## Reactive search: machine learning for memory-based heuristics (2005)

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Venue: | Teofilo F. Gonzalez (Ed.), Approximation Algorithms and Metaheuristics, Taylor & Francis Books (CRC Press |

Citations: | 13 - 5 self |

### BibTeX

@TECHREPORT{Battiti05reactivesearch:,

author = {Roberto Battiti and Mauro Brunato},

title = {Reactive search: machine learning for memory-based heuristics},

institution = {Teofilo F. Gonzalez (Ed.), Approximation Algorithms and Metaheuristics, Taylor & Francis Books (CRC Press},

year = {2005}

}

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### Abstract

1 Introduction: the role of the user in heuristics Most state-of-the-art heuristics are characterized by a certain number of choices and free parameters, whose appropriate setting is a subject that raises issues of research methodology [5, 41, 51]. In some cases, these parameters are tuned through a feedback loop that includes the user as a crucial learning component: depending on preliminary algorithm tests some parameter values are changed by the

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3527 | Optimization by Simulated Annealing
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Citation Context ...ydon't benefit from the deep and wide theoretical background that covers Markovian algorithms. However, asymptotic convergence results of many Markovian search algorithms, such as Simulated Annealing =-=[48]-=-, areoften irrelevant for their application to optimization. As an example, a comparison of Simulated Annealing and Reactive Search has been presented in [12, 13].In any finite-time approximation one ... |

1692 | A theory of the learnable
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Citation Context ...tive documentation of the tuning process when the algorithm is presented to the scientific community. Although formal learning frameworks do exist in the CS community (notably, the PAC learning model =-=[67, 46]-=-) one should not reach the conclusion that these models can be simply adapted to the new context. On the contrary, the theoretical framework of computational learning theory and machine learning is ve... |

1270 |
Combinatorial Optimization: Algorithms and Complexity
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Citation Context ...l solutions are generated) and in branch and bound algorithms (subtrees are not considered if the leaves cannot correspond to better solutions). For many examples of such techniques, see the textbook =-=[57]-=-. The renaissance and full blossoming of “intelligent prohibition-based heuristics” starting from the late eighties is greatly due to the role of F. Glover in the proposal and diffusion of a rich vari... |

811 | Ant System:Optimization by a Colony of Cooperating Agent
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Citation Context ...uted computation, and the use of a constructive greedy heuristic. For example ”pheromone trail” information to perform modifications on solutions for the quadratic assignment problem is considered in =-=[27, 34]-=-. Dynamic local search, which increases penalties of some solution components to move the tentative solution away from a given local minimum can also be considered as a form of learning based on the p... |

596 |
An Introduction to Computational Learning Theory
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Citation Context ...tive documentation of the tuning process when the algorithm is presented to the scientific community. Although formal learning frameworks do exist in the CS community (notably, the PAC learning model =-=[67, 46]-=-) one should not reach the conclusion that these models can be simply adapted to the new context. On the contrary, the theoretical framework of computational learning theory and machine learning is ve... |

510 |
Optimization by simulated annealing: an experimental evaluation
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Citation Context ...sitive heuristics Randomized Markovian local search algorithms have enjoyed a long period of scientific and applicative excitement, in particular see the flourishing literature on Simulated Annealing =-=[48, 44]-=-. SA generates a Markov chain: the successor of the current point is chosen stochastically, with a probability that does not depend on the previous history (standard SA does not learn). A consequence ... |

472 |
Tabu Search - Part I
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Citation Context ...ms [63]. 2 Reactive Search applied to Tabu Search (RTS) In this Section, we illustrate the potential of Reactive Search by installing a reaction mechanism on the prohibition period T of a Tabu Search =-=[35]-=- algorithm. For the complete description of Tabu Search, the Reader can refer to the dedicated Chapter of this book. 2.1 Prohibition-based diversification: Tabu Search The Tabu Search meta-heuristic i... |

275 | A Survey of Optimization by Building and Using Probabilistic Models
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Citation Context ...ion of interesting related papers. Probabilistic methods that explicitly maintain statistics about the search space by creating models of the good solutions found so far are considered for example in =-=[59, 4]-=-. Implicit models of the configuration space are built by a population of searchers in Genetic Algorithms, where learning comes in the form of ”survival of the fittest” and generation of new sampling ... |

251 |
1965] “Computer Solutions of the Traveling Salesman Problem
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Citation Context ...milar to those proposed in TS can be found in the denial strategy of [62] (once common features are detected in many suboptimal solutions, they are forbidden) or in the opposite reduction strategy of =-=[49]-=- (in an application to the Travelling Salesman Problem, all edges that are common to a set of local optima are fixed). In very different contexts, prohibition-like strategies can be found in cutting p... |

246 | Making data structures persistent
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- 1989
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Citation Context ...on the average. 2.3.2 Persistent dynamic sets Persistent dynamic sets are proposed to support memory–usage operations in history-sensitive heuristics in [6, 7]. Ordinary data structures are ephemeral =-=[28]-=- because when a change is executed the previous version is destroyed. Now, in many contexts like computational geometry, editing, implementation of very high level programming languages, and, last but... |

238 |
Stochastic Local Search: Foundations and Applications
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Citation Context ...inimum can also be considered as a form of learning based on the previous history of the search. An example is the dynamic local search algorithm on the MAXSAT problem in [43],sREFERENCES 19 see also =-=[42]-=- for additional references about stochastic local search methods including adaptive versions. In the area of computer systems management, ”autonomic” systems are based on self-regulating biological sy... |

236 | Parameter Control in Evolutionary Algorithms
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Citation Context ...ng points depends on the previous evolution, see for example [64]. The issue of controlling parameters of an evolutionary algorithm, including adaptive and ”self-adaptive” techniques is considered in =-=[30]-=-, while fitness landscape analysis for the choice of appropriate operators in ”memetic” algorithms (combining genetic algorithms with local search) is considered in [52]. In the area of stochastic opt... |

231 |
A dichromatic framework for balanced trees
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- 1978
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Citation Context ... for inserting and deleting a given index i from the set. As cited above, configuration X can be considered as a set of indices in [1, L] with a possible realization as a balanced red-black tree, see =-=[18, 38]-=- for two seminal papers about red-black trees. The binary string can be immediately obtained from the tree bys2 REACTIVE SEARCH APPLIED TO TABU SEARCH (RTS) 10 visiting it in symmetric order, in time ... |

224 | The Reactive Tabu Search
- Battiti, Tecchiolli
- 1994
(Show Context)
Citation Context ...idely in the different regions (in these cases a fixed T would be inappropriate). An example of the behavior of T during the search is illustrated in Fig. 1.1, for a Quadratic Assignment Problem task =-=[11]-=-. T increases in an exponential way when repetitions are encountered, it decreases in a gradual manner when repetitions disappear. 2.2.2 The escape mechanism The basic tabu mechanism based on prohibit... |

213 |
Optimization by simulated annealing, Science 220
- Kirkpatrick, Gelatt, et al.
- 1983
(Show Context)
Citation Context ... don’t benefit from the deep and wide theoretical background that covers Markovian algorithms. However, asymptotic convergence results of many Markovian search algorithms, such as Simulated Annealing =-=[48]-=-, ares2 REACTIVE SEARCH APPLIED TO TABU SEARCH (RTS) 4 often irrelevant for their application to optimization. As an example, a comparison of Simulated Annealing and Reactive Search has been presented... |

204 | Free bits, PCPs and nonapproximability -- towards tight results
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Citation Context ...and strong negative results have been shown about its approximability [3, 25]. In particular, if P �= NP, MC is not approximable within n 1/4−ǫ for any ǫ > 0, n being the number of nodes in the graph =-=[19]-=-, and it is not approximable within n 1−ǫ for any ǫ > 0, unless coRP = NP [40]. These theoretical results stimulated a research effort to design efficient heuristics for this problem, and computationa... |

172 |
Planar point location using persistent search trees
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Citation Context ...re update sequence is stored and the desired version is rebuilt from scratch each time an access is performed, while a systematic study of techniques with better space-time complexities is present in =-=[60, 28]-=-. Let us now summarize from [60] how a partially persistent red-black tree can be realized. An example of the realizations that we consider is presented in Fig. 1.3. The trivial way is that of keeping... |

166 |
Clique is hard to approximate within n 1−ɛ
- Hastad
- 1999
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Citation Context ... In particular, if P �= NP, MC is not approximable within n 1/4−ɛ for any ɛ > 0, n being the number of nodes in the graph [19], and it is not approximable within n 1−ɛ for any ɛ > 0, unless coRP = NP =-=[40]-=-. These theoretical results stimulated a research effort to design efficient heuristics for this problem, and computational experiments to demonstrate that optimal or close approximate values can be e... |

119 | Testing heuristics: We have it all wrong
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Citation Context ... in heuristics Most state-of-the-art heuristics are characterized by a certain number of choices and free parameters, whose appropriate setting is a subject that raises issues of research methodology =-=[5, 41, 51]-=-. In some cases, these parameters are tuned through a feedback loop that includes the user as a crucial learning component: depending on preliminary algorithm tests some parameter values are changed b... |

113 |
Symmetric Binary B-trees: Data structures and maintenance algorithms
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Citation Context ... for inserting and deleting a given index i from the set. As cited above, configuration X can be considered as a set of indices in [1, L] with a possible realization as a balanced red-black tree, see =-=[18, 38]-=- for two seminal papers about red-black trees. The binary string can be immediately obtained from the tree bys2 REACTIVE SEARCH APPLIED TO TABU SEARCH (RTS) 10 visiting it in symmetric order, in time ... |

106 |
Algorithms for the maximum satisfiability problem
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Citation Context ...nt prohibition-based heuristics” starting from the late eighties is greatly due to the role of F. Glover in the proposal and diffusion of a rich variety of meta-heuristic tools [35, 36], but see also =-=[39]-=- for an independent seminal paper. A growing number of TS-based algorithms has been developed in the last years and applied with success to a wide selection of problems [37]. It is therefore difficult... |

104 | Designing and reporting on computational experiments with heuristic methods
- Barr, Golden, et al.
- 1995
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Citation Context ... in heuristics Most state-of-the-art heuristics are characterized by a certain number of choices and free parameters, whose appropriate setting is a subject that raises issues of research methodology =-=[5, 41, 51]-=-. In some cases, these parameters are tuned through a feedback loop that includes the user as a crucial learning component: depending on preliminary algorithm tests some parameter values are changed b... |

101 |
The maximum clique problem
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Citation Context ...t to design efficient heuristics for this problem, and computational experiments to demonstrate that optimal or close approximate values can be efficiently obtained for significant families of graphs =-=[45, 58]-=-. In particular, a new reactive heuristic (Reactive Local Search or RLS) is proposed for the Maximum Clique problem in [10]. The present description is a summarized version of the cited paper. The exp... |

87 | Scaling and probabilistic smoothing: Efficient dynamic local search for SAT
- Hutter, Tompkins, et al.
- 2002
(Show Context)
Citation Context ...ion away from a given local minimum can also be considered as a form of learning based on the previous history of the search. An example is the dynamic local search algorithm on the MAXSAT problem in =-=[43]-=-,sREFERENCES 19 see also [42] for additional references about stochastic local search methods including adaptive versions. In the area of computer systems management, ”autonomic” systems are based on ... |

79 | Ant colonies for the quadratic assignment problem
- Gambardella, Taillard, et al.
- 1999
(Show Context)
Citation Context ...uted computation, and the use of a constructive greedy heuristic. For example ”pheromone trail” information to perform modifications on solutions for the quadratic assignment problem is considered in =-=[27, 34]-=-. Dynamic local search, which increases penalties of some solution components to move the tentative solution away from a given local minimum can also be considered as a form of learning based on the p... |

64 | A compendium of NP optimization problems
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Citation Context ...tion we consider with some detail only the application to the maximum clique problem. The Maximum Clique (MC) problem is NP-hard, and strong negative results have been shown about its approximability =-=[3, 25]-=-. In particular, if P �= NP, MC is not approximable within n 1/4−ǫ for any ǫ > 0, n being the number of nodes in the graph [19], and it is not approximable within n 1−ǫ for any ǫ > 0, unless coRP = NP... |

62 | B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem
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Citation Context ...e” techniques is considered in [30], while fitness landscape analysis for the choice of appropriate operators in ”memetic” algorithms (combining genetic algorithms with local search) is considered in =-=[52]-=-. In the area of stochastic optimization, which considers noise in the evaluation process, memory based schemes for validation and tuning of function approximators are used in [53, 29]. Guided local s... |

61 |
Clique is hard to approximate within n 1−ǫ
- H˚astad
- 1999
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Citation Context ... In particular, if P �= NP, MC is not approximable within n 1/4−ǫ for any ǫ > 0, n being the number of nodes in the graph [19], and it is not approximable within n 1−ǫ for any ǫ > 0, unless coRP = NP =-=[40]-=-. These theoretical results stimulated a research effort to design efficient heuristics for this problem, and computational experiments to demonstrate that optimal or close approximate values can be e... |

59 | Learning evaluation functions for global optimization and Boolean satisfiability
- Boyan, Moore
- 1998
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Citation Context ... aims at exploiting the problem and search-related information to effectively guide local search heuristics [68]. Evaluation functions for global optimization and Boolean satisfiability are learnt in =-=[20]-=-. Learning mechanisms with biological motivations are used in Ant Colony Optimization based on feedback, distributed computation, and the use of a constructive greedy heuristic. For example ”pheromone... |

49 | Guided Local Search and its application to the travelling salesman problem
- Voudouris, Tsang
- 1999
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Citation Context ...or validation and tuning of function approximators are used in [53, 29]. Guided local search aims at exploiting the problem and search-related information to effectively guide local search heuristics =-=[68]-=-. Evaluation functions for global optimization and Boolean satisfiability are learnt in [20]. Learning mechanisms with biological motivations are used in Ant Colony Optimization based on feedback, dis... |

42 |
A tabu search approach to the constraint satisfaction problem as a general problem solver
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Citation Context ...5, 21], structural acoustic control problems [47], special-purpose VLSI realizations [2], graph partitioning [16], electric power distribution [66], maximum satifiability [8], constraint satisfaction =-=[9, 54]-=-, optimization of continuous functions [15, 22], traffic grooming in optical networks [17], maximum clique [10], real-time dispatch of trams in storage yards [69], increasing internet capacity [32]. B... |

41 | Stochastic optimization
- Schneider, Kirkpatrick
- 2006
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Citation Context ...h) is considered in [52]. In the area of stochastic optimization, which considers noise in the evaluation process, memory based schemes for validation and tuning of function approximators are used in =-=[53, 29]-=-. Guided local search aims at exploiting the problem and search-related information to effectively guide local search heuristics [68]. Evaluation functions for global optimization and Boolean satisfia... |

35 |
Toward an experimental method for algorithm simulation
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Citation Context ... in heuristics Most state-of-the-art heuristics are characterized by a certain number of choices and free parameters, whose appropriate setting is a subject that raises issues of research methodology =-=[5, 41, 51]-=-. In some cases, these parameters are tuned through a feedback loop that includes the user as a crucial learning component: depending on preliminary algorithm tests some parameter values are changed b... |

33 |
Dynamic tabu list management using the reverse elimination method. Aim. Oper Res
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Citation Context ...eletion can be done in O(1) rotations and O(log L) color changes [65]. In addition, the amortized number of color changes per update is O(1), see for example [50]. Now, the Reverse Elimination Method =-=[35, 36, 26]-=- (a technique for the storage and analysis of the ordered list of all moves performed throughout the search) is closely reminiscent of a method studied in [56] to obtain partial persistence, in which ... |

31 |
Reactive search, a history-sensitive heuristic for MAXSAT
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Citation Context ...hicle-routing problems [24, 55, 21], structural acoustic control problems [47], special-purpose VLSI realizations [2], graph partitioning [16], electric power distribution [66], maximum satifiability =-=[8]-=-, constraint satisfaction [9, 54], optimization of continuous functions [15, 22], traffic grooming in optical networks [17], maximum clique [10], real-time dispatch of trams in storage yards [69], inc... |

30 | Greedy, prohibition, and reactive heuristics for graph partitioning
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- 1999
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Citation Context ...nment [11], training neural nets and control problems [14], vehicle-routing problems [24, 55, 21], structural acoustic control problems [47], special-purpose VLSI realizations [2], graph partitioning =-=[16]-=-, electric power distribution [66], maximum satifiability [8], constraint satisfaction [9, 54], optimization of continuous functions [15, 22], traffic grooming in optical networks [17], maximum clique... |

26 |
Tabu Search applied to global optimization
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Citation Context ...47], special-purpose VLSI realizations [2], graph partitioning [16], electric power distribution [66], maximum satifiability [8], constraint satisfaction [9, 54], optimization of continuous functions =-=[15, 22]-=-, traffic grooming in optical networks [17], maximum clique [10], real-time dispatch of trams in storage yards [69], increasing internet capacity [32]. Because of space limitation we consider with som... |

21 |
A Reactive Tabu Search Metaheuristic for the Vehicle Routing Problem with Time Windows
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Citation Context ...the Maximum Clique example Reactive Search principles have been used for example for the problem of Quadratic Assignment [11], training neural nets and control problems [14], vehicle-routing problems =-=[24, 55, 21]-=-, structural acoustic control problems [47], special-purpose VLSI realizations [2], graph partitioning [16], electric power distribution [66], maximum satifiability [8], constraint satisfaction [9, 54... |

20 |
Bounding the probability of success of stochastic methods for global optimization
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Citation Context ...n (e.g., TSP problem) that the complete enumeration of all solutions would take less time than approximating an optimal solution with arbitrary precision by SA [1]. In addition, repeated local search =-=[31]-=-, and even random search [23], have better asymptotic results. According to [1] “approximating the asymptotic behavior of SA arbitrarily closely requires a number of transitions that for most problems... |

20 |
Tarjan, Making data structures persistent
- Driscoll, Samak, et al.
- 1986
(Show Context)
Citation Context ...on the average. 2.3.2 Persistent dynamic sets Persistent dynamic sets are proposed to support memory–usage operations in history-sensitive heuristics in [6, 7]. Ordinary data structures are ephemeral =-=[28]-=- because when a change is executed the previous version is destroyed. Now, in many contexts like computational geometry, editing, implementation of very high level programming languages, and, last but... |

18 |
On the convergence rate of annealing processes
- Chiang, Chow
- 1988
(Show Context)
Citation Context ...e complete enumeration of all solutions would take less time than approximating an optimal solution with arbitrary precision by SA [1]. In addition, repeated local search [31], and even random search =-=[23]-=-, have better asymptotic results. According to [1] “approximating the asymptotic behavior of SA arbitrarily closely requires a number of transitions that for most problems is typically larger than the... |

17 | Real-time dispatch of trams in storage yards
- Winter, Zimmermann
- 2013
(Show Context)
Citation Context ...ility [8], constraint satisfaction [9, 54], optimization of continuous functions [15, 22], traffic grooming in optical networks [17], maximum clique [10], real-time dispatch of trams in storage yards =-=[69]-=-, increasing internet capacity [32]. Because of space limitation we consider with some detail only the application to the maximum clique problem. The Maximum Clique (MC) problem is NP-hard, and strong... |

16 |
Cliques, coloring and satisfiability second DIMACS implementation challenge
- Johnson, Trick
- 1996
(Show Context)
Citation Context ...t to design efficient heuristics for this problem, and computational experiments to demonstrate that optimal or close approximate values can be efficiently obtained for significant families of graphs =-=[45, 58]-=-. In particular, a new reactive heuristic (Reactive Local Search or RLS) is proposed for the Maximum Clique problem in [10]. The present description is a summarized version of the cited paper. The exp... |

16 |
Analysis of Finite Length Annealing Schedules
- Strenski, Kirkpatrick
- 1991
(Show Context)
Citation Context ...sults are not directly applicable. The optimal finite-length annealing schedules obtained on specific simple problems do not always correspond to those intuitively expected from the limiting theorems =-=[63]-=-. 2 Reactive Search applied to Tabu Search (RTS) In this Section, we illustrate the potential of Reactive Search by installing a reaction mechanism on the prohibition period T of a Tabu Search [35] al... |

15 |
search—Part II
- “Tabu
- 1990
(Show Context)
Citation Context ...lossoming of “intelligent prohibition-based heuristics” starting from the late eighties is greatly due to the role of F. Glover in the proposal and diffusion of a rich variety of meta-heuristic tools =-=[35, 36]-=-, but see also [39] for an independent seminal paper. A growing number of TS-based algorithms has been developed in the last years and applied with success to a wide selection of problems [37]. It is ... |

15 |
Tabu search algorithms for the maximum clique problem
- Soriano, Gendreau
(Show Context)
Citation Context ... upper and lower bounds, are realized by the two following functions: Increase(T) = min{max{T · 1.1, T + 1}, n − 2} Decrease(T) = max{min{T · 0.9, T − 1}, 1} The routine Restart is similar to that in =-=[61]-=-. If there are vertices that have never been part of the current clique during the search, i.e., that have never been moved since the beginning of the run, one of them with maximal degree in V is rand... |

14 |
Updating a Balanced Search Tree
- Tarjan
- 1983
(Show Context)
Citation Context ... time, while at most a single node of the tree is allocated or deallocated at each iteration. Rebalancing the tree after insertion or deletion can be done in O(1) rotations and O(log L) color changes =-=[65]-=-. In addition, the amortized number of color changes per update is O(1), see for example [50]. Now, the Reverse Elimination Method [35, 36, 26] (a technique for the storage and analysis of the ordered... |

13 |
Reactive Tabu Search and Sensor Selection in Active Structural Acoustic Control Problems
- Kincaid, Laba
- 1998
(Show Context)
Citation Context ...es have been used for example for the problem of Quadratic Assignment [11], training neural nets and control problems [14], vehicle-routing problems [24, 55, 21], structural acoustic control problems =-=[47]-=-, special-purpose VLSI realizations [2], graph partitioning [16], electric power distribution [66], maximum satifiability [8], constraint satisfaction [9, 54], optimization of continuous functions [15... |

12 |
Using Optimal Dependency Trees for Combinatorial Optimization: Learning the Structure of Search Space
- Baluja, Davies
- 1997
(Show Context)
Citation Context ...ion of interesting related papers. Probabilistic methods that explicitly maintain statistics about the search space by creating models of the good solutions found so far are considered for example in =-=[59, 4]-=-. Implicit models of the configuration space are built by a population of searchers in Genetic Algorithms, where learning comes in the form of ”survival of the fittest” and generation of new sampling ... |

12 |
Searching in the past ii: general transforms
- Overmars
- 1981
(Show Context)
Citation Context ...nodes) can be modified. A review of ad hoc techniques for obtaining persistent data structures is given in [28] that is dedicated to a systematic study of persistence, continuing the previous work of =-=[56]-=-. Hashing combined with persistent red-black trees The basic observation is that, because tabu search is based on local search, configuration X (t+1) differs from configuration X (t) only because of t... |