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Munakata, T. & D. J. Hashier: “A genetic algorithm applied to the maximum flow problem”, Proc. of the 5th Inter. Conf. on Genetic Algorithms, San Francisco, pp.488-493, 1993. Gen, M. & R. Cheng: Genetic Algorithms and Engineering Design, John Wiley & Sons, New York, 1997. Munetomo, M., Y. Takai & Y. Sato: “A migration Scheme for the Genetic Adaptive routing Algorithm”, Proc. of IEEE Int. Conf. Systems, Man, and Cybernetics, pp.2774-2779, 1998. Inagaki, J., M. Haseyama & H. Kitajima: “A Genetic Algorithm for Determining Multiple Routes and Its Applications”, Proc. of IEEE Int. Symp. Circuits and Systems, pp.137-140, 1999. Gen, M. & R. Cheng: Genetic Algorithms and Engineering Optimization, John Wiley & Sons, New York, 2000. Gen, M., R. Cheng & S.S. Oren: "Network design techniques using adapted genetic algorithms", Advances in Engineering Software, Vol.32, pp.731-744, 2001. Ahn, C.W. & R. Ramakrishna: “A Genetic Algorithm for Shortest Path Routing Problem and the Sizing of Populations”, IEEE Trans. on Evol. Comput., Vol.6, No.6, pp.566-579, 2002. Zhou, G. & M. Gen: “A Genetic Algorithm Approach on Tree-like Telecommunication Network Design Problem”, J. of Operational Research Society, Vol. 54, No. 3, pp.248-254, 2003.
18 2 36 s 16 11 13 5 27 3 12 23 12 13 6 38 9 7 4 20 t 15 10 32 8 24
Data table of example network i 1 1 2 3 3 3 4 4 5 6 6 7 8 8 9 j 2 3 4 2 5 6 7 8 4 7 9 8 9 10 10 cij 36 27 18 13 12 23 11 32 16 12 38 20 15 24 13
SPP can be formulated as follows:
2. Maximum Flow (MXF) Problem
3. Minimum Cost Flow (MCF) Problem
4. Bicriteria Network Design Problem (BNP)
5. Multi-criteria Network Design Problem
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Soft Computing Lab.
1. Shortest Path Problem (SPP)
1.1 Basic Concept of Shortest Path Problem
SPP is perhaps the simplest of all network design problems. For this problem, the object is to find a path of minimum cost (or length) from a specified source node s to another specified sink node t, assuming that each arc (i, j)∈A has an associated cost (or length) cij.
vBNS Logical Network Map
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6. Basic Network Design
1. Shortest Path Problem (SPP)
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6. Basic Network Design
In the past few years, the genetic algorithms community has turned much of its attention toward the optimization of network design problems:
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1
1
i
cij
j
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1. Shortest Path Problem (SPP)
1.1 Basic Concept of Shortest Path Problem
Directed graph G=(V, A)
Michalewicz, Z. : Genetic Algorithm + Data Structure = Evolution Programs, 2nd ed., Springer-Verlag, New York, 1994 Gen, M. & R. Cheng: Genetic Algorithms & Engineering Design, John Wiley & Sons, New York, 1997.
1.4.1 Reviewing Encoding Methods 1.4.2 Priority-based Genetic Algorithm 1.4.3 Genetic Operators
1.5 Numerical Examples
2. 3. 4. 5.
Maximum Flow (MXF) Problem Minimum Cost Flow (MCF) Problem Bicriteria Network Design Problem (BNP) Multi-criteria Network Design Problem
Graduate School of Information, Production and Systems, Waseda University
6. Basic Network Design
6. Basic Network Design
Genetic Algorithms (GAs) are one of the most powerful and broadly applicable stochastic search and optimization techniques based on principles from evolution theory (Holland, 1976):
Soft Computing Lab.
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vBNS Backbone Network Map
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4 WASEDA UNIVERSITY , IPS high speed Backbone Network Services vBNS: very
Data table of example network
i 1 1 2 3 3 3 4 4 5 6 6 7 8 8 9 j 2 3 4 2 5 6 7 8 4 7 9 8 9 10 10 cij 36 27 18 13 12 23 11 32 16 12 38 20 15 24 13
where V is a set of nodes, A is a set of links.
WASEDA UNIVERSITY , IPS
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6. Basic Network Design
1. Shortest Path Problem (SPP)
1.1 Basic Concept of Shortest Path Problem 1.2 Application of Shortest Path Problem 1.3 Methods for solving SPP 1.4 Genetic Approach for solving SPP
Recent advances in evolutionary computation have made it possible to solve such practical network optimization problems:
Ali, M. & F. Kamoun： “Neural Networks for Shortest Path Computation and Routing in Computer Networks”, IEEE Trans. on Neural Networks, vol.4, pp.941-954, 1993. Perfetti, R. : “Optimization Neural Network for Solving Flow Problems”, IEEE Trans. on Neural Network, Vol.6, No.5, pp.1287-1291, 1995. Gen, M. & K. Ida: Neural Networks and Optimization with Mathematica, Kyoritsu Shuppan, 1998 in Japanese. Ahn, C. W., R. Ramakrishna, C. Kang & I. Choi: “Shortest Path Routing Algorithm using Hopfield Neural Network”, Electronic Letter, Vol.37, No.19, pp.1176-1178, 2001.
