IEEE WCNC 2011 - Network
Adaptive CAC Using NeuroEvolution to Maximize Throughput in Mobile Networks Xu Yang / Yapeng Wang
John Bigham / Laurie Cuthbert
MPI-QMUL Information Systems Research Centre Macao Polytechnic Institute Macao SAR, China xuy/
[email protected]
School of Electronic Engineering and Computer Science Queen Mary University of London London, UK john.bigham/
[email protected] constraints for each different kind of call, particularly New Call Blocking Rate (NBR) and Handoff Failure Rate (HFR).
Abstract—this paper proposes a learning approach to solve adaptive Connection Admission Control (CAC) schemes in future wireless networks. Real time connections (that require lower delay bounds than non-real-time) are subdivided into hard realtime (requiring constant bandwidth capacity) or adaptive (that have flexible bandwidth requirements). The CAC for such a mix of traffic types is a complex constraint reinforcement learning problem with noisy fitness. Noise deteriorates the final location and quality of the optimum, and brings a lot of fitness fluctuation in the boundary of feasible and infeasible region. This paper proposes a novel approach that learns adaptive CAC policies through NEAT combined with Superiority of Feasible Points. The objective is to maximize the network revenue and also maintain predefined several QoS constraints.
Adaptive CAC is a very complex reinforcement learning problem with constraints, and there has been little research on the problem. Huang [2] proposed a CAC scheme that considers non real-time and real-time traffic but the limitation of that approach is that there is no CAC control on the non realtime calls. Additionally, the network cannot adaptively allocate different bandwidth levels for real-time calls to adapt to the system status, and the bandwidth adaptation feature of realtime calls is not fully exploited to maximize the network utility. In this paper, we propose a learning approach to solve the adaptive CAC problem. NEAT (NeuroEvolution of Augmenting Topologies) is used to generate near optimal solutions, and Superiority of Feasible Points is used to solve constraints. Although learning can be time consuming, the results show that the Adaptive CAC scheme can provide a great deal of benefit compared with traditional CAC schemes.
Keywords-Adaptive CAC; NEAT; noise control; constraint optimization
I.
INTRODUCTION
Next generation mobile networks will offer a wider range of advanced services including high speed internet access and video telephony. QoS (Quality of Service) requirements, such as sufficient bandwidth and tolerable delay, for various types of real-time and non real-time multimedia traffic will vary significantly over a wide range of parameters [1].
The rest of this paper is organized as follows. Section 2 defines the system model; Section 3 gives a brief introduction to NEAT; Section 4 analyses the challenges to solve Adaptive CAC; Section 5 formalizes the fitness function; Section 6 presents the simulation results; and Section 7 concludes.
Multimedia applications can be classified into real-time and non-real-time applications [2] depending on their tolerance to delay and delay variation.
II.
When a request for a real-time connection arrives at a cell, the network allocates a certain amount of bandwidth capacity to that request. The amount of allocated capacity is determined by the network load and the type of the request. For example, although the network may have enough available bandwidth to accept an adaptive real-time connection at its maximum QoS level, this connection may be allocated lower bandwidth, and hence a lower, but still acceptable, QoS level to reserve more bandwidth for future request. Once a real-time connection is admitted, its allocated bandwidth will remain the same while it is handled within that cell, although it can be adjusted if the mobile terminal is handed over to another cell. All the non real-time connections share the capacity left over from real-time connections. The similar approach to model the non real-time calls has been proposed in [5, 6], but that only considers voice calls (that consist of a constant-rate
Real-time traffic can itself be classified as either hard realtime or adaptive real-time. Hard real-time applications include audio with video phone calls, video conferencing and telemedicine [3, 4] and usually consist of a constant-rate packet stream; they can only tolerate a very small degree of packet dropping due to reduced bandwidth allocation. Adaptive realtime applications, such as video on demand [4], can be satisfied with very flexible bandwidth requirements. With such traffic types, Connection Admission Control (CAC) scheme not only needs to make decisions on whether to accept a connection, but also needs to allocate a certain amount of bandwidth capacity to each request for an adaptive real-time call, this capacity being determined by the network load and the type of the request. The objective is not only to maximize the network revenue, but also to maintain predefined QoS
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SYSTEM MODEL
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packet stream) and data calls (that share the bandwidth left over by voice calls). In this paper, we assume that the total network capacity for each network cell keep fixed. In next generation wireless networks, the capacity allocated for adaptive real-time connections could be changed during the connection period. The proposed approach introduced in this paper can easily to be extended to adapt to such situation. III.
generated small set of neural networks with simple topologies. Each of these neural networks is assigned a fitness value depending on how well it suits the solution. Once all the members of the population are assigned fitness values, a selection process is carried out where better individuals (those with a high fitness value) stand a greater chance to be selected for the next operation. Selected individuals undergo recombination and mutation to create new ones. Low fitness individuals are discarded from the population and better ones are included. Structural mutations add new connections and nodes to neural networks in the population, leading to incremental growth. The whole process is repeated with this new population until some termination criteria is satisfied. [8] In [8], the experiments demonstrated that NEAT has beaten a traditional RL algorithm and another NE algorithm on difficult reinforcement learning tasks like double pole balancing and non-Markovian double pole balancing.
ADAPTIVE CAC AND NEAT
A. Challenges of Adaptive CAC In the Adaptive CAC domain, the feasible area is very small compared with the whole search domain: even if the HFR constraint is 1%, the possible HFR could be from 0 to 100%. If there are m classes of traffic, the feasible area that considers only HFR constraints is 10-m of the search space, which makes the search for feasible policies very difficult.
C. Using NEAT It is first necessary to define the input nodes of the neural network, define the output nodes of the neural network, formulate a fitness function to evaluate the networks created, define how to stop the learning process and then to extract the learned neural network with the highest fitness score. Additionally the issue of handling different kinds of constraints also needs to be considered in detail in the context of the CAC problem. Normally the inputs are the perceived state of the environment that is essential to make the action decision. For the CAC problem, the perceived state may include the type of new connection all request (each input representing one kind of request call), the bandwidth for different kinds of traffic (other inputs) and some statistics on QoS constraints. In this paper, we use seven inputs: 1-6 identify the type of the request call with 7 denoting the total bandwidth of by real-time calls. The outputs are the possible actions that can be performed in the real application. There is only one output to indicate the connection admission control decision: the output value is a real number from 0 to 1, which is then translated into a QoS level to be applied to the request event. The fitness function gives the goal of the learning system, and also defines what is meant by a good or bad policy. Monte Carlo methods are ways of solving the RL problem based on averaging sample returns during operation. When the evolved neural network topology is good enough to operate the application satisfactorily, evolution is stopped, and the policy chosen is the one with the highest fitness score.
Additionally, maintaining HFR and NBR constraints are conflicting requirements as they are dependant parameters, and decreasing one may cause an increase in the other. Moreover, the environment is also dynamic: a CAC action will affect not only the immediate reward but also the next situation, and through that, all subsequent rewards. To make an optimal decision, the network should not only consider the current state, but also the future traffic, which is not known in advance. In the CAC domain, one important feature is the diversity of user profiles and network environment. According to their different geographical location network, cells may have different user scenarios, and different service providers may consider different QoS parameters. Although this paper only considers three kinds of applications, some service providers may classify the traffic into more categories. Therefore, making the system extendable, flexible and easy to implement is a very important design requirements. B. NEAT introduction In the literature, RL (Reinforcement Learning) algorithms and traditional GAs (Genetic Algorithm) have been implemented in the CAC domain. However these technologies have their own limitations: RL is difficult to scale up to a large state space and requires very complicated function approximation methods to handle constraints; GAs require experts to design the encoding, decoding scheme and other operator parameters. NEAT is a kind of NeuroEvolution (NE) method. Neuroevolution (NE) [7] is policy search method, which uses evolutionary computation to optimize a population of neural networks, where neural networks are the phenotype being evaluated, and the genotype is a compact representation that can be translated into an artificial neural network [8]. NEAT can evolve both weights and network topologies, and it can evolve the right topology with unlimited hidden nodes on its own [9]. The evolution of NEAT starts with a randomly
IV.
OBJECTIVE FUNCTION
It is assumed that network reward (utility) is a linear function related to bandwidth consumed, formulated as, R=β×b×(1/µ) where β is a reward (utility) coefficient that indicates the importance level of a call being carried in a cell, b is the bandwidth consumed, and (1/µ) is the holding time. Normally β is different according to the type of call. As non real-time traffic can tolerate large delay and delay variance,
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(more tolerable at low QoS level) it is assumed that its reward (utility) coefficient (βnr) is less than that for real-time traffic (βr). Additionally it is assumed that the reward (utility) coefficient of adaptive real-time traffic is the same as for hard real-time traffic, although this could be changed without modifying the approach).
evaluated during each iteration of the genetic algorithm, the results can be improved. Chu [11] concludes that increasing the sample size is equivalent to reducing the variance of the estimated fitness. However the fitness calculation is the most time consuming part of the EA.
As βnr< βr and non real-time traffic can only occupy the capacity left over from real-time traffic, the only way to maximize the network revenue is to maximize the revenue from carrying real-time traffic. Therefore the network needs to allocate as much bandwidth as possible to real-time calls after guarantee that the total for non real-time, Tnr is satisfied. The objective function Fobjective is defined as average reward per request call. NEAT has the objective to maximize Fobjective.
Fobjective = +
β r λX ,s ×( λ μ X ,s
q
∑ dk ,s × bk + k =1
λ X ,h μ X ,h
∑ dk ,h × bk
•
Inheritance of rescaled mutation rate: This requires a down-scaling of the mutations and has been proposed in [18]. This method has not been intensively tested in experiments and remains for future research.
However noise has much more influence in constraint optimization problems as it not only affects the end phase of the optimization but has an effect on the assessment of the feasibility or infeasibility of a potential solution when it is near the boundary region. The boundary between the feasible and infeasible region is quite important as many of optimal solutions are found there. In most constraint handling methods, an infeasible policy has much less fitness than a feasible policy as it is usually penalized by a negative fitness. Due to noise effects, the policies in the boundary of feasible and infeasible region can be feasible in one training episode but infeasible in another training episode. While a feasible policy can be selected to create offspring; however an infeasible policy may be discarded, leading to the loss of a potentially optimal genotype. Therefore noise brings more uncertainty into the evolution process for constrained optimization problems.
k =1
CONSTRAINT HANDLING WITH NOISY FITNESS
For the CAC domain the state space is huge. Each policy can only be evaluated by a limited amount of events, and it is not possible to go through the whole state space in a short time period. Therefore the fitness evaluation is noisy due to measurement limitations or incomplete training data. This section analyses the noise effect in constraint optimization problems and provides our solution. A. Noise Effect in optimization problem Noise is a common phenomenon in most real world optimization problems, e.g. [10, 11]. It can come from different sources as measurement limitations, stochastic simulation procedures, and user input [12]. EAs (Evolutionary Algorithms) have been shown to perform better than several local search methods on a class of simple noisy problems in [13], and many EA approaches have been applied to optimising noisy objective functions effectively [14-16], which also gives a detailed theoretic analysis of the influence of noise on the performance of evolution strategies and the main effect of fitness noise., which are: •
Reduction of convergence velocity as noise deteriorates the final location of the optimum.
•
Deterioration of the final optimum location quality.
B. Handling constraints-Superority of Feasible Points In this paper, we use the Superiority of Feasible Points (SFP) method to handling constraints, as this can reduce the noise effect on the boundary of feasible and infeasible region. SFP has shown promising success in many GA applications. This method differentiates between feasible solutions and infeasible solutions [19, 20]. The basic principles are:
The main convergence improvement techniques to handle noise in GAs from [15] are: •
Increasing the population size. [12, 15] suggests that if the population size is increased, the performance of the EA can be improved when it is faced with a noisy fitness function. With a large population, the influence of noise in evaluating an individual may be compensated by a similar individual, so a simple approach to reducing the influence of noise on optimisation is to use a large population size.
q
λY ,s λ × pY ,s × bY + Y ,h × pY ,h × bY ) μY ,s μY ,h V.
•
•
Any feasible solution is preferred to any infeasible solution;
•
Among two feasible solutions, the one having the better objective function value is preferred;
•
Among two infeasible solutions, the one having smaller constraint violation is preferred.
The fitness of infeasible policies is only measured by constraint violation and is not affected by fluctuations caused by fitness noise. However in many other penalty handling techniques, the fitness of infeasible policies is determined by the combination of constraints violation and objective fitness, which will enlarge the noise effect in many cases.
Resampling or enlarging the sample size of each individual policy. Resampling is a simple method to improve the convergence toward the optimum of EAs. Given the individual’s genome y, the fitness F(y) is measured m times and noise strength and standard deviation is reduced by √m. [17] demonstrates that by changing (i) the amount of time spent on evaluating each candidate solution and (ii) the number of candidates
A fitness function that follows these rules is defined in [19]:
899
()
⎧f x ⎪ F x =⎨ m ⎪ f worst + ∑ gi x i =1 ⎩
()
()
becoming trapped into local optima. This is valuable since in many complex constrained problems, the global optimum is located on the boundary between the feasible and infeasible regions.
x ∈ feasible region 2
x ∈ infeasible region
of the worst where fworst is the objective function value G feasible solution in the last population, and gi ( x) only refers to inequality constraints (the equality constraints are transformed into inequality constraints). Thus the fitness of an infeasible solution not only depends on the amount of constraint violation, but also on the feasible solutions in the population.
In many RL tasks, NEAT has better performance than GAs and other NE algorithms.
By following the rules, during the evolution when most solutions in a population are infeasible, the search forces solutions to come closer to the feasible region. Once sufficient solutions exist inside the feasible region, the search is mainly guided by the objective function to find a feasible optimum.
The evolution results indicate that NEAT combined with SFP can successfully handle a complex constraint optimization problem with noisy fitness in a large search space.
The first shortcoming in this approach is that it used tournament selection to select good parents to generate offspring. The tournament selection process has two stages: (i) select a group of, N (N ≥ 2) then select the individual with the highest fitness from the group and discard all others. It does not require any penalty parameter to handle constraints or objective function. The selection pressure can be easily adjusted by changing the tournament size N. If the tournament size is larger, weak individuals have a smaller chance to be selected. Although the pair-wise selection can avoid the definition of any penalty factor, a major drawback of tournament selection is that randomly selecting individuals within each group may discard very competitive individuals if these individuals are in the same group with the best individual [21].
This simulation model we used in this paper has been widely used in several research papers, e.g. [22, 23]. A single cell with fixed channel capacity C=20 (bandwidth unit BWU) was constructed in the simulator. We assume that each kind of call arrives according to a Poisson distribution with the holding time for each kind of call being negatively exponentially distributed. All arrival distributions and call holding distributions are independent of each other. The average holding time for different kinds of calls is the same value: 20. Arrival events include new call arrival events and handoff arrival events and as call departures do not affect the CAC decisions, we do not consider departures.
Also in this paper we used a different selection method, not tournament selection: each individual will be assigned a total fitness according to its objective and penalty fitness, and only 20% of best individuals are selected to create offspring.
VI.
The QoS levels for adaptive real-time calls have 11 levels (0 to 10) with those allocated at QoS level 0 rejected, and those allocated at QoS level 10 accepted at the maximum QoS level. Other traffic parameters are shown in Table 1.
Additionally, it is mentioned in [24] that in cases where the ratio between the feasible region and the whole search space is too small (e.g, when there are constraints that are very difficult to satisfy), this approach may fail unless a feasible point is introduced in the initial population.
TABLE I.
•
TRAFFIC PARAMETERS
Parameters
To overcome these disadvantages, we combined NEAT with SFP to solve the problem. In our approach, two features of NEAT can work cooperatively with SFP to handle constraints: •
SIMULATION RESULTS
NEAT begins with a uniform population of simple networks with no hidden nodes and inputs connected directly to outputs, and new structures are introduced incrementally by adding new genes. It continually elaborates on its solutions, leading to increasingly sophisticated strategies. In this way, NEAT tends to search through a minimal number of weight dimensions and finds an appropriate complexity level for the problem, significantly reducing the search dimension and the number of generations needed to find a feasible solution.
HR
AR
NR
BWU consumed
1
[0.1,1]
≥ 0.05
Reward rate
1
1
(0,1)
2/1
2/1
New call arrival rate/handoff arrival rate Ratio of new call arrival rates
2/1
1:1:2
Each simulation evolved 200 generations; each generation contains 500 policies and each policy was evaluated by 50000 events. The target species size is 5. After 200 generations, the percentage of improvement was very low. For example, in one simulation, the highest fitness in the 500th generation only has 1.04% of improvement compared with 200th generation. The simulation results are compared with a Greedy Policy (GP) in which the network always accepts a real-time call at its highest QoS level if there is bandwidth available to carry this call, otherwise it rejects it. The following Figures demonstrate the performance of Adaptive CAC at different offered loads; this is evaluated based on an average of 5 simulation runs. Offered load is
NEAT speciates the population so that individuals compete primarily within their own niches; in this way topological innovations are protected and have time to optimize their structure before they have to compete with other niches in the population. Throughout evolution, NEAT maintains a list of species. This feature can help to maintain the diversity of the population, a very important feature to handle constraints. Maintaining a few infeasible solutions close to the feasible region can help avoid
900
∑
defined as Offered load =
λ μ
1.1
Comparision of Total Revenue %
Total Capacity Figure 1, Figure 2 and Figure 3 compare total NBR, total HFR, and total revenue of Adaptive CAC and GP at different offered loads. We can see that Adaptive CAC scheme not only satisfies all the predefined total NBR and HFR constraints at different offered loads, but also decreases NBR and HFR to very low levels. For example when the offered load is 2.0, the total NBR is reduced from 14% to 4%, and total HFR reduced from 14% to less than 1% compared with the GP scheme. With all different offered loads, the Adaptive CAC generates significantly higher revenue than GP because, when the offered load is high, there are many arriving connections that cannot be accepted in the GP scheme due to the lack of capacity.
GP AdaptiveCAC
1.0
0.9
0.8
0.7 1.0
1.2
1.4
1.6
1.8
2.0
Offered Load
Figure 3 Comparision of Total Revenue at Different Offered Load
16 14 12
20 18
10
16
8
Total Capacity (BWU)
Total HFR %
Non Real Time Calls Hard Real Time Calls Adaptive Real Time Calls
HFR constraints AdaptiveCAC
6
Predefined HFR Constraints
4 2
14 12 10 8 6
0 1.0
1.2
1.4
1.6
1.8
4
2.0
2
Offered Load
0
Figure 1 Comparision of Total HFR at Different Offered Load
GP1
16 14
10
6
99.19
Predefined NBR Constraints
8
100
Offered Load 1.0 Offered Load 2.0
0
0
1
2
3
4
5
6
7
8
11.15
20
24.83
40
12.93
Figure 2 Comparision of Total NBR at Different Offered Load
0.06
Offered Load
60
10.02
2.0
0.01
1.8
0.04 7.21
1.6
0.09 8.18
1.4
0.15 5.92
1.2
0.04 5.86
1.0
0.09 5.19
0
0.07 5.28
2
80
0.23 3.43
Allocation Percentages (%)
4
0.04
Total NBR %
GP1.2 AD1.2 GP1.4 AD1.4 GP1.6 AD1.6 GP1.8 AD1.8 GP2.0 AD2.0
Figure 4 Comparison of Occupied Capacity for Different Offered Load (GP 1.0 means the offered load is 1.0, the CAC scheme is GP; AD1.0 means the CAC scheme is Adaptive CAC)
GP AdaptiveCAC
12
AD1
9
10
QoSLevels
Figure 5 Comparison of Allocation Percentages at Different QoS Levels for AR Calls when Offered Load is 1.0 and 2.0
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Figure 4 compares the occupied capacity for different traffic. It can be seen that when the offered load is 1.0, GP and Adaptive CAC have similar figures and NR calls occupy half of the total capacity of the cell; however when the offered load is 2.0, NR calls only occupies about one quarter of total traffic capacity. Additionally, compared with GP, Adaptive CAC reduces the allocated capacity to AR calls so as to handle more HR calls because HR calls require fixed bandwidth capacity. Figure 5 shows the percentages of adaptive real time calls allocated to different QoS levels at different traffic loads. When offered load is 1.0, almost all the AR calls are allocated at their highest QoS levels to maximize the network revenue. When offered load is 2.0, the scheme starts allocate more AR calls at a lower level in order to release capacity for handling more calls so as to maintain QoS constraints. In that case, nly 25% of AR calls are allocated at the highest QoS level.
[5]
[6]
[7] [8] [9] [10]
[11]
VII. CONCLUSION Adaptive CAC can dynamically allocate adaptive real time calls at different QoS levels, which is a complex constraint optimization problem with noisy fitness. Noise deteriorates the final location and quality of the optimum, and brings lots of fitness fluctuation in the boundary of feasible and infeasible region. In this paper we proposed a novel approach that learns adaptive CAC policies through NEAT combined with Superiority of Feasible Points. The simulation results demonstrate that Adaptive CAC maximizes the network revenue, and maintains predefined QoS constraints. The simulation results show that when the offered load is high and the network cannot accept all the connections, Adaptive CAC accepts more adaptive real-time connections at lower QoS levels to release capacity for handling more connections, thus decreasing HFR and NBR. When the offered load is lower, Adaptive CAC maximizes the network revenue by allocating more adaptive real-time connections at the maximum QoS level, thus enhancing the users’ satisfaction.
[12] [13] [14]
[15] [16] [17] [18] [19] [20]
REFERENCES [1] [2] [3]
[4]
K. Geng-Sheng, A. Mishra, and R. Prasad, "QoS and resource allocation in the 3rd-generation wireless networks [Guest Editorial]," Communications Magazine, IEEE, vol. 39, pp. 115-115, 2001. S. K. Lei Huang; Kumar, C.-C.J., "Adaptive resource allocation for multimedia QoS management in wireless networks," Vehicular Technology, IEEE Transactions on, vol. 53, pp. 547 - 558 2004 J. G. V. Rakocevic, and G. Cope, "Performance Analysis of Bandwidth Allocation Schemes in Multiservice IP Networks Using Utility Functions," in Proceedings of the 17th International Teletraffic Congress (ITC ’17), 2001. C. Oliveira, J. B. Kim, and T. Suda, "An Adaptive Bandwidth Reservation Scheme for High-Speed Multimedia Wireless Networks,"
[21]
[22]
[23]
902
IEEE Journal on Selected Areas in Communications, vol. 16, pp. 858874, Aug. 1998. S. K. S. Das, S.K.; Basu, K.; Haitao Lin;, "A framework for bandwidth degradation and call admission control schemes for multiclass traffic in next-generation wireless networks," Selected Areas in Communications, IEEE Journal on, vol. 21, pp. 1790 - 1802 Dec 2003. C. W. Leong, W. Zhuang, Y. Cheng, and L. Wang, "Optimal resource allocation and adaptive call admission control for voice/data integrated cellular networks," Vehicular Technology, IEEE Transactions on, vol. 55, pp. 654-669, March 2006. Y. Xin, "Evolving artificial neural networks," Proceedings of the IEEE, vol. 87, pp. 1423-1447, 1999. K. O. Stanley, "Efficient Evolution of Neural Networks through Complexification," in the Faculty of the Graduate School of. vol. Doctor of Philosophy: The University of Texas at Austin, 2004. K. O. Stanley and R. Miikkulainen, "Evolving neural networks through augmenting topologies," Evol. Comput., vol. 10, pp. 99-127, 2002. Y. Matsumura, K. Ohkura, and K. Ueda, "Evolutionary dynamics of evolutionary programming in noisy environment," in Evolutionary Computation, 2001. Proceedings of the 2001 Congress on, 2001, pp. 1724 vol. 1. J. Yaochu and J. Branke, "Evolutionary optimization in uncertain environments-a survey," Evolutionary Computation, IEEE Transactions on, vol. 9, pp. 303-317, 2005. D. V. Arnold and H. G. Beyer, "Local performance of the (1 + 1)-ES in a noisy environment," Evolutionary Computation, IEEE Transactions on, vol. 6, pp. 30-41, 2002. E. B. Baum, D. Boneh, and C. Garrett, "On genetic algorithms," in Proceedings of the eighth annual conference on Computational learning theory Santa Cruz, California, United States: ACM, 1995. T. Back and U. Hammel, "Evolution strategies applied to perturbed objective functions," in Evolutionary Computation, 1994. IEEE World Congress on Computational Intelligence., Proceedings of the First IEEE Conference on, 1994, pp. 40-45 vol.1. H.-G. Beyer, "Evolutionary algorithms in noisy environments: theoretical issues and guidelines for practice " Computer Methods in Applied Mechanics and Engineering, vol. 186, pp. 239-267, 31 May 2000. V. Nissen and J. Propach, "Optimization with Noisy Function Evaluations," in Proceedings of the 5th International Conference on Parallel Problem Solving from Nature: Springer-Verlag, 1998. T. W. Then and E. K. P. Chong, "Genetic algorithms in noisy environment," in Intelligent Control, 1994., Proceedings of the 1994 IEEE International Symposium on, 1994, pp. 225-230. I. Rechenberg, Evolutionsstrategie'94: Stutgard-Bad Cannstatt: frommann-Holzboog, 1994. K. Deb, "An efficient constraint handling method for genetic algorithms," Computer Methods in Applied Mechanics and Engineering, vol. 186:22, pp. 311-338, 2000. D. Powell and M. M. Skolnick, "Using Genetic Algorithms in Engineering Design Optimization with Non-Linear Constraints," in Proceedings of the 5th International Conference on Genetic Algorithms: Morgan Kaufmann Publishers Inc., 1993. H. Xie, M. Zhang, and P. Andreae, "Another investigation on tournament selection: modelling and visualisation," in Proceedings of the 9th annual conference on Genetic and evolutionary computation London, England: ACM, 2007. C. L. P. Y. W. Yang Xiao; Chen, "A near optimal call admission control with genetic algorithm formultimedia services in wireless/mobile networks," in National Aerospace and Electronics Conference, 2000, pp. 787 - 792. S. Sidi-Mohammed, Andr, B. Luc, and P. Guy, "Call admission control in cellular networks: a reinforcement learning solution," Int. J. Netw. Manag., vol. 14, pp. 89-103, 2004.
