Evolutionary-Fragmentary Model of the Routing Problem

One of the variants of the routing problem on a plane integer lattice is considered. It is shown that this problem can be represented as a problem of searching for words with certain properties over a finite alphabet. In turn, the problem of finding optimal words can be considered as a problem of fr...

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Veröffentlicht in:	Cybernetics and systems analysis Jg. 51; H. 3; S. 432 - 437
Hauptverfasser:	Kozin, I. V., Kryvtsun, O. V., Pinchuk, V. P.
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Springer US 01.05.2015 Springer Springer Nature B.V
Schlagworte:	Artificial Intelligence Combinatorial analysis Combinatorics Control Cybernetics Density Feasibility Lattices Lower bounds Mathematical analysis Mathematics Mathematics and Statistics Optimization Optimization algorithms Processor Architectures Routing Software Engineering/Programming and Operating Systems Studies Systems Theory combinatorial optimization routing density routing problem fragmentary structure evolutionary model
ISSN:	1060-0396, 1573-8337
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Abstract	One of the variants of the routing problem on a plane integer lattice is considered. It is shown that this problem can be represented as a problem of searching for words with certain properties over a finite alphabet. In turn, the problem of finding optimal words can be considered as a problem of fragmentary structure. A combinatorial estimate for the set of feasible words is derived and the lower bound of the density is established for the problem of finding optimal line density. An evolutionary-fragmentary model of the routing problem is constructed. Optimal and near-optimal solutions are obtained for this problem for small dimensions.
AbstractList	One of the variants of the routing problem on a plane integer lattice is considered. It is shown that this problem can be represented as a problem of searching for words with certain properties over a finite alphabet. In turn, the problem of finding optimal words can be considered as a problem of fragmentary structure. A combinatorial estimate for the set of feasible words is derived and the lower bound of the density is established for the problem of finding optimal line density. An evolutionary-fragmentary model of the routing problem is constructed. Optimal and near-optimal solutions are obtained for this problem for small dimensions. One of the variants of the routing problem on a plane integer lattice is considered. It is shown that this problem can be represented as a problem of searching for words with certain properties over a finite alphabet. In turn, the problem of finding optimal words can be considered as a problem of fragmentary structure. A combinatorial estimate for the set of feasible words is derived and the lower bound of the density is established for the problem of finding optimal line density. An evolutionary-fragmentary model of the routing problem is constructed. Optimal and near-optimal solutions are obtained for this problem for small dimensions. Keywords: routing problem, routing density, combinatorial optimization, fragmentary structure, evolutionary model.
Audience	Academic
Author	Pinchuk, V. P. Kryvtsun, O. V. Kozin, I. V.
Author_xml	– sequence: 1 givenname: I. V. surname: Kozin fullname: Kozin, I. V. email: ainc00@gmail.com organization: Zaporizhzhya National University – sequence: 2 givenname: O. V. surname: Kryvtsun fullname: Kryvtsun, O. V. organization: Zaporizhzhya National University – sequence: 3 givenname: V. P. surname: Pinchuk fullname: Pinchuk, V. P. organization: Zaporizhzhya National University
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References	SchneckeVZalzalaAMSFlemmingPJGenetic design of VLSI layoutsGenetic Algorithms in Engineering Systems1997LondonThe Institution of Electrical Engineers22925310.1049/PBCE055E_ch10 A. Kernytskyy, R. Kryvyy, and S. Tkatchenko, “VLSI topology synthesis using the method of parallel genetic algorithms,” in: Proc. 3rd Intern. Conf. of Young Scientists MEMSTECH’2007, May 23–26, 2007, Polyana, Lviv (2007), pp. 151–152. Chi Keong Goh, Wei Ling, Yong Han Chew, and Kay Chen Tan, “A multi-objective evolutionary algorithm for channel routing problems,” in: K. P. Dahal and P. I. Cowling (eds.), Evolutionary Scheduling, Springer, Berlin (2007), pp. 404–436. LebedevBKVoroninEIGenetic algorithm of the distribution of connecting layers for multilayered global routing of VLSIIzv. YuFU, Tekhn. Nauki, Special Issue: Intelligent CAD201213271421 L. A. Gladkov and S. N. Shcheglov, “Synthesis of the architecture of hybrid intelligent systems on the basis of self-organization and self-regulation principles,” in: Trans. of Intern. Conf. IEEE AIS’02 and ISAPR’2002, Fizmatlit, Moscow (2002), pp. 173–180. LienigJDasguptaDMichalewiczZPhysical design of VLSI circuitsEvolutionary Algorithms in Engineering Applications1997BerlinSpringer27729310.1007/978-3-662-03423-1_16 I. V. Kozin and S. I. Polyuga, “Properties of fragmentary structures,” Visnyk Zapor. Nats. Univer., Mathematical Modeling and Applied Mechanics, No. 1, 99–106 (2012). I. Sh. Nevlyudov, S. V. Kurapov, et al., “Routing of the connecting plate of a multiple-sonde devices for monitoring of BGA-components,” in: Proc. 6th Intern. Sci. Conf. “Functional basis of nanoelectronics,” KhNURE, Kharkov (2013), pp. 129–132. D. Korpyljov, T. Sviridova, and S. Tkachenko, “Using of genetic algorithms in design of Hybrid Integrated Circuits,” in: Proc. 9th Intern. Conf. on the Experience of Designing and Application of CAD Systems in Microelectronics, February, 20–24, 2007, Polyana, Lviv (2007), p. 302. I. V. Kozin and S. I. Polyuga, “Using EVF algorithms to solve the rectangular cut problem,” Issues of Applied Mathematics and Mathematical Modeling, Izd. Dnipropetr. Nats. Univer., Dnipropetrovsk (2009), pp. 199–208. 9734_CR8 9734_CR9 9734_CR1 BK Lebedev (9734_CR2) 2012; 132 J Lienig (9734_CR5) 1997 9734_CR4 9734_CR3 9734_CR6 V Schnecke (9734_CR7) 1997 9734_CR10
References_xml	– reference: L. A. Gladkov and S. N. Shcheglov, “Synthesis of the architecture of hybrid intelligent systems on the basis of self-organization and self-regulation principles,” in: Trans. of Intern. Conf. IEEE AIS’02 and ISAPR’2002, Fizmatlit, Moscow (2002), pp. 173–180. – reference: A. Kernytskyy, R. Kryvyy, and S. Tkatchenko, “VLSI topology synthesis using the method of parallel genetic algorithms,” in: Proc. 3rd Intern. Conf. of Young Scientists MEMSTECH’2007, May 23–26, 2007, Polyana, Lviv (2007), pp. 151–152. – reference: D. Korpyljov, T. Sviridova, and S. Tkachenko, “Using of genetic algorithms in design of Hybrid Integrated Circuits,” in: Proc. 9th Intern. Conf. on the Experience of Designing and Application of CAD Systems in Microelectronics, February, 20–24, 2007, Polyana, Lviv (2007), p. 302. – reference: I. Sh. Nevlyudov, S. V. Kurapov, et al., “Routing of the connecting plate of a multiple-sonde devices for monitoring of BGA-components,” in: Proc. 6th Intern. Sci. Conf. “Functional basis of nanoelectronics,” KhNURE, Kharkov (2013), pp. 129–132. – reference: Chi Keong Goh, Wei Ling, Yong Han Chew, and Kay Chen Tan, “A multi-objective evolutionary algorithm for channel routing problems,” in: K. P. Dahal and P. I. Cowling (eds.), Evolutionary Scheduling, Springer, Berlin (2007), pp. 404–436. – reference: LienigJDasguptaDMichalewiczZPhysical design of VLSI circuitsEvolutionary Algorithms in Engineering Applications1997BerlinSpringer27729310.1007/978-3-662-03423-1_16 – reference: I. V. Kozin and S. I. Polyuga, “Properties of fragmentary structures,” Visnyk Zapor. Nats. Univer., Mathematical Modeling and Applied Mechanics, No. 1, 99–106 (2012). – reference: LebedevBKVoroninEIGenetic algorithm of the distribution of connecting layers for multilayered global routing of VLSIIzv. YuFU, Tekhn. Nauki, Special Issue: Intelligent CAD201213271421 – reference: I. V. Kozin and S. I. Polyuga, “Using EVF algorithms to solve the rectangular cut problem,” Issues of Applied Mathematics and Mathematical Modeling, Izd. Dnipropetr. Nats. Univer., Dnipropetrovsk (2009), pp. 199–208. – reference: SchneckeVZalzalaAMSFlemmingPJGenetic design of VLSI layoutsGenetic Algorithms in Engineering Systems1997LondonThe Institution of Electrical Engineers22925310.1049/PBCE055E_ch10 – start-page: 277 volume-title: Evolutionary Algorithms in Engineering Applications year: 1997 ident: 9734_CR5 doi: 10.1007/978-3-662-03423-1_16 – ident: 9734_CR10 – ident: 9734_CR3 – ident: 9734_CR6 doi: 10.1007/978-3-540-48584-1 – ident: 9734_CR1 doi: 10.1109/MEMSTECH.2007.4283452 – volume: 132 start-page: 14 issue: 7 year: 2012 ident: 9734_CR2 publication-title: Izv. YuFU, Tekhn. Nauki, Special Issue: Intelligent CAD – start-page: 229 volume-title: Genetic Algorithms in Engineering Systems year: 1997 ident: 9734_CR7 doi: 10.1049/PBCE055E_ch10 – ident: 9734_CR8 – ident: 9734_CR9 – ident: 9734_CR4 doi: 10.1109/CADSM.2007.4297557
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SubjectTerms	Artificial Intelligence Combinatorial analysis Combinatorics Control Cybernetics Density Feasibility Lattices Lower bounds Mathematical analysis Mathematics Mathematics and Statistics Optimization Optimization algorithms Processor Architectures Routing Software Engineering/Programming and Operating Systems Studies Systems Theory
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Title	Evolutionary-Fragmentary Model of the Routing Problem
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