Genetic Algorithm for Routing and Spectrum Allocation in Elastic Optical Networks

Transcription

1 2016 Third European Network Intelligence Conference Genetic Algorithm for Routing and Spectrum Allocation in Elastic Optical Networks Piotr Lechowicz, Krzysztof Walkowiak Dept. of Systems and Computer Networks Wroclaw University of Science and Technology Wroclaw, Poland Abstract Elastic Optical Network (EON) architecture has been proposed as a promising technology for a new generation of OFDM networks. It is based on the concept that spectrum can be split into smaller slices than are used currently in the fixed-grid network. It allows better spectral utilization and support for bit rates over 100 Gb/s. EONs arise with the problem of routing and spectrum allocation (RSA). In this paper, we propose a Genetic Algorithm (GA) to solve the RSA problem with multicast flows. Different selection and crossover strategies are presented. Extensive numerical experiments are performed to select the most appropriate combination of operators and tuning parameters of the GA algorithm in the context of the RSA problem. Obtained results show that GA can be applicable. Index Terms elastic optical networks, routing and spectrum allocation, genetic algorithm I. INTRODUCTION Due to the innovations in technology, current single carrier Wavelength-Division Multiplexing (WDM) networks allow to use 40, 100 and greater Gb/s bandwidths per channel. However, the available optical spectrum range nm is divided by the International Telecommunication Union (ITU) into fixed grid with the width of each single spectrum slot equal to 50 GHz. It results with the necessity of allocating full wavelength to a connection even if the required traffic between nodes is much smaller. The low level of granularity results with inefficient usage of available spectrum resources. Currently deployed fixed grid does not support directly bit rates over 400 Gb/s because they overlap with at least one 50 GHz ITU grid boundary. As opposite, allocating small bit rates results with an inefficient spectrum utilization. In view of increasing network traffic, the Elastic Optical Network (EON) architecture has been proposed. It allows to assign either huge or small bandwidth and create flexible connections in optical networks. However, EON s technology arises with the problem of Routing and Spectrum Allocation (RSA), which according to [1] is NP-complete. Different optimization methods were proposed to solve the RSA problem. In [1], RSA is formulated as an Integer Linear Programming (ILP) and a heuristic algorithm Adaptive Frequency Assignment Collision Avoidance (AFA-CA) is proposed. There were also proposed other meta-heuristics Tabu Search (TA) [2], Simulated Annealing (SA) [3] and GA [4]. In the paper [5] the RSA problem is extended to the Routing, Modulation Level, and Spectrum Assignment/Allocation (RMLSA). The problem is further studied in [6], where an effective heuristic called Adaptive Frequency Assignment Division and Collision Avoidance (AFA-DCA) is proposed. EON with dedicated path protection is considered in [7], [8], [9], with proposed algorithms: AFA-DPP, TS, hybrid AFA-TS and GA. In the literature there are already proposed good algorithms for the RSA problem. Therefore, we decided to select one of them Genetic Algorithm implement it in the way which allows adding new strategies easily, and evaluate the best design approach. Our GA is implemented with different crossover and selection strategies. In order to decorrelate GA from the parameters selection, we tune them for each of the combinations separately. Moreover, we decided to compare GA with two initial solutions. After investigating the best strategies combination and parameters tuning, we compare effectiveness of our algorithm with the reference ones. Obtained results show that GA is appropriate in specific scenarios. Our research was conducted to prepare fundamental core for further development of the GA algorithm in the RSA domain. The remainder of the paper is organized as follows. In Section 2, we discuss some features of EON s technology. In Section 3, there is presented ILP formulation to that problem. In section 4, we describe proposed solution GA. In the last two sections, there are shown results of numerical experiments, our conclusions and description of future works. II. ELASTIC OPTICAL NETWORKS The problem of network granularity, which will provide required capacity and better spectrum usage for sub- and super- wavelength, has been solved through Orthogonal Frequency-Division Multiplexing (OFDM) technology. It allows to distribute data in multi-carrier system, where each subcarrier is orthogonally modulated. This fact allows them to overlap each other, and as a result, provides better transmission spectral efficiency. It is possible to allocate variable number of low-band subcarriers to a transmission, which results in a much more granulated and flexible spectrum grid. Each of the subcarriers can be modulated individually using different modulation formats. The transmission over shortest /16 $ IEEE DOI /ENIC

2 optical paths is able to use higher modulation levels, and the further ones can still provide required quality of connection transmission. To make usage of the OFDM technology possible in the optical networks, it is necessary to use alongside bandwidth variable transponders (BVTs), bandwidth variable cross-connects (BV-WXCs) and intelligent clients. The combination of these technologies creates term Elastic Optical Networks (EON) the network whose components will be able to adjust to the network s conditions, transmitted demands, and to select most suitable modulation format according to the bit rate and distance. As an analogy to the Routing and Wavelength Assignment (RWA) problem in DWDM optical networks, the Routing and Spectrum Allocation problem arises in EONs. RSA problem involves assigning adjacent frequency spectrum slices to connection request. The assignment is restricted to the frequency non-overlapping by many requests and selecting the same optical corridor (channel) for the whole lightpath. III. PROBLEM FORMULATION There is given a network topology which contains some nodes and fibre links which interconnect them. In the network, there are transmitted different demands. In this paper, we consider two types of them unicast and multicast. The unicast demand can be uniquely described by its source node, volume of data which has to be transmitted, and the destination node. The multicast demand has a similar representation, but instead of one destination node, it contains a set of them. It is assumed that in each node the incoming data can be retransmitted on any number of links. Each link consists of available spectrum on which the data can be transmitted. That spectrum is divided into small frequency slices, which are described by the integer indices. The demand can be only allocated on integer, non-negative number of slices. For each demand, there are available candidate routing structures. The candidate routing structure describes which links have to be involved to realize the demand. In case of a unicast demand, the structure is a path from the source node to the destination node. In case of a multicast demand, it is a tree without loops. The required number of slices which have to be allocated, depends on the volume (bit-rate) of the demand and the length of the routing structure. In more details, we apply the distance-adaptive transmission (DAT) rule as in [10]. The process of allocating demands has to meet the following constraints: spectrum contiguity for each demand on each link, adjacent slices in frequency spectrum should be allocated, spectrum continuity for each demand it should be allocated on the same slices on each link, spectrum non-overlapping only one demand can allocate one slice in frequency grid on particular link. For each demand, a single routing structure (path or tree) has to be selected. On that structure the range of slices (channel) is selected and the demand is realized on that channel. The goal function is to minimize the required size of spectrum in the network. To be more specific: the cost of allocation is represented by the highest occupied slice index on any link, and that value has to be minimized. A. ILP formulation There is given a directed graph G = (V,E), where V there is the set of nodes in the network. E is the set of links. Each link contains certain number of frequency slices S. Slices on each link are grouped in channels C. The channel is created from a set of adjacent slices. There is given a list of demands D which have to be allocated in the network. Each demand is described by the tuple of source node, volume and destination node/nodes. For each demand there are available candidate paths P. For each candidate path, there is a correspondent list of available channels on which the demand could be allocated. There are some constants, which help to formulate constraints and objective function. δ edp is a binary value which provides the information whether given link belongs to certain available path of the demand. The requested number of slices for realizing certain demand on path is represented by n dp. The γ dpcs provides information whether channel associated with the demand and path contains certain slice. The allocation process is made by selecting one available channel and path for each demand. The binary variable x dpc is equal to 1 if channel c is used to realize demand d on path p. Variable z s informs whether slice with index s is occupied by any demand on at least one link. The goal is to minimize the span of necessary spectrum in the network which is equivalent to equation 1. indices: v =1, 2,...,V e =1, 2,...,E d =1, 2,...,D s =1, 2,...,S p =1, 2,...,P d c =1, 2,...,C dp constants: δ edp n dp γ dpcs variables: nodes links demands frequency slices candidate structures for demand d; if demand is a unicast demand, structure p is a path connecting end nodes of the demand. If d is a multicast demand, structure p is a tree with the root in the source node and including all client nodes candidate channels for demand d allocated on structure p =1, if link e belongs to structure p realizing demand d; 0, otherwise requested number of slices for demand d on structure p =1, if channel c associated with demand d on candidate structure p uses slice s; 0, otherwise 274

3 x dpc =1, if channel c on candidate structure p is used to realize demand d; 0, otherwise (binary) z es =1, if slice s is occupied on link e; 0, otherwise (binary) z s =1, if slice with index s is allocated on any network link; 0, otherwise (binary) z maximum slice index used in the network (integer) objective: min Φ = z (1) constraints: P C x dpc =1, d D (2) p=1 c=1 D P d=1 p=1 c=1 C γ dpcs δ edp x dpc z es, e E,s S (3) E z es E z s, s S (4) e=1 S z s z, s S (5) s=1 To reduce the problem complexity, candidate structures are represented in the link-path notation [11]. For unicast demands there can be selected k shortest paths, and for multicast ones, minimal spanning trees (MST) [12]. Furthermore, to simplify the problem, there is considered only one modulation level regardless of the selected lightpath for the demand, there is used the same modulation format previously selected, according to the DAT rule. Thus, depending on the length of the path or tree, the different number of slices are required to establish the demand. IV. GENETIC ALGORITHM As a solution to the above-mentioned problem, we present a genetic algorithm, which can provide suboptimal solution in a reasonable time. In GA each chromosome corresponds to a possible solution to the problem, therefore it is necessary to represent search space, in the form which will allow to apply genetic operators. To unambiguously represent allocation of available demands, the First-Fit method can be used. Demands are stored in ordered list (figure 1) and for each one of them there is selected a candidate structure. Demands are represented by variables,,...d n. Selected path candidate is represented as a function of the chromosome, because different path candidates can be selected for different chromosomes for the same demand. Each demand is placed exactly once in the list. For each demand, preserving list order and according to the selected structure candidate, it is allocated in the first free channel on that path. The allocation process restricts all of the RSA constraints on all links involved in that path. The population is represented as a list of chromosomes. In each generation the number of individuals in the population is constant. C : p 1 (C) p 2 (C) Fig. 1. Ordered list of demands. d i p i (C) d n 1 p n 1 (C) d n p n (C) According to the shape of the chromosome, the problem is split into two separate parts (contexts). First part is to select order of demands in the list. According to that order, demands will be allocated in the available spectrum. Second part is to determine which candidate structure m(path or tree) will be used for which demand. These two steps do not have to be performed successively. Ordering of demands can be done in parallel to the selection of candidate paths. Therefore algorithm can operate on two different contexts, and to manage that duality, it works in cycles. For a predefined number of iterations, it tries to improve demands order, and after that it switches to path selection. For some time it works on that context, and when the cycle is over, it comebacks to improving demands order. A. Mutation For the path selection context, the mutation can be defined as follows: in chromosome are randomly selecte0% of genes. For each one of them is randomly selected other candidate path with equal probability (excluding the same candidate path). In terms of the demand strategy, there are selected two demands in the chromosome. The positions of those demands in the chromosome are swapped. B. Crossover For the path selection context, the crossover operation is done as follows: there is randomly selected the same crossing point in two parents. First child has demands order as it is in the first parent. From the beginning till the crossing point of the child s chromosome, the selected structures are as in the first parent. However, from that point, they are selected as they are in the second parent (for corresponding demands, because the order can be different). The second child is created analogically. In the figure 2 there are selected two parents: C 1 and C 2. The splitting point is marked with triangle. Child C 3 has the same demands order as the child C 1. Up to the splitting point it has paths selected as they were in the chromosome C 1. After that point, paths are selected from parent C 2 (marked with bold font). Chromosome C 4 is created similarly, but with opposite parent s selection. In the chromosome C 3 candidate structure for demands and is selected from the chromosome C 2 instead of the C 1. There is an equal probability, that for the child there will be copied values up to the splitting point from one parent and replaced from the second one, or there will be copied values 275

4 C 1 : C 2 : C 3 : C 4 : p 3 (C 2 ) p 3 (C 2 ) p 2 (C 1 ) p 4 (C 2 ) p 2 (C 1 ) p 4 (C 2 ) p 3 (C 1 ) p 2 (C 2 ) p 3 (C 1 ) p 2 (C 2 ) p 4 (C 1 ) p 4 (C 1 ) p 5 (C 1 ) p 5 (C 2 ) p 5 (C 2 ) p 5 (C 1 ) p 6 (C 1 ) p 1 (C 2 ) parent s chromosomes: C 1 and C 2. The child C 3 has demands from to copied from the parent C 1. After the splitting point, the demands and are placed as they occur in the chromosome C 2. Selected operations always provide feasible solution, so there is no need to create a fix or a penalty function [13]. C. Selection There were implemented two strategies of selecting chromosomes to produce offspring roulette wheel (RW) and rank (RA). In the roulette wheel the probability of selecting chromosome C i from the population is presented in the equation 6, where PRW i is the probability, FRW i is the fitness of i-th chromosome, and N is the number of all chromosomes in current population. Fig. 2. Crossover of path strategy PRW i = FRW i N j=1 FRW j (6) from the splitting point till the end of the chromosome, and replaced from the beginning, up to the splitting point. For demands crossover, there are implemented three different strategies single, double and triple-splitting point (SP, DP, TP). The crossover process is described on the single splitting point strategy and the others are created analogically. There is randomly selected one splitting point, same in both parents. First child is created by copying demands order from the first parent in the range from start till to that point. The rest of the chromosome is filled up with the missing demands in the order as they occur in the second parent. Second child is created in the analogous way. There is an equal probability that demands will be copied from the start of the chromosome till the splitting point, or from the splitting point till the end of it. When demands are placed from other parent, there are also copied selected candidate paths for those demands. In the figure 3 there are two C 1 : C 2 : C 3 : C 4 : p 3 (C 2 ) p 3 (C 2 ) p 2 (C 1 ) p 4 (C 2 ) p 2 (C 1 ) p 4 (C 2 ) p 3 (C 1 ) p 2 (C 2 ) p 3 (C 1 ) p 2 (C 2 ) Fig. 3. Crossover of demands strategy p 4 (C 1 ) p 4 (C 1 ) p 5 (C 1 ) p 5 (C 2 ) p 6 (C 1 ) p 1 (C 2 ) p 5 (C 2 ) p 5 (C 1 ) Roulette wheel approach is not directly applicable for the current problem formulation, because there is determined a cost function instead of the a function. Hence, the cost has to be transformed into fitness. This can be done with the equation 7, where C i is the cost of i-th chromosome. N j=1 FRW i = C j (7) C i As an alternative, chromosomes can be selected according to their rank. Firstly, they are sorted in the descending cost order, after that to each one of them is assigned a rank value, according to the equation 8. r i = i, i 1, 2,...,N (8) The probability of selecting a chromosome is shown in the equation 9 [14]. r i P RANK i = N j=1 r (9) j In the algorithm there was also introduced an elitism mechanism which adds exact copy of n best chromosomes in the current population to the next one. D. Initial population The initial population of GA can strongly affect obtained result. Therefore, there are considered two approaches randomly selecting demands and candidate paths in the initial population and heuristic Maximum Spectrum First (MSF) [13]. When MSF is used, it is only applied to the first chromosome and the rest is filled up randomly to provide diversity in the population. For each multicast there is calculated a metric equal to the volume of the demand, multiplied by the number of receiving nodes. Those demands are sorted according to the decreasing value of that metric. Unicast demands are sorted in a descending order of their volume. Firstly, there are processed multicast demands and after that, unicast ones. For each demand, there are successively checked available paths and there is selected one, providing lowest cost function with the First-Fit spectrum allocation. 276

5 According to the selected initial solution, the algorithm is further distinguished as GA (random initial solution) and GA-MSF (MSF initial solution). E. Pseudocode The pseudocode of implemented GA is presented in the algorithm 1. Algorithm 1 Genetic algorithm 1: initialize values: P - size of population N - number of generations SC - strategy cycle SR - strategy ratio CR - crossover rate MR - mutation rate E - elitism amount 2: if initial solution: initialize first chromosome with MSF initialize rest of the population randomly 3: else: initialize population randomly 4: i := 0 5: calculate fitness of each individual using First-Fit 6: if i % SC == 0 OR i % SC == R: change algorithm strategy context 7: copy E best individuals to the next population j := E 8: select two individuals from the population (make a copy of them) 9: if random() < CR: 9.1: if both selected chromosomes are the same individual, mutate one of them 9.2: perform crossover 10: if random() < MR: mutate first selected chromosome 11: if random() < MR: mutate second selected chromosome 12: add copied two chromosomes to the next population 13: j += 2, if j < P go to step 8 14: assign next population to the current one, i += 1 15: if i >= N then return best result and STOP, else go to the step 5 V. NUMERICAL RESULTS In this section we present performance of our GA. The first part is focused on finding the best parameters and strategies. In the second part the results are compared with other reference algorithms. The efficiency of an algorithm is presented according to the allocated spectrum resources (equation 1). As a reference, the following algorithms are selected: KW - Adaptive Frequency Assignment heuristic [13] MSF - Maximum Spectrum First heuristic [5] Numerical experiments are performed on EURO28 (28 nodes, 82 links) network topology (figure 4). We consider candidate structures k 4, 6, 8, 10, 20 for unicast demands and p 50, 100, 200, 300, 500 for multicast demands. The experiments are performed for scenarios with the multicast and unicast demands (MUD) at the same time and only with the multicast (MD) ones. However, due to the fact that results obtained for the MUD scenarios are not satisfactory, only the MD scenarios are studied deeper. The results for the MUD scenarios are only presented in the table, as a reference that the algorithm is not applicable for them. Each MUD scenario contains aroun20 demands and MD scenario aroun0. The tuning process is done for 6 demand s sets. Experiments for best strategies selection and comparison to reference algorithms are obtained as an average result of 20 different scenarios. Fig. 4. Network topology In the table I, there are presented implemented strategies for GA operations and in the table II there are shown values of tuning parameters. In the table III there are presented best found parameters of GA. GA operation Demands crossover Selection TABLE I AVAILABLE STRATEGIES FOR GA. Strategies single point, double point, triple point rank, roulette wheel A. Tuning of GA The GA Algorithm is tuned separately for each of the possible combinations of selection strategies, demand crossover strategies and random or MSF initial solutions (12 combinations). Parameters are tuned consecutively, it is first investigated crossover ratio value and rest of the parameters are taken as initial ones (table II). The second step is the mutation tuning, where best found crossover ratio value is 277

6 Algorithm GA GA-MSF Selection strategy Rank Roulette wheel Rank Roulette wheel TABLE III SELECTED BEST PARAMETERS AFTER TUNING OF GA. Demands strategy Crossover rate Mutation rate Nr of generations Nr of individuals Strategy ratio Strategy cycle Single point Double point Triple point Single point Double point Triple point Single point Double point Triple point Single point Double point Triple point TABLE II VALUES OF TUNING PARAMETERS. Parameter name Values Initial value crossover ratio 0.80, 0.85, 0.90, 0.95 mutation ratio 0.2, 0.3, 0.4, number of generations upper boun number of individuals 10, 20, strategy cycle 10, strategy ratio 0.0, 0.2, 0.5, 0.8, elitism amount 1 during all experiments 1 Fig. 6. Tuning number of generations in GA-MSF. set instead of the initial one. The replacement of initial values with the found ones is repeated in further steps, where there is tuned a number of generations, number of individuals and strategies ratio and cycle. Fig. 7. Average improvement in GA for different strategy cycles and ratios (random initial solution). Fig. 5. Tuning number of generations in GA. In figures 5 an are presented results for tuning number of generations. For all tested cases, the significant improvement occurs after first several tens of iterations. After around 60 iterations, the algorithm starts to saturate. In further considerations the number of generations is selected as 100, as a compromise between cost decreasing and required computational time. The tuning of strategy cycle and ratio is presented in the figures 7 and 8. Presented values are of average improvement, referring to the initial solution. The ratio and cycle are described as a pair of values, where first one denotes how many iterations were considered as a cycle, and the second one, how many iterations were considered for the ratio. When ratio is equal to 0.0, the algorithm spends whole cycle on paths selection. As opposite, value 1.0 stands for the situation when only demand s order is changed in the whole cycle. According to the results, operating only on demand s order is the worst possibility, however focusing on path selection is often the second best result. The best result, in most cases, is either for ratio 50% 50% or 80% 20%. Therefore, manipulation on the order of demands also puts important impact on the obtained final result. 278

7 TABLE VI SELECTED STRATEGIES AND PARAMETERS FOR ALGORITHMS COMPARISON. Parameter name GA GA-MSF Selection strategy Rank Roulette wheel Demands strategy Single point Triple point Crossover rate Mutation rate Nr of generations Nr of individuals Strategy ratio Strategy cycle Fig. 8. Average improvement in GA-MSF for different strategy cycles and ratios. B. Best strategies selection To select best strategies for GA and GA-MSF, the experiments are extended to 20 different demands sets. The results presented in tables IV and V are averaged over number of structure candidates and different scenarios. There are compared according to three metrics competitive ratio (CR), ranking and amount of best results for each of the demands set. Selection criteria TABLE IV SELECTED BEST STRATEGIES FOR GA. Rank Roulette SP DP TP SP DP TP CR 2.41% 3.38% 2.82% 2.74% 2.50% 2.73% Ranking Best result In case of random initial solution, results are close one to each other, however, two metrics show that rank with single point crossover strategy provides best results. In case of MSF initial solution, all metrics indicate that the roulette with triple point should be selected. Fig. 9. Average cost as a function of number of candidate structures for scenarios with multicast demands. Average cost as a function of number of candidate structures is presented in the figure 9 for MD. GA-MSF provides better results than other algorithms. Best cost as a function of tested scenarios is presented in the figure 10 for MD. For each scenario there is taken an average cost from a different number of candidate structures. In most cases GA-MSF leads. TABLE V SELECTED BEST STRATEGIES FOR GA-MSF. Selection criteria Rank Roulette SP DP TP SP DP TP CR 3.06% 1.91% 2.60% 1.63% 1.32% 0.73% Ranking Best result C. GA against reference algorithms During comparison of GA and GA-MSF against reference algorithms, the best strategies combination obtained in the previous section are used. Best parameters are selected, according to obtained results for corresponding strategies (table III). Selected parameters and strategies are presented in the table VI. Algorithms are compared for different number of candidate structures, for MD and MUD sets. Fig. 10. Best cost as a function of scenarios with multicast demands. Table VII shows results for competitive ratio for different number of candidate structures. For unicast demands, the GA-MSF provides best results and for mixed demands KW. According to the obtained results, GA-MSF is an appropriate solution for scenarios with multicast demands. Worse results for mixed scenarios may be caused by a significantly bigger number of demands to process. In the RSA problem, evaluating the cost (fitness) function with all of its constraints is time consuming, which is multiplied by the 279

8 TABLE VII COMPETITIVE RATIO AND RANKING FOR DIFFERENT NUMBER OF CANDIDATE STRUCTURES Criteria Competitive ratio Ranking Number of candidate structures Scenarios with mutlticast demands Scenarios with unicast and multicast demands GA GA-MSF MSF KW GA GA-MSF MSF KW k=4,p= % 0.00% 11.69% 17.44% 16.74% 10.46% 24.03% 0.09% k=6,p= % 1.66% 14.95% 13.36% 25.31% 16.11% 29.20% 0.00% k=8,p= % 0.67% 15.10% 9.15% 29.62% 18.13% 30.61% 0.00% k=10,p= % 0.33% 10.26% 9.23% 32.36% 21.90% 40.73% 0.00% k=20,p= % 0.17% 10.98% 9.93% 38.65% 23.45% 43.12% 0.00% k=4,p= k=6,p= k=8,p= k=10,p= k=20,p= number of individuals in the population and the amount of demands. Therefore, it is not possible to provide sufficiently big population and number of generations for GA in reasonable time, to fully exploit benefits from its operators, especially when the number of demands is big. Promising results are obtained when the search space is narrowed to only several tens of demands. The amount of candidate structures provides less impact than demands on algorithm efficiency. Furthermore, when algorithm starts with worse initial solution, rank selection strategy provides better results than roulette wheel. When algorithm starts with an initial result provided by heuristic MSF, roulette wheel is better. The RW has a tendency to more often select best results for operations than RA. It seems reasonable to narrow down the selection tendency to best results when individuals are closer to the optimal, and, as opposite, to allow wider selection providing bigger search space when algorithm is far from optimal solution. VI. CONCLUDING REMARKS In this paper we proposed GA-MSF algorithm for RSA problem and provided its detailed description. We performed numerical experiments to find the best parameters and strategies set. Finally, we compared efficiency of GA-MSF with reference algorithms: KW and MSF. Obtained results show that GA-MSF can provide good spectral utilization for scenarios with small demands set and big number of candidate structures. In the future, we plan to extend our research to other network topologies with different number of nodes and links. We are also considering further GA extensions adding different strategies for path s selection crossover and mutation operations. Furthermore, we want to perform investigation, how big different strategies make an impact on improving the result, as a function of iteration s ranges. It would allow to decide which strategies combination is the best for which period of algorithm execution. The strategy could also be adapted to the population, considering spread of cost or diversity of genomes in the chromosomes. ACKNOWLEDGEMENTS This work was supported by the Polish National Science Centre (NCN) under Grant DEC-2012/07/B/ST7/01215, FP7 project ENGINE (Grant Agreement No ) and statutory funds of the Department of Systems and Computer Networks, Wroclaw University of Science and Technology. The authors are grateful to FP7 project ENGINE, Grant No for the access to the computing infrastructure built in the project. REFERENCES [1] M. Klinkowski and K. Walkowiak, Routing and spectrum assignment in spectrum sliced elastic optical path networks, IEEE Community Letter, vol. 15, no. 8, pp , August [2] R. Goścień, M. Klinkowski, and K. Walkowiak, A tabu search algorithm for routing and spectrum allocation in elastic optical networks, IEEE, vol. 14, [3] M. Aibin and K. Walkowiak, Simulated annealing algorithm for optimization of elastic optical networks with unicast and anycast traffic, in ICTON, July [4] J. H. L. Capucho and L. C. 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