Evolution in time and space - the parallel genetic algorithm. In Foundations of Genetic Algorithms, How genetic algorithms really work: I. In Parallel Problem Solving from Nature 2, pages 15—26, Prototype and feature selection by sampling and random mutation hill climbing algorithms.
In Proceedings of the eleventh international conference on machine learning, pages — It is an extension of Multi-Restart Search and may be consid- ered a parent of many two-phase search approaches such as the Greedy Randomized Adaptive Search Procedure Section 2.
Iterated Local Search explores a sequence of solutions created as perturbations of the current best solution, the result of which is refined using an embedded heuristic. Iterated Local Search 45 2. No history represents a random walk in a larger neighborhood of the best solution and is the most common implementation of the approach.
The problem seeks a permutation of the order to visit cities called a tour that minimizes the total distance traveled. The optimal tour distance for Berlin52 instance is units. The Iterated Local Search runs for a fixed number of iterations.
The double-bridge move involves partitioning a permutation into 4 pieces a,b,c,d and putting it back together in a specific and jumbled ordering a,d,c,b. Specifically he proposed con- strains on what constitutes an Iterated Local Search algorithm as 1 a single chain of candidate solutions, and 2 the method used to im- prove candidate solutions occurs within a reduced space by a black-box heuristic. Local optima avoidance in depot location.
Journal of the Operational Research Society, —, Local optimization and the travelling salesman problem. Johnson and L. Local Search in Combinatorial Optimization, chapter The travelling salesman problem: A case study in local optimization, pages — Lourenco, O.
Martin, and T. A beginners intro- duction to iterated local search. Martin and S. Combining simulated annealing with local search heuristics. Annals of Operations Research, —75, Martin, S. Otto, and E. Large-step markov chains for the traveling salesman problems. Complex Systems, 5 3 —, Iterated Local Search 49 [8] H. Ramalhinho-Lourenco, O. Handbook of Metaheuristics, chapter Iterated Local Search, pages — Applying iterated local search to the permutation flow shop problem.
Iterated local search for the quadratic assignment prob- lem. Analyzing the run-time behaviour of iterated local search for the TSP. A Local Search algorithm is run until it gets stuck in a local optima. The features from the local optima are evaluated and penalized, the results of which are used in an augmented cost function employed by the Local Search procedure.
The Local Search is repeated a number of times using the last local optima discovered and the augmented cost function that guides exploration away from solutions with features present in discovered local optima. The augmented cost function is only used by the local search procedure, the Guided Local Search algorithm uses the problem specific cost function without augmentation.
Penalties are only updated for those features in a locally optimal solution that maximize utility, updated by adding 1 to the penalty for the future a counter. Guided Local Search 51 Algorithm 2. A suitable domain-specific search procedure should be identified and employed. Stochastic Algorithms the order to visit cities called a tour that minimizes the total distance traveled. The implementation of the algorithm for the TSP was based on the configuration specified by Voudouris in [7].
A TSP-specific local search algorithm is used called 2-opt that selects two points in a permutation and reconnects the tour, potentially untwisting the tour at the selected points. The stopping condition for 2-opt was configured to be a fixed number of non-improving moves. The cost of a local optima was fixed to the approximated value of for the Berlin52 instance.
Guided Local Search was presented by Voudouris and Tsang in a series of technical reports that were later published that described the technique and provided example applications of it to constraint satisfaction [8], combinatorial optimization [5, 10], and function optimization [9]. Mills et al. Guided Local Search 55 2.
Guided Genetic Algorithm. Lau and E. The guided genetic algorithm and its application to the general assignment problems. Extensions to Guided Local Search. Mills, E. Tsang, and J.
Applying an extended guided local search on the quadratic assignment problem. Annals of Operations Research, —, Tsang and C. A generic neural network approach for constraint satisfaction problems. In Taylor G, editor, Neural network applications, pages 12—22, Guided local search for combinatorial optimisation problems.
Voudouris and E. The tunneling algorithm for partial csps and combinatorial optimization problems. Function optimization using guided local search. Guided local search. Guided local search joins the elite in discrete optimisation.
Handbook of Metaheuristics, chapter 7: Guided Local Search, pages — Stochastic Algorithms [13] C. Wang and E. Solving constraint satisfaction problems using neural networks. Variable Neighborhood Search 57 2. It is related to the Iterative Local Search algorithm Section 2.
The strategy is motivated by three principles: 1 a local minimum for one neighborhood structure may not be a local minimum for a different neighborhood structure, 2 a global minimum is a local minimum for all possible neighborhood structures, and 3 local minima are relatively close to global minima for many problem classes. The Pseudocode shows that the systematic search of expanding neighborhoods for a local optimum is abandoned when a global improvement is achieved shown with the Break jump.
Stochastic Algorithms Algorithm 2. The problem seeks a permuta- tion of the order to visit cities called a tour that minimizes the total distance traveled. The Variable Neighborhood Search uses a stochastic 2-opt procedure as the embedded local search. The neighborhood structure used in the search is the number of times the 2-opt procedure is performed on a permutation, between 1 and 20 times. The stopping condition for the local search procedure is a maximum number of iterations without improvement.
The same stop condition is employed by the higher-order Variable Neighborhood Search procedure, although with a lower boundary on the number of non-improving iterations. Variable Neighborhood Search 59 7 perm. The approach is explained in terms of three different variations on the general theme.
Variable Neighborhood Descent VND refers to the use of a Local Search procedure and the deterministic as opposed to stochastic or probabilistic change of neigh- borhood size. Reduced Variable Neighborhood Search RVNS involves performing a stochastic random search within a neighborhood and no refinement via a local search technique. Variable Neighborhood Search 61 Search is the canonical approach described by Mladenovic and Hansen in the seminal paper.
Learn More There are a large number of papers published on Variable Neighborhood Search, its applications and variations. Hansen and Mladenovic provide an overview of the approach that includes its recent history, extensions and a detailed review of the numerous areas of application [4]. For some additional useful overviews of the technique, its principles, and applications, see [1—3].
There are many extensions to Variable Neighborhood Search. Hansen and N. Meta-heuristics, Advances and trends in local search paradigms for optimization, chapter An introduction to Variable neighborhood search, pages — Variable neighborhood search: Prin- ciples and applications.
European Journal of Operational Research, 3 —, Handbook of Applied Optimization, chapter Variable neighbourhood search, pages — Handbook of Metaheuristics, chapter 6: Variable Neighborhood Search, pages — Hansen, N. Variable neighbor- hood decomposition search. Journal of Heuristics, 7 4 —, A variable neighborhood algorithm - a new meta- heuristic for combinatorial optimization. In Abstracts of papers presented at Optimization Days, Stochastic Algorithms [7] N.
Variable neighborhood search. Greedy Randomized Adaptive Search 63 2. The iterative application of an embedded Local Search technique relate the approach to Iterative Local Search Section 2. The strategy of the procedure is centered on the stochastic and greedy step-wise construction mechanism that constrains the selection and order-of-inclusion of the components of a solution based on the value they are expected to provide.
The function involves the step-wise construction of a candidate solution using a stochastically greedy construction process. Stochastic Algorithms from each cycle. The stochastic and greedy step-wise construction of a tour involves evaluating candidate cities by the the cost they contribute as being the next city in the tour.
The algorithm uses a stochastic 2-opt procedure for the Local Search with a fixed number of non-improving iterations as the stopping condition. The general approach was inspired by greedy heuristics by Hart and Shogan [9]. Greedy Randomized Adaptive Search 67 preliminary paper is by Feo and Resende [4], and provides a coherent description of the GRASP technique, an example, and review of early applications. An early application was by Feo, Venkatraman and Bard for a machine scheduling problem [7].
Other early applications to scheduling problems include technical reports [2] later published as [1] and [5] also later published as [6]. Festa and Resende provide an annotated bibliography as a review chapter that provides some needed insight into large amount of study that has gone into the approach [8].
Bard, T. Feo, and S. Feo, J. Bard, and S. Feo and M. A probabilistic heuristic for a computationally difficult set covering problem. Operations Research Letters, —71, Greedy randomized adaptive search procedures.
Feo, K. Sarathy, and J. A GRASP for single machine scheduling with sequence dependent setup costs and lin- ear delay penalties. A grasp for single machine scheduling with sequence dependent setup costs and linear delay penalties. Stochastic Algorithms [7] T. Venkatraman, and J. Festa and M. Hart and A. Semi—greedy heuristics: An empirical study.
Operations Research Letters, —, Pardalos, L. Pitsoulis, and M. Pitsoulis and M. Handbook of Applied Optimiza- tion, chapter Greedy randomized adaptive search procedures, pages — Prais and C. Resende and C.
Handbook of Metaheuristics, chapter Greedy randomized adaptive search procedures, pages — Scatter Search 69 2. It is also sometimes associated with the field of Evolutionary Computation given the use of a population and recombination in the structure of the technique.
Scatter Search is a sibling of Tabu Search Section 2. The principle of the approach is that useful information about the global optima is stored in a diverse and elite set of solutions the reference set and that recombining samples from the set can exploit this information. The strategy involves an iterative process, where a population of diverse and high-quality candidate solutions that are partitioned into subsets and linearly recombined to create weighted centroids of sample-based neighborhoods.
The results of recombination are refined using an embedded heuristic and assessed in the context of the reference set as to whether or not they are retained. The procedure is based on the abstract form presented by Glover as a template for the general class of technique [3], with influences from an application of the technique to function optimization by Glover [3].
Scatter Search 71 2. The optimal solution for this basin function is v1 ,. The algorithm is an implementation of Scatter Search as described in an application of the technique to unconstrained non-linear optimization by Glover [6].
The seeds for initial solutions are generated as random vectors, as opposed to stratified samples. The example was further simplified by not including a restart strategy, and the exclusion of diversity maintenance in the ReferenceSet. A stochastic local search algorithm is used as the embedded heuristic that uses a stochastic step size in the range of half a percent of the search space.
The approach remained idle until it was revisited by Glover and combined with Tabu Search [2]. The modern canonical reference of the approach was proposed by Glover who provides an abstract template of the procedure that may be specialized for a given application domain [3].
Heuristics for integer programming using surrogate con- straints. Decision Sciences, 8 1 —, Tabu search for nonlinear and parametric optimization with links to genetic algorithms. Discrete Applied Mathematics, —, Sprinter, New Ideas in Optimization, chapter Scatter search and path relinking, pages — McGraw-Hill Ltd. Scatter Search 75 [5] F.
Glover, M. Laguna, and R. Fundamentals of scatter search and path relinking. Control and Cybernetics, 39 3 —, Springer-Verlag, Laguna and R. Scatter search: methodology and imple- mentations in C. Laguna, and F. Principles of scatter search. European Journal of Operational Research, 1 —, Tabu Search is a parent for a large family of derivative approaches that introduce memory structures in Metaheuristics, such as Reactive Tabu Search Section 2. The strategy of the approach is to maintain a short term memory of the specific changes of recent moves within the search space and preventing future moves from undoing those changes.
Additional intermediate-term memory structures may be introduced to bias moves toward promising areas of the search space, as well as longer-term memory structures that promote a general diversity in the search across the search space. The listing shows the simple Tabu Search algorithm with short term memory, without intermediate and long term memory management.
Tabu Search 77 Algorithm 2. Strategies may include generating solutions with rarely used components and bi- asing the generation away from the most commonly used solution components. The optimal tour distance for Berli52 instance is units. Stochastic Algorithms with a short term memory structure that executes for a fixed number of iterations.
The starting point for the search is prepared using a random permutation that is refined using a stochastic 2-opt Local Search procedure. The stochastic 2-opt procedure is used as the embedded hill climbing heuristic with a fixed sized candidate list.
The two edges that are deleted in each 2-opt move are stored on the tabu list. Glover provided a seminal overview of the algorithm in a two-part journal article, the first part of which introduced the algorithm and reviewed then-recent applications [6], and the second which focused on advanced topics and open areas of research [7]. Learn More Glover provides a high-level introduction to Tabu Search in the form of a practical tutorial [8], as does Glover and Taillard in a user guide format [10].
The best source of information for Tabu Search is the book dedicated to the approach by Glover and Laguna that covers the principles of the technique in detail as well as an in-depth review of applications [11]. The approach appeared in Science, that considered a modification for its application to continuous function optimization problems [1]. Finally, Gendreau provides an excellent contemporary review of the algorithm, highlighting best practices and application heuristics collected from across the field of study [3].
Cvijovic and J. Taboo search: An approach to the multiple minima problem. Science, —, A parallel tabu search algorithm for large traveling salesman problems. Discrete Applied Mathematics, 3 6 —, Heuristics for integer programming using surrogate constraints. Future paths for integer programming and links to arti- ficial intelligence. Computers and Operations Research, 13 5 — , Tabu search — Part I. Tabu search — Part II. Tabu Search 81 [8] F. Tabu search: A tutorial.
Interfaces, —94, Glover and C. The general employee scheduling problem: an integration of MS and AI. Computers and Operations Research, 13 5 —, Glover and E. Annals of Operations Research, 41 1 :1—28, Glover and M. Tabu Search. Tabu search performance on the symmetric traveling salesman problem. It is an extension of Tabu Search Section 2. The Reactive Tabu Search addresses this objective by explicitly monitoring the search and reacting to the occurrence of cycles and their repetition by adapting the tabu tenure tabu list size.
The strategy of the broader field of Reactive Search Optimization is to automate the process by which a practitioner configures a search procedure by monitoring its online behavior and to use machine learning techniques to adapt a techniques configuration. The Pseudocode is based on the version of the Reactive Tabu Search described by Battiti and Tecchiolli in [9] with supplements like the IsTabu function from [7]. The procedure has been modified for brevity to exude the diversification procedure escape move.
The function permits prohibited moves in the case where a prohibited move is better than the best know solution and the selected admissible move called aspiration. Reactive Tabu Search 83 Algorithm 2. Reactive Tabu Search 85 2. The procedure is based on the code listing described by Battiti and Tecchiolli in [9] with supplements like the IsTabu function from [7].
The implementation does not use efficient memory data structures such as hash tables. The algorithm is initialized with a stochastic 2-opt local search, and the neighborhood is generated as a fixed candidate list of stochastic 2-opt moves. The edges selected for changing in the 2-opt move are stored as features in the tabu list. The example does not implement the escape procedure for search diversification. The technique also used efficient memory structures that were based on an earlier work by Battiti and Tecchiolli that considered a parallel tabu search [6].
Some early application papers by Battiti and Tecchiolli include a comparison to Simulated Annealing applied to the Quadratic Assignment Problem [8], benchmarked on instances of the knapsack problem and N-K models and compared with Repeated Local Minima Search, Simulated Annealing, and Genetic Algorithms [9], and training neural networks on an array of problem instances [10].
Reactive Tabu Search 89 Learn More Reactive Tabu Search was abstracted to a form called Reactive Local Search that considers adaptive methods that learn suitable parameters for heuristics that manage an embedded local search technique [4, 5]. This framework was further extended to the use of any adaptive machine learning techniques to adapt the parameters of an algorithm by reacting to algorithm outcomes online while solving a problem, called Reactive Search [1]. The best reference for this general framework is the book on Reactive Search Optimization by Battiti, Brunato, and Mascia [3].
Additionally, the review chapter by Battiti and Brunato provides a contemporary description [2]. Machine learning methods for parameter tuning in heuristics. Battiti and M. Springer Verlag, 2nd edition, Battiti, M. Brunato, and F. Reactive Search and Intel- ligent Optimization. Reactive local search for the maxi- mum clique problem. Reactive local search for the maximum clique problem.
Algorithmica, 29 4 —, Battiti and G. Parallel biased search for combinatorial optimization: genetic algorithms and tabu. Microprocessors and Microsystems, 16 7 —, The reactive tabu search. Simulated annealing and tabu search in the long run: a comparison on qap tasks. Computer and Mathe- matics with Applications, 28 6 :1—8, Local search with memory: Bench- marking RTS.
Stochastic Algorithms [10] R. Training neural nets with the reactive tabu search. Chapter 3 Evolutionary Algorithms 3.
The process of evolution by means of natural selection descent with modification was proposed by Darwin to account for the variety of life and its suitability adaptive fit for its environment. An encyclopedic algorithm reference, this book is intended for research scientists, engineers, students, and interested amateurs. Each algorithm description provides a working code example in the Ruby Programming Language.
Pro TBB. Written by TBB and parallel programming experts, this book reflects their collective decades of experience in developing and teaching parallel programming with TBB, offering their insights in an approachable manner. Throughout the book the authors present Elements of Robotics. Practitioners, students, and interested amateurs may implement state-of-the-art algorithms to address business or scientific needs, or simply play with the fascinating systems they represent.
This introductory chapter provides relevant background information on Artificial Intelligence and Algorithms. The core of the book provides a large corpus of algorithms presented in a complete and consistent manner.
The final chapter covers some advanced topics to consider once a number of algorithms have been mastered. This book has been designed as a reference text, where specific techniques are looked up, or where the algorithms across whole fields of study can be browsed, rather than being read cover-to-cover.
This is a repository for the book project. Implementing an Artificial Intelligence algorithm is difficult. Algorithm descriptions may be incomplete, inconsistent, and distributed across a number of papers, chapters and even websites. This can result in varied interpretations of algorithms, undue attrition of algorithms, and ultimately bad science. This book is an effort to address these issues by providing a handbook of algorithmic recipes drawn from the fields of Metaheuristics, Biologically Inspired Computation and Computational Intelligence, described in a complete, consistent, and centralized manner.
These standardized descriptions were carefully designed to be accessible, usable, and understandable. Most of the algorithms described were originally inspired by biological and natural systems, such as the adaptive capabilities of genetic evolution and the acquired immune system, and the foraging behaviors of birds, bees, ants and bacteria. An encyclopedic algorithm reference, this book is intended for research scientists, engineers, students, and interested amateurs.
Each algorithm description provides a working code example in the Ruby Programming Language.
0コメント