Homogeneous Network Optimization
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Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152. DOI: 10.15514/ISPRAS201628(6)10Automatic Analysis, Decomposition and Parallel Optimization of Large HomogeneousNetworksISPRAS Open 2016Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X.
HUAWEI TECHNOLOGIES CO., LTD.www.huawei.com
Presentation of the new algorithm of Homogeneous Network Optimization15 October 2015
S1
A0Signals of sector antennas A0 A7A1A2A3A4A5A6
A7Homogeneous NetworksElementCrossroadSwitchAntennaOptimized integral indexAverage speed of trafficAverage power ofprevalent radio signalCorrelation formula for 2 elements1 / (1 + [elements quantity on the shortest path])1 / (distance between antennas)
WirelessWiredCommunication NetworksRoad networkIgnatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
The life of the modern world essentially depends on the work of the large artificial networks, such as networks of roads, pipelines, wired and wireless communication systems. The support of their effective functioning requires permanent screening and optimization. The network consists of the active elements, such as crossroads, switches or antennas, and can be optimized by the integral indices, such as average speed of traffic in crossroads or switches, or average power of prevalent radio signal of antennas. To perform optimization the large networks are decomposed into subnets on the basis of correlation between their elements.25 October 2015
Background: Sector Planning with full optimizationGraphbased representationHomogeneous network is represented as a weighted complete graph, where each vertex corresponds to network element each edge has weight equals to correlation between correspondent elements Optimization loop:Decomposition of network into subnets by the rule of minimal sum of crossing edges weights Parallel optimization of subnetsUpdate of network parametersMain drawback:Crossing edges are ignored => poor accuracy
Optimization ofall parameters
DECOMPOSITIONWhile stopping criterion isnt metThreadThreadFull network2
 SubnetsElementAgenda

12111111222222
UPDATEIgnatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
For example in the method of sector planning with full optimization the Homogeneous Network is represented as a weighted complete graph, where each vertex corresponds to network element and each edge has weight equals to correlation between connected elements. In optimization loop : 1) Network is decomposed into subnets by the rule of minimal sum of crossing edges weights; 2) Subnets are optimized in parallel processes; 3) Network parameters are updated. Main drawback: crossing edges are ignored, and so accuracy of optimization is poor.35 October 2015
Idea 1: Alternative splittingOptimization
While stopping criterion is not metThreadThreadThreadThreadSplit by split
Advantage: All crossing edges are taken into account
Discard light edges under threshold
Alternative splits
Full networkReduced network1234123412341234
 SubnetsElementAgenda12
34UPDATE NETWORKIgnatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
Idea 1: alternative splitting. In complete graph of network the light edges under predefined threshold are discarded and we've got reduced network. Then network is decomposed into alternative splits. Algorithm iterates through these splits, and perform optimization of subnets in separate threads.45 October 2015
COMBINE NONOVERLAPPING SUBNETS
Idea 2: Independent optimizationAdvantage: Parallel optimization of the fully independent elements
Reduced networkFOR EVERY OPTIMIZED UNIT FIND SUBNET
 Subnets Border element Optimized unitAgenda22221111Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
Idea 2: independent optimization. In reduced network the optimized units are selected. For every unit we find subnet consisting of optimized unit and all connected to it elements. Then nonoverlapping subnets are combined into alternative splits. In every split only independent elements are optimized. As you can see while we move through all splits we optimize all elements, but every optimization effects only independent parts of network. Advantage: parallel optimization of the most independent elements.55 October 2015
Splitting with thresholdIdea 3: Regulation of thresholdThreshold increasing
O p t i m i z a t i o n
1 subnet
2 subnets
3 subnetsOptimized unit = 2 elements
Advantage: Optimization process is regulated by thresholdIgnatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
Idea 3: regulation of threshold. Decomposition begins with the minimal level of threshold and as a result just one subnet is selected in every split . As you can see the optimized unit consists of 2 elements and all other elements are connected to it. When threshold is increased then the number of subnets is increased and their complexity is decreased. Advantage: optimization process is regulated by threshold.
65 October 2015
Optimization ofindependent elementsUPDATE NETWORK
If stopping criterion is not met ThreadThreadAlternative splits of network into nonoverlapping subnets for optimized units:Split by split
DISCARD EDGES UNDER THRESHOLD
DECOMPOSITION
Full cycle of alternative splitting with regulated threshold
If threshold under limit increase its value and continue
Reduced network
111222
112
Full network
 Subnets Border element Optimized unitAgenda1111122222Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
The full cycle of alternative splitting with regulated threshold includes discarding of edges under threshold, alternative splitting of reduced network on the basis of optimized units, parallel optimization of the most independent parts of networks as long as optimization gives improvement. After that, the threshold is increased and optimization is performed on the next level of splitting.75 October 2015
Optimization process regulation StartQuantity of alternative calculationsComplexityRough search of global optimum in small number of complex subnets (avoiding of stuck in local optimum)Precise search of optimums in big number of simple subnets (maximal precision at the end)QuantityStrength of distant interactionsPrecision of optimizing procedureSubnetsQuantity of processes = available cores
Precision of optimizationEndUsage of all computational resources on computer / cluster
Colored arrows ( ) increase (up) or decrease (down) of parameter valueEmpty arrows impact on optimization process
Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
Optimization process regulation includes increase of networks quantity and decrease of the number of alternative calculations during optimization process, so that the quantity of parallel processes equals to quantity of available cores and we use all computational resources available on computer or cluster. From other side, the complexity of subnets and the strength of their distant interactions are decreased and we increase precision of optimizing procedure. As a result during optimization the accuracy is increased and we progressively move from rough search of global optimum in small number of complex subnets to precise search of optimum in big number of simple subnets. In such way we avoid the stack in local optimum at the beginning of optimization and have the best precision at the end.85 October 2015
Optimization of mobile network coverage and qualityHigh optimization complexity:300 antennas * 4 parameters, n states of parameter => n1200 statesRegulated parameters of sector antenna: power, height, tilt, azimuth
Initial subnetOptimized subnetIgnatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
To demonstrate the efficiency of proposed approach, the optimization of mobile network is implemented with visualization of quality of radio signal. As you can see the sector antennas transmit radio signal (green and yellow colors). In initial network there are red problem areas with low quality of radio signal. Every antenna was optimized by 4 regulated parameters, each with n states. So, the number of states of full network is n^1200 optimization complexity is high. After optimization is finished the red areas are disappeared and the quality of radio signals is increased. 2014/9/8916 October 2015
Alternative splitting vs. Sector planning
n number of optimized areas in network Pi the power of the prevalent signal in ith areaIi the power of the other (interfering) signals in ith areaNi other noise in ith areaOptimized integral index average Signal to Interference plus Noise Ratio:
Optimizing procedure modified Simulated Annealing: procedure optimize(S0, precision) { Snew := S0 step := maxStep (1 precision) Sgen := random neighbor of S0 within step t := T(1 precision) if A(E(S0), E(Sgen), t) random(0, 1) then Snew := Sgen Output: state Snew}S0, Sgen, Snew current, generated, new states of subnetmaxStep maximal value of stepT, E, A temperature, energy, acceptance functions9 times faster1 hour SINR 15 % higher (p < 0.01)Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
As an optimized integral index we use Signal to Interference plus Noise Ratio (SINR). As an optimizing procedure modified Simulated Annealing, which takes as input precision parameter. On the plot you can see that the alternative splitting gives speedup 9 times, and after 1 hour shows better quality of radio signal SINR is 15 % higher in logarithmic scale.105 October 2015
Benefits of Independent optimization of alternativesFaster optimization due to reduction of optimization complexity and efficient usage of all computational resourcesBetter quality of optimization due to progressive shift of optimization strategy from rough search of global optimum at the beginning of optimization process to precise search of optimum at the end of optimizationIgnatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152.
Thus, the benefits of proposed method for independent optimization of alternatives: 1) Faster optimization due to reduction of optimization complexity and efficient usage of all computational resources; 2) Better quality of optimization due to progressive shift of optimization strategy from rough search of global optimum at the beginning of optimization process to precise search of optimum at the end of optimization.115 October 2015
Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proc. ISP RAS, 2016, vol. 28, issue 6, pp. 141152. DOI: 10.15514/ISPRAS201628(6)10Automatic Analysis, Decomposition and Parallel Optimization of Large HomogeneousNetworksISPRAS Open 2016Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X.
HUAWEI TECHNOLOGIES CO., LTD.www.huawei.com
Presentation of the new algorithm of Homogeneous Network Optimization125 October 2015