On the design of multi-type networks via the cross-entropy method

We apply the cross-entropy method to a network design problem with multi-type links and nodes, in which the network's reliability is to be maximized subject to a fixed budget. Numerical experiments illustrate the simplicity and effectiveness of the method.

[1]  Shie Mannor,et al.  A Tutorial on the Cross-Entropy Method , 2005, Ann. Oper. Res..

[2]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[3]  Alice E. Smith,et al.  Heuristic optimization of network design considering all-terminal reliability , 1997, Annual Reliability and Maintainability Symposium.

[4]  Tito Homem-de-Mello,et al.  Solving the Vehicle Routing Problem with Stochastic Demands using the Cross-Entropy Method , 2005, Ann. Oper. Res..

[5]  Tim Hesterberg,et al.  Introduction to Stochastic Search and Optimization: Estimation, Simulation, and Control , 2004, Technometrics.

[6]  R. Jan,et al.  Topological optimization of a communication network subject to a reliability constraint , 1993 .

[7]  Dirk P. Kroese,et al.  Designing an Optimal Network Using the Cross-Entropy Method , 2005, IDEAL.

[8]  Alice E. Smith,et al.  Reliability optimization of computer communication networks using genetic algorithms , 1998, SMC'98 Conference Proceedings. 1998 IEEE International Conference on Systems, Man, and Cybernetics (Cat. No.98CH36218).

[9]  Miro Kraetzl,et al.  The Cross-Entropy Method for Network Reliability Estimation , 2005, Ann. Oper. Res..

[10]  Lih-Yuan Deng,et al.  The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning , 2006, Technometrics.

[11]  Dirk P. Kroese,et al.  A Fast Cross-Entropy Method for Estimating Buffer Overflows in Queueing Networks , 2004, Manag. Sci..

[12]  Ehl Emile Aarts,et al.  Simulated annealing and Boltzmann machines , 2003 .

[13]  Dirk P. Kroese,et al.  Application of the Cross-Entropy Method to the Buffer Allocation Problem in a Simulation-Based Environment , 2005, Ann. Oper. Res..

[14]  Alice E. Smith,et al.  Efficient optimization of all-terminal reliable networks, using an evolutionary approach , 1997 .

[15]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[16]  Alistair I. Mees,et al.  Convergence of an annealing algorithm , 1986, Math. Program..

[17]  R. Rubinstein Combinatorial Optimization, Cross-Entropy, Ants and Rare Events , 2001 .

[18]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.