{"title": "Experiments with Neural Networks for Real Time Implementation of Control", "book": "Advances in Neural Information Processing Systems", "page_first": 973, "page_last": 979, "abstract": null, "full_text": "Experiments with Neural Networks for Real \n\nTime Implementation of Control \n\nP. K. Campbell, M. Dale, H. L. Ferra and A. Kowalczyk \n\nTelstra Research Laboratories \n\n770 Blackburn Road Clayton, Vic. 3168, Australia \n\n{p.campbell, m.dale, h.ferra, a.kowalczyk}@trl.oz.au \n\nAbstract \n\nThis paper describes a neural network based controller for allocating \ncapacity in a telecommunications network. This system was proposed in \norder to overcome a \"real time\" response constraint. Two basic \narchitectures are evaluated: 1) a feedforward network-heuristic and; 2) a \nfeedforward network-recurrent network. These architectures are \ncompared against a linear programming (LP) optimiser as a benchmark. \nThis LP optimiser was also used as a teacher to label the data samples \nfor the feedforward neural network training algorithm. It is found that \nthe systems are able to provide a traffic throughput of 99% and 95%, \nrespectively, of the throughput obtained by the linear programming \nsolution. Once trained, the neural network based solutions are found in a \nfraction of the time required by the LP optimiser. \n\n1 Introduction \nAmong the many virtues of neural networks are their efficiency, in terms of both execution \ntime and required memory for storing a structure, and their practical ability to approximate \ncomplex functions. A typical drawback is the usually \"data hungry\" training algorithm. \nHowever, if training data can be computer generated off line, then this problem may be \novercome. In many applications the algorithm used to generate the solution may be \nimpractical to implement in real time. In such cases a neural network substitute can \nbecome crucial for the feasibility of the project. This paper presents preliminary results for \na non-linear optimization problem using a neural network. The application in question is \nthat of capacity allocation in an optical communications network. The work in this area is \ncontinuing and so far we have only explored a few possibilities. \n2 Application: Bandwidth Allocation in SDH Networks \nSynchronous Digital Hierarchy (SDH) is a new standard for digital transmission over \noptical fibres [3] adopted for Australia and Europe equivalent to the SONET \n(Synchronous Optical NETwork) standard in North America. The architecture of the \nparticular SDH network researched in this paper is shown in Figure 1 (a). \n\n1) Nodes at the periphery of the SDH network are switches that handle individual \n\ncalls. \n\n\f974 \n\nP. CAMPBELL, M. DALE, H. L. FERRA, A. KOWALCZYK \n\n2) Each switch concentrates traffic for another switch into a number of streams. \n3) Each stream is then transferred to a Digital Cross-Connect (DXC) for switching and \ntransmission to its destination by allocating to it one of several alternative virtual \npaths. \n\nThe task at hand is the dynamic allocation of capacities to these virtual paths in order to \nmaximize SDH network throughput. \nThis is a non-linear optimization task since the virtual path capacities and the constraints, \ni.e. the physical limit on capacity of links between DXC's, are quantized, and the objective \nfunction (Erlang blocking) depends in a highly non-linear fashion on the allocated \ncapacities and demands. Such tasks can be solved 'optimally' with the use of classical \nlinear programming techniques [5], but such an approach is time-consuming - for large \nSDH networks the task could even require hours to complete. \nOne of the major features of an SDH network is that it can be remotely reconfigured using \nsoftware controls. Reconfiguration of the SDH network can become necessary when \ntraffic demands vary, or when failures occur in the DXC's or the links connecting them. \nReconfiguration in the case of failure must be extremely fast, with a need for restoration \ntimes under 60 ms [1]. \n\n(b) \n\noutput: path \ncapacities \n\nsynaptic weights \n(22302) \nhidden units: \n'AND' gates \n(l10) \n\nthresholds \n(738,67 used) \n\ninput \n\no DXC (Digital \u00ae Switch \n\nCross-Connect) \n\nFigure 1 \n\nlink \ncapacities \n\noffered \ntraffic \n\n(a) Example of an Inter-City SDH/SONET Network Topology used in experiments. \n(b) Example of an architecture of the mask perceptron generated in experiments. \n\nIn our particular case, there are three virtual paths allocated between any pair of switches, \neach using a different set of links between DXC's of the SDH network. Calls from one \nswitch to another can be sent along any of the virtual paths, leading to 126 paths in total (7 \nswitches to 6 other switches, each with 3 paths). \nThe path capacities are normally set to give a predefined throughput. This is known as the \n\"steady state\". If links in the SDH network become partially damaged or completely cut, \nthe operation of the SDH network moves away from the steady state and the path \ncapacities must be reconfigured to satisfy the traffic demands subject to the following \nconstraints: \n\n(i) Capacities have integer values (between 0 and 64 with each unit corresponding to a \n\n2 Mb/s stream, or 30 Erlangs), \n\n(ii) The total capacity of all virtual paths through anyone link of the SDH network \n\n\fExperiments with Neural Networks for Real Time Implementation of Control \n\n975 \n\ncannot exceed the physical capacity of that link. \n\nThe neural network training data consisted of 13 link capacities and 42 traffic demand \nvalues, representing situations in which the operation of one or more links is degraded \n(completely or partially). The output data consisted of 126 integer values representing the \ndifference between the steady state path capacities and the final allocated path capacities. \n3 Previous Work \nThe problem of optimal SDH network reconfiguration has been researched already. In \nparticular Gopal et. al. proposed a heuristic greedy search algorithm [4] to solve this non(cid:173)\nlinear integer programming problem. Herzberg in [5] reformulated this non-linear integer \noptimization problem as a linear programming (LP) task, Herzberg and Bye in [6] \ninvestigated application of a simplex algorithm to solve the LP problem, whilst Bye [2] \nconsidered an application of a Hopfield neural network for this task, and finally Leckie [8] \nused another set of AI inspired heuristics to solve the optimization task. \nAll of these approaches have practical deficiencies; the linear programming is slow, while \nthe heuristic approaches are relatively inaccurate and the Hopfield neural network method \n(simulated on a serial computer) suffers from both problems. \nIn a previous paper Campbell et al. [10] investigated application of a mask perceptron to \nthe problem of reconfiguration for a \"toy\" SDH network. The work presented here \nexpands on the work in that paper, with the idea of using a second stage mask perceptron \nin a recurrent mode to reduce link violationslunderutilizations. \n4 The Neural Controller Architecture \nInstead of using the neural network to solve the optimization task, e.g. as a substitute for \nthe simplex algorithm, it is taught to replicate the optimal LP solution provided by it. \nWe decided to use a two stage approach in our experiments. For the first stage we \ndeveloped a feedforward network able to produce an approximate solution. More \nprecisely, we used a collection of 2000 random examples for which the linear \nprogramming solution of capacity allocations had been pre-computed to develop a \nfeedforward neural network able to approximate these solutions. \nThen, for a new example, such an \"approximate\" neural network solution was rounded to \nthe nearest integer, to satisfy constraint (i), and used to seed the second stage providing \nrefinement and enforcement of constraint (ii). \nFor the second stage experiments we initially used a heuristic module based on the Gopal \net al. approach [4]. The heuristic firstly reduces the capacities assigned to all paths which \ncause a physical capacity violation on any links, then subsequently increases the capacities \nassigned to paths across links which are being under-utilized. \nWe also investigated an approach for the second stage which uses another feedforward \nneural network. The teaching signal for the second stage neural network is the difference \nbetween the outputs from the first stage neural network alone and the combined first stage \nneural networkiheuristic solution. This time the input data consisted of 13 link usage \nvalues (either a link violation or underutilization) and 42 values representing the amount \nof traffic lost per path for the current capacity allocations. The second stage neural \nnetwork had 126 outputs representing the correction to the first stage neural network's \noutputs. \nThe second stage neural network is run in a recurrent mode, adjusting by small steps the \ncurrently allocated link capacities, thereby attempting to iteratively move closer to the \ncombined neural-heuristic solution by removing the link violations and under-utilizations \nleft behind by the first stage network. \nThe setup used during simulation is shown in Figure 2. For each particular instance tested \nthe network was initialised with the solution from the first stage neural network. The \noffered traffic (demand) and the available maximum link capacities were used to \ndetermine the extent of any link violations or underutilizations as well as the amount of \nlost traffic (demand satisfaction). This data formed the initial input to the second stage \nnetwork. The outputs of the neural network were then used to check the quality of the \n\n\f976 \n\nP. CAMPBELL, M. DALE, H. L. FERRA, A. KOWALCZYK \n\nsolution, and iteration continued until either no link violations occurred or a preset \nmaximum number of iterations had been performed. \n\noffered traffic \n\nlink capacities \n\ncomputation of \nconstraint -demand \nsatisfaction \n\n[ ........ ~ ........ -..... -----~(+) \n\nsolution (t) \n\nsolution (t-l) \n\ncorrection (t) \n\n! \n! \nI \n! \n\ninitialization: \nsolution (0) \nfrom stage 1 \n\ndemand satisfaction (t-l \n42 inputs \n\nlink capacities \nviolation!underutilization (t-l) \n13 inputs \n\nFigure 2. Recurrent Network used for second stage experiments. \n\nWhen computing the constraint satisfaction the outputs of the neural network where \ncombined and rounded to give integer link violations/under-utilizations. This means that \nin many cases small corrections made by the network are discarded and no further \nimprovement is possible. In order to overcome this we introduced a scheme whereby \nerrors (link violations/under-utilizations) are occasionally amplified to allow the network a \nchance of removing them. This scheme works as follows : \n\n1) an instance is iterated until it has either no link violations or until 10 iterations have \n\nbeen performed; \nif any link violations are still present then the size of the errors are multiplied by an \namplification factor (> 1); \n\n2) \n\n3) a further maximum of 10 iterations are performed; \n4) \n\nif subsequently link violations persist then the amplification factor is increased; \n\nthe procedure repeats until either all link violations are removed or the amplification factor \nreaches some fixed value. \nS Description of Neural Networks Generated \nThe first stage feedforward neural network is a mask perceptron [7], c.f. Figure 1 (b). Each \ninput is passed through a number of arbitrarily chosen binary threshold units. There were a \ntotal of 738 thresholds for the 55 inputs. The task for the mask perceptron training \nalgorithm [7] is to select a set of useful thresholds and hidden units out of thousands of \npossibilities and then to set weights to minimize the mean-square-error on the training set. \nThe mask perceptron training algorithm automatically selected 67 of these units for direct \nconnection to the output units and a further 110 hidden units (\"AND\" gates) whose \n\n\fExperiments with Neural Networks for Real Time Implementation of Control \n\n977 \n\noutputs are again connected to the neural network outputs, giving 22,302 connections in \nall. \nSuch neural networks are very rapid to simulate since the only operations required are \ncomparison and additions. \nFor the recurrent network used in the second stage we also used a mask perceptron. The \ntraining algori thIn used for the recurrent network was the same as for the first stage, in \nparticular note that no gradual adaptation was employed. The inputs to the network are \npassed through 589 arbitrarily chosen binary threshold units. Of these 35 were selected by \nthe training algorithm for direct connection to the output units via 4410 weighted links. \n6 Results \nThe results are presented in Table 1 and Figure 3. The values in the table represent the \ntraffic throughput of the SDH network, for the respective methods, as a percentage of the \nthroughput determined by the LP solution. Both the neural networks were trained using \n2000 instances and tested against a different set of 2000 instances. However for the \nrecurrent network approximately 20% of these cases still had link violations after \nsimulation so the values in Table 1 are for the 80% of valid solutions obtained from either \nthe training or test set. \n\nSolution type \nFeedforward Net/Heuristic \nFeedforward Net/Recurrent Net \nGopal-S \nGopal-O \n\nTraining \n\n99.08% \n94.93% (*) \n96.38% \n85.63% \n\nTest \n98.90%, \n94.76%(*) \n96.20% \n85.43% \n\n(*) these numbers are for the 1635 training and 1608 test instances (out of 2000) for which the \nrecurrent network achieved a solution with no link violations after simulation as described in \nSection 3. \n\nTable 1. Efficiency of solutions measured by average fraction of the ' optimal' \n\nthroughput of the LP solution \n\nAs a comparison we implemented two solely heuristic algorithms. We refer to these as \nGopal-S and Gopal-O. Both employ the same scheme described earlier for the Gopal et al. \nheuristic. The difference between the two is that Gopal-S uses the steady state solution as \nan initial starting point to determine virtual path capacities for a degraded network, \nwhereas Gopal-O starts from a point where all path capacities are initially set to zero. \nReferring to Figure 3, link capacity ratio denotes the total link capacity of the degraded \nSDH network relative to the total link capacity of the steady state SDH network. A low \nvalue of link capacity ratio indicates a heavily degraded network. The traffic throughput \nratio denotes the ratio between the throughput obtained by the method in question, and the \nthroughput of the steady state solution. \nEach dot in the graphs in Figure 3 represents one of the 2000 test set cases. It is clear from \nthe figure that the neural network/heuristic approach is able to find better solutions for \nheavily degraded networks than each of the other approaches. Overall the clustering of \ndots for the neural network/heuristic combination is tighter (in the y-direction) and closer \nto 1.00 than for any of the other methods. The results for the recurrent network are very \nencouraging being qUalitatively quite close to those for the Gopal-S algorithm. \nAll experiments were run on a SPARCStation 20. The neural network training took a few \nminutes. During simulation the neural network took an average of 9 ms per test case with \na further 36.5 ms for the heuristic, for a total of 45.5 ms. On average the Gopal-S \nalgorithm required 55.3 ms and the Gopal-O algorithm required 43.7 ms per test case. The \nrecurrent network solution required an average of 55.9 ms per test case. The optimal \nsolutions calculated using the linear programming algorithm took between 2 and 60 \nseconds per case on a SPARCStation 10. \n\n\f978 \n\nP. CAMPBELL, M. DALE, H. L. FERRA, A. KOWALCZYK \n\nNeural Network/Heuristic \n\nRecurrent Neural Network \n\n1.00 \n\n.2 \n~ 0.95 \n8. 0.90 \n.r: \n0> \nis 0.85 \n.c t-\n.!.! 0.80 \n~ \n~ 0.75 \n\n\u2022\u2022 , _ ._0 \u2022\u2022 _ \u2022 \u2022\u2022 \u2022 \u2022 \u2022 \u2022\u2022 : \u2022 \u2022 \u2022\u2022 :.' \u2022\u2022\u2022 :.~' \u2022\u2022 : \u2022 \u2022\u2022\u2022\u2022 :. '0\"\" _ \u2022\u2022 \u2022 \u2022 \u2022 _ \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 \n\n0.70 0.50 0.60 0 .10 0.80 0.90 1.00 \n\n0.70 0.50 0.60 0.70 0.80 0.90 1.00 \n\nlink Capacity Ratio \n\nGopal-S \n\nLink Capacity Ratio \n\nGopal-O \n\n\u00b7\u00b7\u00b7\u00b7\u00b7\u00b7:\u00b7\u00b7\u00b7\u00b7:\u00b7 \u00b7:,,~i~ffI~ \n\n- -' - \"~':' ........ ~ ...... -... --- -.. . . \n\n.-. -,. \"\n\n\"\n\n1.00 \n.2 ra 0 .95 \ncr \n~ 0.90 \n.r: \n0> \n6 0.85 \n\n.c t-,g 0.80 \n\n~ \n~ 0.75 \n\n1.00 \n\n.2 \nr.; 0.95 \ncr \n~ 0.90 \n.r: \n0> 5 0.85 \n.c t-\n. ~ 0.80 \n~ \n~ 0.75 \n\n0.70 0.50 0.60 0.70 0.80 0.90 1.00 \n\n0.70 0.50 0.60 0.70 0.80 0.90 100 \n\nlink Capacity Ratio \n\nLink Capacily Ratio \n\nFigure 3. Experimental results for the Inter-City SDH network (Fig. 1) on the \nindependent test set of 2000 random cases. On the x axis we have the ratio \nbetween the total link capacity of the degraded SDH network and the steady state \nSDH network. On the y axis we have the ratio between the throughput obtained \nby the method in question, and the throughput of the steady state solution. \nFig 3. (a) shows results for the neural network combined with the heuristic \nsecond stage. Fig 3. (b) shows results for the recurrent neural network second \nstage. Fig 3. (c) shows results for the heuristic only, initialised by the steady state \n(Gopal-S) and Fig 3. (d) has the results for the heuristic initialised by zero \n(Gopal-O). \n\n7 Discussion and Conclusions \nThe combined neural network/heuristic approach performs very well across the whole \nrange of degrees of SDH network degradation tested. The results obtained in this paper are \nconsistent with those found in [10]. The average accuracy of -99% and fast solution \ngeneration times \u00ab ffJ ms) highlight this approach as a possible candidate for \nimplementation in a real system, especially when one considers the easily achievable \nspeed increase available from parallelizing the neural network. The mask perceptron used \nin these experiments is well suited for simulation on a DSP (or other hardware): the \noperations required are only comparisons, calculation of logical \"AND\" and the \nsummation of synaptic weights (no multiplications or any non-linear transfonnations are \nrequired). \nThe interesting thing to note is the relatively good perfonnance of the recurrent network, \nnamely that it is able to handle over 80% of cases achieving very good perfonnance when \ncompared against the neural network/heuristic solution (95% of the quality of the teacher). \nOne thing to bear in mind is that the heuristic approach is highly tuned to producing a \nsolution which satisfies the constraints, changing the capacity of one link at a time until \nthe desired goal is achieved. On the other hand the recurrent network is generic and does \nnot target the constraints in such a specific manner, making quite crude global changes in \n\n\fExperiments with Neural Networks for Real Time Implementation of Control \n\n979 \n\none hit, and yet is still able to achieve a reasonable level of performance. While the speed \nfor the recurrent network was lower on average than for the heuristic solution in our \nexperiments, this is not a major problem since many improvements are still possible and \nthe results reported here are only preliminary, but serve to show what is possible. It is \nplanned to continue the SOH network experiment in the future; with more investigation on \nthe recurrent network for the second stage and also more complex SDH architectures. \nAcknowledgments \nThe research and development reported here has the active support of various sections and \nindividuals within the Telstra Research Laboratories (TRL), especially Dr. C. Leckie, Mr. \nP. Sember, Dr. M. Herzberg, Mr. A. Herschtal and Dr. L. Campbell. The permission of the \nManaging Director, Research and Information Technology, Telstra, to publish this paper is \nacknowledged. \nThe research and development reported here has the active support of various sections and \nindividuals within the Telstra Research Laboratories (TRL), especially Dr. C. Leckie and \nMr. P. Sember who were responsible for the creation and trialling of the programs \ndesigned to produce the testing and training data. \nThe SOH application was possible due to co-operation of a number of our colleagues in \nTRL, in particular Dr. L. Campbell (who suggested this particular application), Dr. M. \nHerzberg and Mr. A. Herschtal. \nThe permission of the Managing Director, Research and Information Technology, Telstra, \nto publish this paper is acknowledged. \nReferences \n[1] \n[2] \n\nE. Booker, Cross-connect at a Crossroads, Telephony, Vol. 215, 1988, pp. 63-65. \nS. Bye, A Connectionist Approach to SDH Bandwidth Management, Proceedings \nof the 19th International Conference on Artificial Neural Networks (ICANN-93), \nBrighton Conference Centre, UK, 1993, pp. 286-290. \nR. Gillan, Advanced Network Architectures Exploiting the Synchronous Digital \nHierarchy, Telecommunications Journal of Australia 39, 1989, pp. 39-42. \nG. Gopal, C. Kim and A. Weinrib, Algorithms for Reconfigurable Networks, \nProceedings of the 13th International Teletraffic Congress (ITC-13), Copenhagen, \nDenmark, 1991, pp. 341-347. \n\n[3] \n\n[4] \n\n[5] M. Herzberg, Network Bandwidth Management - A New Direction in Network \nManagement, Proceedings of the 6th Australian Teletraffic Research Seminar, \nWollongong, Australia, pp. 218-225. \n\n[6] M. Herzberg and S. Bye, Bandwidth Management in Reconfigurable Networks, \n\n[7] \n\n[8] \n\nAustralian Telecommunications Research 27, 1993, pp 57-70. \nA. Kowalczyk and H.L. Ferra, Developing Higher Order Networks with \nEmpirically Selected Units, IEEE Transactions on Neural Networks, pp. 698-711, \n1994. \nto Telecommunication Network \nC. Leckie, A Connectionist Approach \nOptimisation, in Complex Systems: Mechanism of Adaptation, R.J. Stonier and \nX.H. Yu, eds., lOS Press, Amsterdam, 1994. \n\n[9] M. Schwartz, Telecommunications Networks, Addison-Wesley, Readings, \n\n[10] \n\nMassachusetts, 1987. \np. Campbell, H.L. Ferra, A. Kowalczyk, C. Leckie and P. Sember, Neural Networks \nin Real Time Decision Making, Proceedings of the International Workshop on \nApplications of Neural Networks to Telecommunications 2 (IWANNT-95), Ed. J \nAlspector et. al. Lawrence Erlbaum Associates, New Jersey, 1995, pp. 273-280. \n\n\f", "award": [], "sourceid": 1162, "authors": [{"given_name": "Peter", "family_name": "Campbell", "institution": null}, {"given_name": "Michael", "family_name": "Dale", "institution": null}, {"given_name": "Herman", "family_name": "Ferr\u00e1", "institution": null}, {"given_name": "Adam", "family_name": "Kowalczyk", "institution": null}]}