1. D.Yu. Ignatov, A.N. Filippov, A.D. Ignatov, X. Zhang
5 October 2015
Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks
D.Yu. Ignatov, A.N. Filippov, A.D. Ignatov, X. Zhang
ISPRAS Open 2016

2. Homogeneous Networks Communication Networks Road network Wired
5 October 2015
Communication Networks
Road network
Wired
Wireless
Signals of sector antennas A0 – A7 S1 A3 A6 A0 A2 A5 A1 A7 A4
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)

3. Background: Sector Planning with full optimization
5 October 2015
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:
Decomposition of network into subnets by the rule of minimal sum of crossing edges weights
Parallel optimization of subnets
Update of network parameters
While stopping criterion isn’t met
Full network
DECOMPOSITION 1 1 1 1 1 2 2
UPDATE 2 2 2 2
Main drawback:
Crossing edges are ignored => poor accuracy 1 2
Agenda
Optimization of
all parameters
Thread
Thread -
Element 1 2
- Subnets

4. Idea 1: Alternative splitting
5 October 2015
Full
network
Discard light edges
under threshold
Reduced network
Alternative splits 1 2 1 1 2 4 2 3 4 4 3 3 1
While stopping criterion
is not met 2
UPDATE NETWORK 3 4
Thread
Optimization
Split by split
Thread
Thread
Thread
Agenda -
Element 1 2
- Subnets 3 4
Advantage: All crossing edges are taken into account

5. Idea 2: Independent optimization
5 October 2015
FOR EVERY OPTIMIZED UNIT FIND SUBNET
Reduced
network
COMBINE NON-OVERLAPPING SUBNETS 1 2
Agenda
- Optimized unit 2 1
- Border element 1 2
- Subnets 1 2
Advantage: Parallel optimization of the fully independent elements

6. Idea 3: Regulation of threshold Optimized unit = 2 elements
5 October 2015
Optimized unit = 2 elements
O p t i m i z a t i o n
1 subnet
Threshold increasing
Splitting with threshold
2 subnets
3 subnets
Advantage: Optimization process is regulated by threshold

7. … Full cycle of alternative splitting with regulated threshold
5 October 2015
Full network
DISCARD EDGES UNDER THRESHOLD
Reduced network
DECOMPOSITION
Alternative splits of network into non-overlapping subnets for optimized units: 1 2
If threshold under limit increase its value and continue 1 1 1 1 1 1 1 2 2 … 2 2 2 2
UPDATE NETWORK
If stop-ping criterion
is not met 1 2
Optimization of
independent elements
Thread
Thread
Split by split
Agenda
- Optimized unit
- Border element 1 2
- Subnets

8. Optimization process regulation
5 October 2015
Usage of all computational resources on computer / cluster
Quantity
Quantity of alternative calculations
Subnets
Quantity of processes = available cores
Strength of distant interactions
Precision of optimization
Com-plexity
Precision of
optimizing
procedure
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)
Start
End
Colored arrows ( ) – increase (up) or decrease (down) of parameter value
Empty arrows – impact on optimization process

9. Optimization of mobile network coverage and quality
16 October 2015
Optimization of mobile network coverage and quality
2014/9/8
The optimized mobile network consists of sector antennas which transmit radio signal (green and yellow colors).
And we can see the red problem areas with low level of radio signal and/or high level of noise.
Coverage and Quality of network are regulated by power, height, tilt and azimuth of Antennas
Optimized model includes non-differentiable functions:
Radio Propagation models which depend on the type of area,
signal-to-interference-plus-noise ratio - integral index which consists of ratio between prevalent signal and noise.
This function has large optimization complexity (number of states): For example in optimized network with 300 sector antennas and 4 parameters, if every parameter has n states, then total number of states is n1200
So, we optimize multivariable non-differentiable function with large optimization complexity.
Initial subnet
Optimized subnet
Regulated parameters of sector antenna: power, height, tilt, azimuth
High optimization complexity:
300 antennas * 4 parameters, n states of parameter => n1200 states

10. Alternative splitting vs. Sector planning
5 October 2015
Optimized integral index – average Signal to Interference plus Noise Ratio:
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
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)

11. Benefits of Independent optimization of alternatives
5 October 2015
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

12. D.Yu. Ignatov, A.N. Filippov, A.D. Ignatov, X. Zhang
5 October 2015
Automatic Analysis, Decomposition and Parallel Optimization of Large Homogeneous Networks
D.Yu. Ignatov, A.N. Filippov, A.D. Ignatov, X. Zhang
ISPRAS Open 2016