M¨uller-Hannemann for his invaluable support and advice on my research, excellent and critical review to improve the presentation of my work, and for his friendship, and making it possible for my young family be close with me during my doctoral study in Germany. I would like to express my warm and sincere thanks to the colleagues and members of Algorithmics Group at the Department of Computer Science of Technische Universit¨at Darmstadt for their support and valuable comments on my research. My special ackno- wledgment goes to Dr. Roland Martin for his unforgettable support and encouragement during my doctoral study, and his detailed review and constructive criticism during the writing process of my dissertation. I wish to extend my warmest thanks to all people, who have helped me with my work at the Department of Computer Science at Technische Universit¨at Darmstadt.
    [Show full text]
  • Coupling Ant Colony System with Local Search
    UNIVERSITE´ LIBRE DE BRUXELLES Ecole´ Polytechnique de Bruxelles IRIDIA - Institut de Recherches Interdisciplinaires et de D´eveloppements en Intelligence Artificielle Coupling Ant Colony System with Local Search Luca Maria Gambardella Promoteur de Th`ese: Prof. Marco DORIGO Th`esepr´esent´eeen vue de l'obtention du titre de Docteur en Sciences de l'Ing´enieur Ann´eeacad´emique2014-2015 2 Summary In the last decades there has been a lot of interest in computational models and algorithms inspired by the observation of natural systems. Nature seems to be very good at inventing processes that have many of the qualities we would like to be able to put into artificial systems. Consider for example genetic algorithms and evolutionary computation (Holland 1975): by reproducing in a simplified way the approach taken by Nature to develop living beings, researchers were able to develop both control systems for learning autonomous agents, and robust optimiza- tion algorithms for function optimization or combinatorial optimization. We can also think of work in reinforcement learning (Kaelbling et al. 1996): again, the observation of how animals learn to accomplish some simple tasks has suggested a useful and productive set of reinforcement- based learning algorithms. There are many such examples, some already very widespread, like simulated annealing (Kirkpatrick et al. 1983), ge- netic algorithms (Holland 1975), neural networks (Rumelhart et al. 1986), and others that still exist mostly in research labs, like immune networks (Bersini & F.Varela 1993) and classifier systems (Holland & Reitman 1978). In this thesis we present another ethological approach to combinatorial optimization, which has been inspired by the observation of ant colonies: the Ant Colony System (ACS, Gambardella & Dorigo 1996; Dorigo & Gambardella 1997).
    [Show full text]
  • A Guided Tabu Search for the Vehicle Routing Problem with Two-Dimensional Loading Constraints
    Available online at www.sciencedirect.com European Journal of Operational Research 195 (2009) 729–743 www.elsevier.com/locate/ejor A Guided Tabu Search for the Vehicle Routing Problem with two-dimensional loading constraints Emmanouil E. Zachariadis a, Christos D. Tarantilis b,*, Christos T. Kiranoudis a a Department of Process Analysis and Plant Design, Department of Chemical Engineering, National Technical University of Athens, Athens, Greece b Department of Management Science and Technology, Athens University of Economics and Business, Hydras Street 28, Athens 11362, Greece Received 12 January 2007; accepted 31 May 2007 Available online 21 November 2007 Abstract We present a metaheuristic methodology for the Capacitated Vehicle Routing Problem with two-dimensional loading constraints (2L- CVRP). 2L-CVRP is a generalisation of the Capacitated Vehicle Routing Problem, in which customer demand is formed by a set of two- dimensional, rectangular, weighted items. The purpose of this problem is to produce the minimum cost routes, starting and terminating at a central depot, to satisfy the customer demand. Furthermore, the transported items must be feasibly packed into the loading surfaces of the vehicles. We propose a metaheuristic algorithm which incorporates the rationale of Tabu Search and Guided Local Search. The loading aspects of the problem are tackled using a collection of packing heuristics. To accelerate the search process, we reduce the neigh- bourhoods explored, and employ a memory structure to record the loading feasibility information. Extensive experiments were con- ducted to calibrate the algorithmic parameters. The effectiveness of the proposed metaheuristic algorithm was tested on benchmark instances and led to several new best solutions.
    [Show full text]
  • Ant Colony Optimization Marco Dorigo and Thomas Stützle Ant Colony Optimization
    Ant Colony.qxd 6/9/04 12:15 PM Page 1 Ant Colony Optimization Marco Dorigo and Thomas Stützle Optimization Ant Colony The complex social behaviors of ants have been much studied by science, and computer scientists are now finding that these behavior patterns can provide models for solving difficult combinatorial optimization problems. The attempt to develop algorithms inspired by one aspect of ant behavior, the ability to find what computer scientists would call shortest paths, has become the field of ant colony optimization (ACO), the most successful and widely recognized algorithmic Ant Colony technique based on ant behavior. This book presents an overview of this rapidly growing field, from its theoretical inception to practical applications, including descriptions of many available ACO algorithms and their uses. The book first describes the translation of observed ant behavior into working optimization algorithms. The ant Optimization colony metaheuristic is then introduced and viewed in the general context of combinatorial optimization. This is followed by a detailed description and guide to all major ACO algorithms and a report on current theoretical findings. The book surveys ACO applications now in use, including routing, assignment, scheduling, subset, machine learning, and bioin- formatics problems. AntNet, an ACO algorithm designed for the network routing problem, is described in detail. The authors conclude by summarizing the progress in the field and outlining future research directions. Each chapter ends Marco Dorigo and Thomas Stützle with bibliographic material, bullet points setting out important ideas covered in the chapter, and exercises. Ant Colony Optimization will be of interest to academic and industry researchers, graduate students, and practitioners who wish to learn how to implement ACO algorithms.
    [Show full text]
  • Subgradient Based Multiple-Starting-Point Algorithm for Non-Smooth Optimization of Analog Circuits
    Subgradient Based Multiple-Starting-Point Algorithm for Non-Smooth Optimization of Analog Circuits Wenlong Lv1, Fan Yang1∗, Changhao Yan1, Dian Zhou1,2 and Xuan Zeng1∗ 1State Key Lab of ASIC & System, School of Microelectronics, Fudan University, Shanghai, P. R. China 2Department of Electrical Engineering, University of Texas at Dallas, Richardson, TX, U.S.A. Abstract—Starting from a set of starting points, the multiple- is to transform the general polynomial optimization problem starting-point optimization searches the local optimums by to convex programming by Semidefinite-Programming (SDP) gradient-guided local search. The global optimum is selected relaxations [4]. The advantage of model based algorithms from these local optimums. The region-hit property of the multiple-starting-point optimization makes the multiple-starting- is that given the circuit performance models, the optimal point approach more likely to reach the global optimum. solutions can be found very efficiently even for large-scale However, for non-smooth objective functions, e.g., worst-case problems. But what limits their usage is the generation of optimization, the traditional gradient based local search methods accurate performance models. Even with a large number of may stuck at non-smooth points, even if the objective function simulations, the accuracy of the generated performance models is smooth “almost everywhere”. In this paper, we propose a subgradient based multiple-starting-point algorithm for non- still cannot be guaranteed for the whole design space. smooth optimization of analog circuits. Subgradients instead of The simulation based analog circuit optimization methods traditional gradients are used to guide the local search of the non- require no explicit analytical performance models.
    [Show full text]
  • Hybrid Metaheuristics an Emerging Approach to Optimization.Pdf
    Christian Blum, Maria Jose´ Blesa Aguilera, Andrea Roli and Michael Sampels (Eds.) Hybrid Metaheuristics Studies in Computational Intelligence, Volume 114 Editor-in-chief Prof. Janusz Kacprzyk Systems Research Institute Polish Academy of Sciences ul. Newelska 6 01-447 Warsaw Poland E-mail: [email protected] Further volumes of this series can be found on our Vol. 104. Maria Virvou and Lakhmi C. Jain (Eds.) homepage: springer.com Intelligent Interactive Systems in Knowledge-Based Environment, 2008 Vol. 93. Manolis Wallace, Marios Angelides and Phivos ISBN 978-3-540-77470-9 Mylonas (Eds.) Vol. 105. Wolfgang Guenthner Advances in Semantic Media Adaptation and Enhancing Cognitive Assistance Systems with Inertial Personalization, 2008 Measurement Units, 2008 ISBN 978-3-540-76359-8 ISBN 978-3-540-76996-5 Vol. 94. Arpad Kelemen, Ajith Abraham and Yuehui Chen ¨ (Eds.) Vol. 106. Jacqueline Jarvis, Dennis Jarvis, Ralph Ronnquist Computational Intelligence in Bioinformatics, 2008 and Lakhmi C. Jain (Eds.) ISBN 978-3-540-76802-9 Holonic Execution: A BDI Approach, 2008 ISBN 978-3-540-77478-5 Vol. 95. Radu Dogaru Systematic Design for Emergence in Cellular Nonlinear Vol. 107. Margarita Sordo, Sachin Vaidya and Lakhmi C. Jain Networks, 2008 (Eds.) ISBN 978-3-540-76800-5 Advanced Computational Intelligence Paradigms in Healthcare - 3, 2008 Vol. 96. Aboul-Ella Hassanien, Ajith Abraham and Janusz ISBN 978-3-540-77661-1 Kacprzyk (Eds.) Computational Intelligence in Multimedia Processing: Vol. 108. Vito Trianni Recent Advances, 2008 Evolutionary Swarm Robotics, 2008 ISBN 978-3-540-76826-5 ISBN 978-3-540-77611-6 Vol. 97. Gloria Phillips-Wren, Nikhil Ichalkaranje and Vol.
    [Show full text]
  • Word, the GA Is Able to Generate Near Optimal Solutions with Some Unlike Local Search Methods, the Genetic Algorithm Method Compromise in the CPU Time
    Comparing Genetic Algorithm and Guided Local Search Methods by Symmetric TSP Instances Mehrdad Nojoumian Divya K. Nair David R. Cheriton School of Computer Science David R. Cheriton School of Computer Science University of Waterloo University of Waterloo Waterloo, Canada Waterloo, Canada [email protected] [email protected] ABSTRACT methods proposed for finding better-quality solutions for the TSP This paper aims at comparing Genetic Algorithm (GA) and problem within an acceptable time limit. Although, GA and LS Guided Local Search (GLS) methods so as to scrutinize their methods aim at achieving the same goal of yielding near optimal behaviors. Authors apply the GLS program with the Fast Local solutions for the hard optimization problems, we are interested to Search (FLS), developed at University of Essex [24], and analyze their problem solving behaviors, by executing two classes implement a genetic algorithm with partially-mapped and order of methods on the standard s-TSP instances. The main concern crossovers, reciprocal and inversion mutations, and rank and regarding local search is the escape from the local optimum, once tournament selections in order to experiment with various it is caught in the local optimum, it becomes almost impossible to Travelling Salesman Problems. The paper then ends up with two advance further to more optimal solutions. This issue is handled prominent conclusions regarding the performance of these meta- easily by an existing array of techniques called meta-heuristics heuristic techniques over wide range of symmetric-TSP instances. which are built on top of local search methods. One of the First, the GLS-FLS strategy on the s-TSP instances yields the simplest and the oldest meta-heuristic is the Repeated Local most promising performance in terms of the near-optimality and Search [1] where a few restarts are applied each time the search is the mean CPU time.
    [Show full text]
  • Reactive Search and Intelligent Optimization
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Unitn-eprints Research DEPARTMENT OF INFORMATION AND COMMUNICATION TECHNOLOGY 38100 Povo — Trento (Italy), Via Sommarive 14 http://dit.unitn.it/ REACTIVE SEARCH AND INTELLIGENT OPTIMIZATION Roberto Battiti, Mauro Brunato, and Franco Mascia Technical Report # DIT-07-049 Reactive Search and Intelligent Optimization Roberto Battiti, Mauro Brunato and Franco Mascia Dipartimento di Informatica e Telecomunicazioni, Universit`adi Trento, Italy Version 1.02, July 6, 2007 Technical Report DIT-07-049, Universit`adi Trento, July 2007 Available at: http://reactive-search.org/ Email for correspondence: [email protected] ii Contents Preface 1 1 Introduction 1 1.1 Parameter tuning and intelligent optimization . .............. 2 1.2 Bookoutline ..................................... ... 3 Bibliography ....................................... .... 4 2 Reacting on the neighborhood 5 2.1 Local search based on perturbation . ......... 5 2.2 Learninghowtoevaluatetheneighborhood . .......... 7 2.3 Learning the appropriate neighborhood in variable neighborhood search . 8 2.4 Iteratedlocalsearch. ....... 12 Bibliography ....................................... 16 3 Reacting on the annealing schedule 19 3.1 Stochasticity in local moves and controlled worsening of solution values . 19 3.2 SimulatedAnnealingandAsymptotics . ......... 19 3.2.1 Asymptoticconvergenceresults . ....... 20 3.3 Online learning strategies in simulated annealing . .............. 22 3.3.1 Combinatorial optimization problems . ......... 23 3.3.2 Global optimization of continuous functions . ........... 24 Bibliography ....................................... 25 4 Reactive prohibitions 27 4.1 Prohibitions for diversification (Tabu Search) . .............. 27 4.1.1 FormsofTabuSearch. ............. ............. .. 28 4.1.2 Dynamicalsystems .. ............. ............. .. 28 4.1.3 An example of Fixed Tabu Search . 29 4.1.4 Relation between prohibition and diversification . ............ 30 4.1.5 Howtoescapefromanattractor .
    [Show full text]