Using the Cross-Entropy Method to Guide/Govern Mobile Agent’s Path Finding in Networks

Helvik, Bjarne E.; Wittner, Otto J.

doi:10.1007/3-540-44651-6_24

Cited by 55 publications

(36 citation statements)

References 7 publications

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“…The CE method has been successfully applied to a diverse range of estimation and optimization problems, including buffer allocation [1], queueing models of telecommunication systems [14,16], optimal control of HIV/AIDS spread [48,49], signal detection [30], combinatorial auctions [9], DNA sequence alignment [24,38], scheduling and vehicle routing [3,8,11,20,23,53], neural and reinforcement learning [31,32,34,52,54], project management [12], rare-event simulation with light-and heavy-tail distributions [2,10,21,28], clustering analysis [4,5,29]. Applications to classical combinatorial optimization problems including the max-cut, traveling salesman, and Hamiltonian cycle 1…”

Section: Introductionmentioning

confidence: 99%

A Tutorial on the Cross-Entropy Method

et al. 2005

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Abstract:The cross-entropy method is a recent versatile Monte Carlo technique. This article provides a brief introduction to the cross-entropy method and discusses how it can be used for rare-event probability estimation and for solving combinatorial, continuous, constrained and noisy optimization problems. A comprehensive list of references on cross-entropy methods and applications is included.Keywords: cross-entropy, Kullback-Leibler divergence, rare events, importance sampling, stochastic search.The cross-entropy (CE) method is a recent generic Monte Carlo technique for solving complicated simulation and optimization problems. The approach was introduced by R.Y. Rubinstein in [41,42], extending his earlier work on variance minimization methods for rare-event probability estimation [40].The CE method can be applied to two types of problem:, where X is a random variable or vector taking values in some set X and H is function on X . An important special case is the estimation of a probability = P(S(X) γ), where S is another function on X .2. Optimization: Optimize (that is, maximize or minimize) S(x) over all x ∈ X , where S is some objective function on X . S can be either a known or a noisy function. In the latter case the objective function needs to be estimated, e.g., via simulation.In the estimation setting, the CE method can be viewed as an adaptive importance sampling procedure that uses the cross-entropy or Kullback-Leibler divergence as a measure of closeness between two sampling distributions, as is explained further in Section 1. In the optimization setting, the optimization problem is first translated into a rare-event estimation problem, and then the CE method for estimation is used as an adaptive algorithm to locate the optimum, as is explained further in Section 2.An easy tutorial on the CE method is given in [15]. A more comprehensive treatment can be found in [45]; see also [46, Chapter 8]. The CE method homepage can be found at www.cemethod.org .The CE method has been successfully applied to a diverse range of estimation and optimization problems, including buffer allocation [1], queueing models of telecommunication systems [14,16], optimal control of HIV/AIDS spread [48,49], signal detection [30], combinatorial auctions [9], DNA sequence alignment [24,38], scheduling and vehicle routing [3,8,11,20,23,53], neural and reinforcement learning [31,32,34,52,54], project management [12], rare-event simulation with light-and heavy-tail distributions [2,10,21,28], clustering analysis [4,5,29]. Applications to classical combinatorial optimization problems including the max-cut, traveling salesman, and Hamiltonian cycle 1

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Section: Introductionmentioning

confidence: 99%

A Tutorial on the Cross-Entropy Method

et al. 2005

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“…This would be an impractical burden to on-line execution of the logic. Instead, given that β is close to 1, it is assumed that changes in γ r are relatively small in subsequent iterations, which enables a first order Taylor expansion of (9), and a second order Taylor expansion of (8), see [13], thus saving memory and processing power.…”

Section: The Cross-entropy Ant Systemmentioning

confidence: 99%

Laying Pheromone Trails for Balanced and Dependable Component Mappings

Csorba

Meling

Heegaard

2009

Self-Organizing Systems

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Abstract. This paper presents an optimization framework for finding efficient deployment mappings of replicated service components (to nodes), while accounting for multiple services simultaneously and adhering to non-functional requirements. Currently, we consider load-balancing and dependability requirements. Our approach is based on a variant of Ant Colony Optimization and is completely decentralized, where ants communicate indirectly through pheromone tables in nodes. In this paper, we target scalability; however, existing encoding schemes for the pheromone tables did not scale. Hence, we propose and evaluate three different pheromone encodings. Using the most scalable encoding, we evaluate our approach in a significantly larger system than our previous work. We also evaluate the approach in terms of robustness to network partition failures.

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“…This algorithm is based on the iterative scheme described at the end of previous subsection and is particularized to the case where the set G is the set of all n-dimensional Bernoulli pmfs defined on U. The algorithm solves the optimization problem (7) by relying on its stochastic counterpart (8) whose solution is computed analytically by exploiting (10).…”

Section: A Practically Implementable Algorithmmentioning

confidence: 99%

“…The main two observations to be drawn from this table are the following. First, we observe that the number of t pt [1] pt [2] pt [3] pt [4] pt [5] pt [6] pt [7] pt [8] pt [9] pt [10] pt [11] pt [12] pt [13] pt [14] pt [15] pt [16] pt [17] pt [18] pt [19] pt [20] max iterations to convergence increases slightly less than linearly with n. Moreover, the number of elements of U for which the performance S(·) must be evaluated is equal to C × n per iteration, where C is a constant. As a result, the number of evaluations of the performance function S(·) required before convergence grows less than quadratically with n. Knowing that #U grows exponentially with n, we have therefore an exponential decrease with n of the percentage of elements u ∈ U whose performances are assessed throughout the course of the algorithm.…”

Section: Performances Of the Ce-based Combinatorial Algorithmmentioning

confidence: 99%