Genetic Algorithm for Joint Routing and Dimensioning of Dynamic WDM Networks

Ignacio de Miguel; Reinaldo Vallejos; Alejandra Beghelli; Ramón J. Durán

doi:10.1364/JOCN.1.000608

Journal of Optical Communications and Networking
Vol. 1,
Issue 7,
pp. 608-621
(2009)
•https://doi.org/10.1364/JOCN.1.000608

Genetic Algorithm for Joint Routing and Dimensioning of Dynamic WDM Networks

Ignacio de Miguel, Reinaldo Vallejos, Alejandra Beghelli, and Ramón J. Durán

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Ignacio de Miguel, Reinaldo Vallejos, Alejandra Beghelli, and Ramón J. Durán, "Genetic Algorithm for Joint Routing and Dimensioning of Dynamic WDM Networks," J. Opt. Commun. Netw. 1, 608-621 (2009)

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Abstract

The dynamic operation of WDM networks might lead to significant wavelength savings, when compared with their static counterpart, at the expense of facing nonzero blocking probability. Hence, efficient dimensioning (i.e., determining each link capacity) and control methods are required to operate these networks. Typically, the dimensioning of WDM networks is carried out only after the routing algorithm has been defined. However, this way of designing the network might result in inefficient solutions in terms of wavelength requirements. We propose a novel genetic algorithm to solve the joint routing and dimensioning problem in dynamic WDM networks, with the aim of obtaining a network cost close to minimum while guaranteeing an upper bound on the blocking probability. Used prior to network operation, the algorithm determines which route should be used for each potential connection and also dimensions the number of wavelengths re quired in each link. The efficiency of the algorithm is validated in ring and mesh topologies, providing wavelength savings of up to 17% when compared with the best existing algorithm to date. Moreover, since the routes provided by the genetic algorithm are stored in routing tables, it also ensures extremely fast on-line network operation.

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Parameter	Value
Main GAlib classes used [17]	Algorithm: GASimpleGA Chromosome: GA1DBinaryStringGenome
Population size $(P)$	$10 N$
Chromosome length $(C)$	$N (N - 1)$
Gene encoding	Binary values: 1 (clockwise route), 0 (anticlockwise route)
Initial population	Randomly generated chromosomes except one of them (see below in “Number of runs”)
Crossover probability $(p_{crossover})$	0.9
Mutation probability $(p_{mutation})$	0.001
Elitism	Yes
Objective function	Minimize $C_{net}$ , as defined in Eq. (1) and calculated according to the dimensioning procedure described in Subsection 3B
Fitness scaling	Linear, with multiplier $C_{mult} = 1.2$
Stopping criterion $(G_{stable})$	10,000 generations with no improvement
Number of runs (with different random number seeds)	2 (the solution is the best of both runs) —First run: the balanced routing solution [18] is included as part of the initial population
	—Second run: a completely unbalanced routing solution (all genes of the chromosome set to one) is included as part of the initial population

ρ	$N = 7$		$N = 8$		$N = 9$		$N = 10$		$N = 11$
ρ	ILP/ GARD	BR-AD	ILP/ GARD	BR-AD	ILP/ GARD	BR-AD	ILP/ GARD	BR-AD	GARD	ILP	BR-AD
0.1	76	84	102	112	133	144	168	180	207	213^*	220
0.2	84	84	122	128	162	180	210	220	268	269^*	286
0.3	84	84	128	128	179	180	238	250	305	307^*	308
0.4	84	84	128	128	180	180	250	250	325	325	330
0.5	84	84	128	128	180	180	250	250	330	330	330
0.6	84	84	128	128	180	180	250	250	330	330	330
0.7	84	84	128	128	180	180	250	250	330	330	330
0.8	84	84	128	128	180	180	250	250	330	330	330
0.9	84	84	128	128	180	180	250	250	330	330	330

ρ	$N = 12$			$N = 13$			$N = 14$			$N = 15$			$N = 16$
ρ	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD
0.1	252	256^*	264	299	—	312	358	—	364	420	—	420	480	—	480
0.2	331	331^*	336	390	—	390	476	—	476	555	—	570	639	—	640
0.3	384	382^*	384	463	—	468	560	—	560	660	—	660	768	—	768
0.4	412	414^*	432	508	—	520	616	—	630	735	—	750	864	—	864
0.5	431	432^*	432	539	—	546	658	—	658	796	—	810	944	—	960
0.6	432	432	432	546	—	546	686	—	686	835	—	840	1004	—	1024
0.7	432	432	432	546	—	546	686	—	686	840	—	840	1024	—	1024
0.8	432	432	432	546	—	546	686	—	686	840	—	840	1024	—	1024
0.9	432	432	432	546	—	546	686	—	686	840	—	840	1024	—	1024

ρ	$N = 17$			$N = 18$			$N = 19$			$N = 20$
ρ	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD
0.1	544	—	544	612	—	612	684	—	684	760	—	760
0.2	732	—	748	846	—	846	950	—	950	1080	—	1080
0.3	884	—	884	1026	—	1026	1160	—	1178	1320	—	1320
0.4	1004	—	1020	1170	—	1170	1330	—	1330	1520	—	1520
0.5	1106	—	1122	1278	—	1296	1482	—	1482	1702	—	1720
0.6	1179	—	1190	1386	—	1386	1596	—	1596	1840	—	1840
0.7	1224	—	1224	1448	—	1458	1695	—	1710	1960	—	1960
0.8	1224	—	1224	1458	—	1458	1710	—	1710	2000	—	2000
0.9	1224	—	1224	1458	—	1458	1710	—	1710	2000	—	2000

Parameter	Value
Main GAlib classes used [17]	Algorithm: GASimpleGA Chromosome: GA1DArrayGenome⟨int⟩
Population size $(P)$	$40 N$
Chromosome length $(C)$	$N (N - 1)$
Gene encoding	Integer values: 0–4 (each value representing a different precalculated candidate route for each source– destination pair)
Initial population	Randomly generated chromosomes
Crossover probability $(p_{crossover})$	0.9
Mutation probability $(p_{mutation})$	0.001
Elitism	Yes
Objective function	Minimize $C_{net}$ , as defined in Eq. (1), and calculated according to the dimensioning procedure described in Subsection 3B
Fitness scaling	Linear, with multiplier $C_{mult} = 1.2$
Stopping criterion $(G_{stable})$	5,000 generations with no improvement
Number of runs (with different random number seeds)	3 (the solution is the best of those runs)

Network	Computing time
Eurocore	$118.99 \pm 9.39 s$ (approx. $2 \min$ )
NSFNet	$347.92 \pm 85.20 s$ (approx. $6 \min$ )
EON	$1693.88 \pm 410.02 s$ (approx. $28 \min$ )
UKNet	$2360.77 \pm 255.31 s$ (approx. $39 \min$ )

ρ	Eurocore			NSFNet			EON			UKNet
ρ	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD
0.1	167	171	174	293	311^*	322	547	—	658	625	—	722
0.2	174	173	174	348	363^*	370	704	—	786	804	—	878
0.3	174	174	174	380	384^*	390	788	—	856	911	—	974
0.4	174	174	174	388	389^*	390	843	—	890	981	—	1032
0.5	174	174	174	390	390^*	390	876	—	898	1029	—	1052
0.6	174	174	174	390	390^*	390	895	—	898	1048	—	1052
0.7	174	174	174	390	390	390	898	—	898	1052	—	1052
0.8	174	174	174	390	390	390	898	—	898	1052	—	1052
0.9	174	174	174	390	390	390	898	—	898	1052	—	1052

ρ	Eurocore			NSFNet			EON			UKNet
ρ	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD	GARD	ILP	BR-AD
0.1	167	171	174	293	311^*	322	547	—	658	625	—	722
0.2	174	173	174	348	363^*	370	704	—	786	804	—	878
0.3	174	174	174	380	384^*	390	788	—	856	911	—	974
0.4	174	174	174	388	389^*	390	843	—	890	981	—	1032
0.5	174	174	174	390	390^*	390	876	—	898	1029	—	1052
0.6	174	174	174	390	390^*	390	895	—	898	1048	—	1052
0.7	174	174	174	390	390	390	898	—	898	1052	—	1052
0.8	174	174	174	390	390	390	898	—	898	1052	—	1052
0.9	174	174	174	390	390	390	898	—	898	1052	—	1052

Genetic Algorithm for Joint Routing and Dimensioning of Dynamic WDM Networks

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Abstract

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Tables (7)

Equations (18)

Journal of Optical Communications and Networking