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
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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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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.
Notes de l'éditeur
Presentation of the new algorithm of Homogeneous Network Optimization
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.
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.
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.
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 non-overlapping 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.
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.
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.
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.
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.
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 speed-up 9 times, and after 1 hour shows better quality of radio signal – SINR is 15 % higher in logarithmic scale.
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.
Presentation of the new algorithm of Homogeneous Network Optimization