A Memetic based Approach for Routing and Wavelength Assignment in Optical Transmission Systems

In optical networks, Routing and Wavelength Assignment (RWA) problem is one of the major optimization problems. This problem can be solved by different algorithms such as Genetic Algorithm (GA), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), etc. Shuffled Frog Leaping Algorithm (SFLA) is implemented in the proposed work, to solve the RWA problem in long-haul optical networks. The goal is to use minimum number of wavelengths and to reduce the number of connection request rejections. Cost, number of wavelengths, hop count and blocking probability are the performance metrics considered in the analysis. Various wavelength assignment methods such as first fit, random, round robin, wavelength ordering and Four Wave Mixing (FWM) priority based wavelength assignment are used in the analysis using SFLA. Number of wavelengths, hop count, cost and setup time are included in the fitness function. The SFLA algorithm proposed, has been analyzed for different network loads and compared with the performance of genetic algorithm.

. Also Genetic Algorithm is used in many application due to less complex computation (Başak et al 2014). Shuffled Frog Leaping Algorithm is used to solve this RWA problem in the proposed research. Certain simpler or similar algorithms lead to poor performance or are too complex to be used. Therefore, a computationally feasible algorithm is used for a good performance of the network.
In this research paper, two optimization algorithmsgenetic algorithm and shuffled frog leaping algorithm are used in the routing and wavelength assignment problem model. In variety of fields, Genetic Algorithm is used to solve many problems and hence comparison between these two algorithms are done. The simulation results and analysis are discussed and the conclusions of the study and possible future work are presented.

Routing and wavelength assignment
In dynamic routing and wavelength assignment, the requests for lightpath will arrive dynamically. Wavelength continuity constraint is that, on all the links in its path, a lightpath should use same wavelength. The time for which a lightpath and the required resources remain occupied is called as holding time. When the holding time expires, the resources allocated are made free and are made available to support other lightpath requests. The RWA model involves a network model, routing model, wavelength assignment model and an optimization algorithm . Routing and Wavelength Assignment model with optimization is shown in Fig.1.

Network and Routing Model
A network which contains N number of nodes can be modeled as a graph NG(R,E), where E denotes the set of edges representing the connectivity between the nodes and R represents the set of nodes like routers or switches. It is assumed that the links between the nodes are bidirectional. National Science Foundation Network (NSFNET), Advanced Research Projects Agency Network (ARPANET) and European Optical Network (EON) are few standard network architectures currently in use.
One of the major problems in optical networking is Routing and Wavelength Assignment (RWA). The goal is to reduce the rejection of connection requests i.e. to maximize the number of optical connection. For every connection request, a particular route and a wavelength should be assigned. If wavelength converters are not used in the network, then same wavelength should be used throughout the path. Same optical link may be shared by two connections requests, if different wavelengths are provided (Bhanjaa et al 2012). Fitness function to be maximized is given by (1) W x is the free wavelength factor. The value of this factor is one, if same wavelength is available in all the links of path x or otherwise, zero. In the first term, the summation defines the total link cost of the path and similarly in the second term, the summation represents the total number of hops in the path. If link (i, j) is a part of path x, the variable H x i,j takes the value of one and otherwise, it is zero. The set up time of the path x is represented by the variable T x . Variable K x represents the length of the x-th chromosome or number of memeplexes. The route is optimal when the objective function maximizes with the following constraints being satisfied. 1, Equations (2) to (6) represent the flow conservation constraint. Equations (7) and (8) represent the hop count constraint. When more than two wavelengths of light interact with each other while propagating through the medium, a spurious component is produced. Since the FWM crosstalk power will be more over the center of transmission window, in the FWM aware wavelength assignment technique priority is given to the wavelengths towards the edges of the transmission window. Complexity of this method is O(N 3 log 2 N), where N is the number of nodes in the network. In the fitness function proposed, Wx the free wavelength factor is updated after the wavelength assignment phase. In the wavelength assignment model, if the link (i, j) is used by the lightpath lp, the variable I ij lp assumes one else it assumes zero. Variable I ijw lp is the lightpath wavelength indicator. It shows whether the lightpath lp uses wavelength 'W' on link (i, j). Variable I ijw lp (x,y) is the lightpath wavelength link indicator and this is one when the lightpath uses wavelength 'W' on link (i, j) between the nodes x and y. l(x,y) takes one if a physical link exists between the nodes x and y (Bhanjaa et al 2010).

Wavelength Assignment Model
The wavelength continuity constraints are (14) 3 Optimization algorithms 3.

Genetic Algorithm
The flow involved in Genetic Algorithm is shown in Fig.2. Initial population is created and it works iteratively on this initial solution set. The algorithm converges to arrive on best solution (Kavian et al 2009).
Chromosome is the route or path encoded from source to destination. A sequence of nodes creates each chromosome and is generated based on the topology of a particular network. Each chromosome may be of different length and each of them encodes the path from the sender node S to the receiver node D. By random selection of solutions, initial population is created. The initial population has only one chromosome.
Position of the nodes in routing paths do not affect the crossover. One pair is randomly chosen and the crossing site of each chromosome is identified by the locus The fitness function is formulated as in equation (1) and is to evaluate the quality of the chromosomes. The steps involved are given as below: a) SFLA involves a population 'P' of possible solution, defined by a group of virtual frogs(n). b) Frogs are sorted in descending order based on their fitness and partitioned into subsets called as memeplexes (m). c) Frog i is expressed as X i = (X i1 , X i2 , …..X i3 ) where X represents number of variables. d) Frogs with worst and best fitness are identified as X w and X b within each memeplex. e) Frog with global best fitness is identified as X g . f )

Shuffled Frog Leaping Algorithm
The frog with worst fitness is improved based on the following equation. D i is the step size of i-th leaping frog and D max is the maximum step size allowed. If the fitness value of new X w is better than the current one, X w will be accepted. Otherwise, the calculated step size of leaping frog D i and new fitness X neww are recomputed with X b replaced by X g . Further if no improvement is achieved, a new X w is generated randomly. The update operation is repeated for specific number of iterations. After a predefined number of memetic evolutionary steps within each memeplex, the solutions of evolved memeplexes are replaced into new population. This is called shuffling process. Global information exchange among the frogs is promoted by the shuffling process. The population is then sorted in order of decreasing performance values and updates the population based on best frog's position, repartition the frog group into memeplexes and progress the evolution within each memeplex until the conversion criteria are satisfied (Samuel and Rajan 2014).

Simulation results
The optimization algorithms have been implemented using the software MATLAB. Simulations are carried out for a 14 node network having 21 bidirectional links similar to NSFNET network topology. The fitness against the execution time for the genetic algorithm and shuffled frog leaping algorithm with 4 number of channels fand a load of 10 Erlangs is shown in Fig.4. Number of hops, holding time and cost are the paramateres in-cluded in the fitness function. The shuffled frog leaping algorithm has a better fitness compared to the genetic algorithm.
The mean blocking probability against number of generations for GA and SFLA with 4 number of channels fand a load of 10 Erlangs are shown in Fig.5 and 6 respectively. By comparing both the figures, its is clear that the blocking probability is lesser in SFLA than in GA. Among the three wavelength assignment techniques Round robin Technique has the least blocking probability. For different wavelength assignment techniques first fit, random, round robin, wavelength ordering and FWM aware priority based wavelength assignment, the rate of convergence of genetic algorithm and shuffled frog leaping algorithm with 4 number of channels fand a load of 10 Erlangs is shown Fig.7. By randomly selecting an individual and choosing the best fitness Figure 4: Fitness function of GA and SFLA value, the graphs are plotted. The average fitness score decreases, as the generations increase. For both GA and SFLA with different wavelength assignment techniques, the average fitness score is approximately the same. Among all the wavelength assignment techniques, FWM priority based assignment has a better average fitness score. The experimental results of mean execution time obtained for different wavelength assignment techniques First Fit, Random, Round Robin, Wavelength Ordering and FWM aware priority based wavelength assignment using GA and SFLA for various network load in Erlangs is as ahown in Table 1. The mean execution time (seconds)varies appropriately with the network loads and is observed that FWM aware priority based wavelength assignment technique requires very minimum mean execution time in both GA and SFLA algorithms for various network loads. When SFLA is compared with GA, SFLA requires minimum mean execution time for all the wavelength asignment techniques.
The imrpovements achieved in the mean execution time while using SFLA compared to GA is showm in Table 2. The experimental results are quantified using t-test to show the improvements in the proposed SFLA algorithm. The parameters t and p-value are dimensionless. The p-values obtained for all the wavelength assignment techniques are less than or equal to the level of significance value 0.05. This shows that the mean execution time is lesser for the proposed shuffled frog leaping algorithm compared to genetic algorithm.

Conclusions
One of the complex optimization problems in optical networks is Routing and Wavelength Assignment  (RWA) problem. In the proposed work, two optimization algorithms Genetic Algorithm and Shuffled Frog Leaping Algorithm are used to solve the problem. The fitness function minimizes the blocking probability, number of hops and cost. Basic wavelength assignment techniques such as first fit, random and round robin and also wavelength ordering and FWM aware priority based wavelength assignment are used to analyze the performance of the algorithms GA and SFLA.
Fitness value achieved is found to be better in SFLA compared to GA. The two optimization algorithms GA and SFLA are compared in terms of mean execution time, mean blocking probability and fitness score. The experimental results show that SFLA has better fitness score, less mean execution time and minimum mean blocking probability. Within the algorithm among various wavelength assignment techniques, FWM aware priority based wavelength assignment technique achieves better average fitness score and also less mean execution time. Time complexity of SFLA approach is lower compared to that of Genetic Algorithm and therefore some flexibility may be provided in the network design.