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Network optimization

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Homogeneous network is a group of active elements of the same type interacting with each other. The uniform elements behave in a similar way and their optimization can be performed on the basis of a single optimization technique. We propose a new meta-algorithm of large homogeneous network analysis, its decomposition into alternative sets of loosely connected subnets, and parallel optimization of the most independent elements. This algorithm is based on a network-specific correlation function, Simulated Annealing technique, and is adapted to work in the computer cluster. On the example of large wireless network, we show that proposed algorithm essentially increases speed of parallel optimization. The elaborated general approach can be used for analysis and optimization of the wide range of networks, including such specific types as artificial neural networks or organized in networks physiological systems of living organisms.

For citation: Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X. Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks // Proceedings of the Institute for System Programming, 2016, vol. 28, issue 6, pp. 141-152. DOI: 10.15514/ISPRAS-2016-28(6)-10

Presentation DOI: 10.13140/RG.2.2.20183.06565/6

Published in: Data & Analytics
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Network optimization

  1. 1. HUAWEI TECHNOLOGIES CO., LTD. www.huawei .com 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. 141-152. DOI: 10.15514/ISPRAS-2016-28(6)-10 Automatic Analysis, Decomposition and Parallel O p t i m i z a t i o n o f L a r g e H o m o g e n e o u s N e t w o r k s ISPRAS Open 2016 Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X.
  2. 2. A0 Signals of sector antennas A0 – A7 A1 A2 A3 A4 A5 A6 A7 Homogeneous Networks Element Crossroad Switch Antenna Optimized integral index Average speed of traffic Average power of prevalent radio signal Correlation formula for 2 elements 1 / (1 + [elements quantity on the shortest path]) 1 / (distance between antennas) WirelessWired Communication Networks Road network 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. 141-152.
  3. 3. Background: Sector Planning with full optimization Graph-based representation Homogeneous 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: 1. Decomposition of network into subnets by the rule of minimal sum of crossing edges weights 2. Parallel optimization of subnets 3. Update of network parameters Main drawback: Crossing edges are ignored => poor accuracy Optimization of all parameters DECOMPOSITION While stopping criterion isn’t met Thread Thread Full network 2 - Subnets Element Agenda - 1 2 1 1 1 1 1 1 2 2 2 2 2 2 UPDATE 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. 141-152.
  4. 4. Idea 1: Alternative splitting Optimization While stopping criterion is not met Thread Thread Thread Thread Split by split Advantage: All crossing edges are taken into account Discard light edges under threshold Alternative splits Full network Reduced network 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 - Subnets Element Agenda - 1 2 3 4 UPDATE NETWORK 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. 141-152.
  5. 5. COMBINE NON-OVERLAPPING SUBNETS Idea 2: Independent optimization Advantage: Parallel optimization of the fully independent elements Reduced network FOR EVERY OPTIMIZED UNIT FIND SUBNET - Subnets - Border element - Optimized unit Agenda 2 2 2 2 1 1 1 1 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. 141-152.
  6. 6. Splitting with threshold Idea 3: Regulation of threshold Thresholdincreasing Optimization 1 subnet 2 subnets 3 subnets Optimized unit = 2 elements Advantage: Optimization process is regulated by threshold 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. 141-152.
  7. 7. Optimization of independent elements UPDATE NETWORK If stop- ping criterion is not met Thread Thread Alternative splits of network into non-overlapping 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 … 1 1 1 2 2 2 1 1 2 Full network - Subnets - Border element - Optimized unit Agenda 1 1 1 1 1 2 2 2 2 2 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. 141-152.
  8. 8. Optimization process regulation Start Quantity of alternative calculations Com- plexity Rough 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) Quantity Strength of distant interactions Precision of optimizing procedure Subnets Quantity of processes = available cores Precision of optimization End Usage of all computational resources on computer / cluster Colored arrows ( ) – increase (up) or decrease (down) of parameter value Empty 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. 141-152.
  9. 9. Optimization of mobile network coverage and quality High optimization complexity: 300 antennas * 4 parameters, n states of parameter => n1200 states Regulated parameters of sector antenna: power, height, tilt, azimuth Initial subnet Optimized subnet 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. 141-152.
  10. 10. Alternative splitting vs. Sector planning n – number of optimized areas in network Pi – the power of the prevalent signal in i-th area Ii – the power of the other (interfering) signals in i-th area Ni – other noise in i-th area Optimized integral index – average Signal to Interference plus Noise Ratio: ) N+I P n 1 (log•10=SINR ∑ n 1=i ii i 10 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 subnet maxStep – maximal value of step T, E, A – temperature, energy, acceptance functions 9 times faster 1 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. 141-152.
  11. 11. Benefits of Independent optimization of alternatives • Faster optimization due to reduction of optimization complexity and efficient usage of all computational resources • 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 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. 141-152.
  12. 12. HUAWEI TECHNOLOGIES CO., LTD. www.huawei .com 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. 141-152. DOI: 10.15514/ISPRAS-2016-28(6)-10 Automatic Analysis, Decomposition and Parallel O p t i m i z a t i o n o f L a r g e H o m o g e n e o u s N e t w o r k s ISPRAS Open 2016 Ignatov D.Yu., Filippov A.N., Ignatov A.D., Zhang X.

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