Total Optimization of Smart City by Global-best Modified Brain
Storm Optimization
Mayuko Sato
1
, Yoshikazu Fukuyama
1
, Tatsuya Iizaka
2
and Tetsuro Matsui
2
1
Graduate School of Advanced Mathematical Sciences, Meiji University, 4-21-1, Nakano, Nakano-ku, Tokyo, Japan
2
Fuji Electric, Co. Ltd., No.1, Fuji-machi, Hino, Tokyo, Japan
Keywords: Smart City, CO
2
Emission Reduction, Large-scale Mixed-integer Nonlinear Optimization Problem,
Evolutionary Computation, Brain Storm Optimization.
Abstract: This paper proposes a total optimization method of a smart city (SC) by Global-best Modified Brain Storm
Optimization (GMBSO). Almost all countries have a goal to reduce CO2 emission as the countermeasures of
global warming. In addition, these countries have conducted SC demonstration projects. The problem of the
paper considers CO
2
emission, energy cost, and electric power load at peak load hours. In order to solve the
problem, Differential Evolutionary Particle Swarm Optimization (DEEPSO), Modified Brain Storm
Optimization (MBSO), and Global-best Brain Storm Optimization (GBSO) have been applied to the problem.
This paper proposes a novel evolutionary computation method, called Global-best Modified Brain Storm
Optimization (GMBSO), which is a combined method of GBSO and MBSO in order to obtain better results.
The total optimization of SC is solved by the proposed GMBSO based method. The results by the proposed
GMBSO based method is compared with those by conventional DEEPSO, BSO, only GBSO, and only MBSO
based methods.
1 INTRODUCTION
Many environmental problems have been focused
recently in the world and one of the main problems is
global warming. Increase of the amount of CO
2
emission can be considered as the reason of the global
warming (Ministry of Economy, Trade, and Industry
of Japan, 2014; Xcel Energy, 2007; Jaber, 2006).
Hence, it is important that we should "efficiently"
utilize energy for reduction of the emission. SC can
be defined that it realizes a sustainable city
considering reduction of carbon dioxide emission
using various IT technologies, and renewable
energies such as wind power and photovoltaic
generation, and storage batteries. In 2011, Great East
Japan Earthquake struck Tohoku in Japan. Hence,
many SC has been considered in Tohoku especially
after 2011 (Tohoku Bureau of Economy, Trade and
Industry, 2012).
Usually it is difficult to obtain quantitative
evaluation of reduction rate of carbon dioxide
emission, and purchased electric power and natural
gas cost. Hence, SC model should be developed for
the numerical evaluation. Various models of each
sector in SC has been separately developed. (Marckle,
et al., 1995; Henze, 2000; Suzuki, et al., 2012;
Makino, et al., 2015). However, as far as the authors
know, no research can be found for the total SC model
which can numerically calculate purchased electric
power and natural gas cost, and environmental loads
with interaction of all sectors in SC. Hence, IEE of
Japan team have developed SC model which can
numerically calculate CO
2
emission and energy cost
with interaction of all sectors (Yasuda, 2015;
Yamaguchi, et al., 2015; Matsui, et al., 2015).
The authors have conducted researches on total
optimization of SC using the SC model with
interaction among all sectors. The SC optimization
problem minimizes purchased electric power and
natural gas cost, shifts peak load, and minimizes CO
2
emission. In addition, the authors have applied many
evolutionary computation techniques (particle swarm
optimization (PSO) (Sato, and Fukuyama, 2016a),
differential evolution (DE) (Sato, and Fukuyama,
2016b), differential evlutionary particle swarm
optimization (DEEPSO) (Sato, and Fukuyama,
2017), and global-best brain storm optimization
(GBSO) (Sato, and Fukuyama, 2018)). As far as
authors know, these researches are the the first trial in
the world. However, it has a possibility to realize
Sato, M., Fukuyama, Y., Iizaka, T. and Matsui, T.
Total Optimization of Smart City by Global-best Modified Brain Storm Optimization.
DOI: 10.5220/0006889301010109
In Proceedings of the 10th International Joint Conference on Computational Intelligence (IJCCI 2018), pages 101-109
ISBN: 978-989-758-327-8
Copyright
c
2019 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved
101
more reduction of CO
2
emission, more shift of actual
electric power, and more reduction of the purchased
electric power and natural gas cost. The optimization
results can be improved when the more effectve
evolutionary computation method is applied to the SC
prroblem.
The paper proposes Global-best Modified Brain
Storm Optimization (GMBSO), which is a new
evolutionary computation method and a combined
method of GBSO and MBSO considering these
backgrounds. The proposed method is applied to a
total optimization problem of SC. The results by the
proposed method are compared with those by
DEEPSO, BSO, only GBSO, and only MBSO based
methods.
2 SMART CITY MODEL
2.1 Concept of the Whole Smart City
IEE of Japan had developed the SC model with
interaction of all sectors. It can numerically calculate
cost of electric power and natural gas which is
purchased and CO
2
emission (Yasuda, 2015). The
model includes various sectors which are divided into
supply-side group and demand-side group (see fig.1).
The supply-side group consists of drinking water and
waste water treatment plants, and electric power and
natural gas utilities sectors. The demand-side group
consists of railroad, residences, building, and
industrial sectors.
2.2 Supply-side Group Sectors
Supply-side group sectors supply natural gas, electric
power, and drinking water. The models can supply
the energies, and the amount of the energies is equal
to the amount of the energies which are consumed by
Figure 1: A Configuration of a smart city model.
demand-side group. Details are shown in Yamaguchi,
et al. (2015).
2.3 Demand-side Group Sectors
The demand-side group cooperates with the supply-
side group. The demand-side group can obtain natural
gas, electric power, and drinking water from the
supply-side group. Loads of various energies in the
demand-side group, which are electric power, heat,
steam, and hot water are obtained with fixed values.
The demand-side group sectors generate or purchase
energies in order to satisfy the energy loads. Details
are shown in Matsui, et al. (2015).
3 PROBALEM FORMULATION
OF TOTAL OPTIMIZATION OF
WHOLE SMART CITY
3.1 Decision Variables
Decision variables are listed as follows:
- Drinking water treatment plant sector
(D1) Inflow from river,
(D2) Inflow of water into a service reservoir,
(D3) Output of electric power of a co-generator
(CoGen),
(D4) Charged or discharged electric power of a
storage battery (SB).
- Waste water treatment plant sector
(W1) Input of Pumped waste water,
(W2) Output of electric power of a CoGen,
(W3) Charged or discharged electric power of a
SB.
- Industrial sector
(I1) Output of electric power of a gas turbine
generator (GTG),
(I2) Heat output of turbo refrigerators (TRs),
(I3) Heat output of stream refrigerators (SRs),
(I4) Charged or discharged electric power of a
SB.
- Building sector
(B1) Output of electric power of a GTG,
(B2) Heat output of TRs,
(B3) Heat output of SRs.
- Residential sector
(R1) Heat output of SRs,
(R2) Output of electric power of a fuel cell,
(R3) Heat output of a heat pump water heater.
(R4) Charged or discharged electric power of a
SB
- Railroad sector
Coal
Renewable
energy
Atomic
fuel
Natural
gas
Oil
River
water
- Energy cost - CO
2
emission
Total evaluation
Natural
Gas utility
Supply-side
group
Elec. power
utility
Demand-side
group
Building
RailroadResidences
Industry
Water
treat.
IJCCI 2018 - 10th International Joint Conference on Computational Intelligence
102
(RR1) The number of passengers / h,
(RR2) Average of journey distance by one
passenger / h,
(RR3) The number of operated trains / h,
(RR4) The numbers of passenger cars / set,
(RR5) Average of journey distance by one train / h,
(RR6) Average of speed / h,
(RR7) The number of passengers / car
24 hour's variables should be considered for each
decision variables. Totally, there are 816 decision
variables. Hence, the problem is one of the large-scale
optimization problems.
3.2 Objective Function
Usually various SC have each purpose for realizing
SC. Three terms are dealt in order to consider each
purpose. Minimization of energy cost is the first term
considering SC such as industrial parks.
Minimization of actual electric power loads at peak
load hours is the second term, namely, peak load
shifting. The actual electric power load at each hour
is summation of electric power changed to the other
energies, the original load of electric power, and
electric power charged to the storage battery at each
hour. Interval of hours, when total actual electric
power loads of all sectors are higher than the average
of total actual electric power loads, are defined as
peak load hours. Minimization of CO
2
emission is the
third term considering SC such as local governments.
(1)
where is the number of all sectors, is the
number of hours per day (=24),
is natural gas
which is purchased of sector s at hour ,
is a unit
cost of natural gas which is purchased of sector at
hour ,
is electric power which is purchased
by sector at hour ,
is a unit cost of electric
power which is purchased by sector at hour ,
is an actual electric power load of sector at hour ,
is the start hour of peak load hours of actual
electric power loads, is the final hour of peak
load hours of actual electric power loads,
is a
coefficient for changing from natural gas, which is
purchased, to CO2 emission,
is a coefficient for
changing from electric power, which is purchased, to
CO2 emission,
,
, and
are weighting
coefficients (
1).
3.3 Constraints
There are two constraints for treatment of energy
balances and facility characteristics.
- Energy balances: In the model, there are many
energies such as electric power, natural gas and so on.
Energy balances are expressed with (2).
,
0,
1,….,,1,…,,
1,…,
(2)
where
is startup or shutdown status of a facility for
decision variable
,
is an input or output value of a
facility for decision variable
,
,
is an
energy balance of energy
in sector
,
is the
number of decision variables,
is the number of
energies in sector
.
- Facility characteristics: Efficiency functions of
Facilities, and upper and lower bounds of various
facilities can be expressed with (3):
,
0,
1,….,,1,…,,
1,…,
(3)
where
,
is a function for efficiency of a
facility or an upper and lower bounds of facility of
sector ,
is the number of facilities in sector .
The problem deals with discrete and continuous
variables. Start-up / shutdown status can be expressed
as discrete variables, and input and output values of
facilities can be expressed as continuous variables.
Some characteristics of various facilities are
expressed as nonlinear functions. Hence, the problem
can be categorized into a mixed integer nonlinear
optimization programming problem. Hence, various
evolutionary computation methods have to be applied.
4 TOTAL OPTIMIZATION OF A
SMART CITY BY GMBSO
4.1 Overview of BSO
This paper proposes a new evolutionary computation
method, GMBSO. The proposed GMBSO is based on
BSO. BSO has been developed by Shi in 2011 (Shi,
Total Optimization of Smart City by Global-best Modified Brain Storm Optimization
103
et al., 2011) inspired by brainstorming. The main
algorithm of BSO is expressed in this section:
Step.1 individuals are randomly generated
and individuals are evaluated.
Step.2 individuals are divided into
clusters by k-means based algorithm.
Step.3 new individuals are generated.
Step.4 The individuals which are generated at step. 3
are compared with the current individuals
with the same individual number. The better
individual is set as the new current individual.
Step.5 Compare the current individuals with the best
individual. The individual is recorded as the
best individual if the current individual is
better than the pre-best individual.
Step.6 The procedure is stopped and go to Step.7 if
the number of current iteration reaches the
maximum number of iteration which was pre-
determined. Otherwise, go to Step.2 and
repeat the procedures.
Step.7 Finally, output the results.
4.1.1 Clustering (Step. 2)
BSO deals with clustering in order to divide search
space to several regions using k-means based
algorithm. The clustering algorithm is explained as
follows:
Step.1 individuals are divided into clusters
by k-means.
Step.2 a value
is generated using random number
in the range from 0 to 1.
Step.3 All individuals are ranked according to the
objective function values of each individual in
each cluster. if
(pre-determined
probability),set the best individual in each
cluster as the cluster center in each cluster.
Otherwise, one individual is randomly
generated, and the generated individual is set
as the cluster centre.
4.1.2 New Individual Generation (Step. 3)
Using one or two current individual(s), a new
individual can be generated. The following equations
are utilized for new individual generation:
1,0
(4)
.
1,0
(5)
1,0
1
11,0
2
(1,…,,1,…,)
(6)
where
is decision variable of new
individual ,
is decision variables of the th
current individual,
is a step size function,
is the maximum number of iteration, is
the current iteration number, is a coefficient in
order to change slope of log sigmoid transfer
function, 1
and 2
are decision variables of
th new generation which are centers or randomly
selected other individuals of selected clusters, 1,0
is a randomly generated value in the range from 0 to
1, and 1,0
is a randomly generated value in the
range from 0 to 1 for individual .
Equations (4) and (5) are utilized when one individual
is utilized in order to generate one new individuals.
Equation (4) to (6) are utilized when two individuals
are utilized in order to generate one new individual.
There are four conditions for determining
as
shown below:
If
is smaller than 1,0,
Randomly select one cluster.
If
is bigger than
1,0
,
Set the cluster centre from the selected
cluster as
. Then, one new individual
is generated using (4) and (5).
Otherwise,
Randomly select one cluster and randomly
select one individual as
from the
selected cluster randomly and generate one
new individual using (4) and (5).
Otherwise,
Randomly select two clusters.
If
is smaller than 1,0,
the two cluster centers are set as 1
and
2
and combined using (6). Using the
combined
, one new individual is
generated using (4) and (5).
Otherwise,
Randomly select two individuals from
each selected cluster. Set these selected
individuals as 1
and 2
, and
combine them using (6). Using the
combined
, one new individual is
generated using (4) and (5).
4.2 Overview of GBSO
GBSO has been proposed by El-Abd in 2017. The
method improves original BSO performance (El-Adb,
2017). Fitness-based grouping (FbG) is utilized as
clustering method instead of k-means in GBSO. In
addition, when a certain condition is satisfied,
information of the best individual among all
IJCCI 2018 - 10th International Joint Conference on Computational Intelligence
104
individuals (gbest) is applied to the current
individuals.
4.2.1 Clustering for GBSO
GBSO utilizes as a clustering method.
Algorithm of FbG can be expressed as follows:
Step. 1 All individuals are ranked according to the
objective function values.
Step. 2 All individuals are divided into groups
using (7).
1
%11,..,
(7)
where
is the group number of individual , and
is a ranking of individual .
4.2.2 New Individual Generation for GBSO
When the following condition (9) is satisfied, t
information is added to the current individuals.
(8)
1,0
(9)
where is a probability utilized to determine
whether the information is utilized or not,
is the maximum value of ,
is the
minimum value of .
When the condition (9) is satisfied, gbest information
is added to current individuals using (10).
,1
(1,…,,1,…,)
(10)
where
is decision variable of the best
individual among all individuals ().
The above equation has been improved in Sato, M.,
and Fukuyama, Y., 2018 as follows. Using above
condition and equations, information of can be
focused at the early iterations more than the final
iterations. In addition, the number of decision
variables of the problem is too large to be considered
in (10). Hence, ,1 of the equation (10) is
changed to 1,0. In addition, it can be usually
considered that exploitation should be focused at the
final search iterations and exploration should be
focused at the early search iterations. Hence, the
condition (9) (1,0) is changed to 1,0.
In the simulation, conditions (9) and (10) are changed
to (11) and (12) as shown below:
1,0
(11)
1,0
(12)
4.3 Overview of MBSO
MBSO has been proposed as one of improved BSOs.
There are two points which are improved in MBSO
from BSO (Zhan, et al., 2012). One is that simple
grouping method (SGM) is utilized as a clustering
method instead of k-means in order to reduce
calculation time. Another one is that a new individual
generation equation focuses more diversification.
4.3.1 Clustering for MBSO
MBSO utilizes SGM as a clustering method instead
of k-means. Algorithm of the SGM is expressed as
follows:
Step. 1 different individuals are selected
randomly from individuals at the current
iteration as group centers.
Step. 2 Distances from the current individuals to
each cluster centre are calculated and these
are compared each other. Then, the
individuals are divided into the group which
has the nearest distance from the current
individual to the cluster centers.
Step.3 a value
is randomly generated in the range
from 0 to 1.
Step.4 All individuals are ranked according to the
objective function values of each individual
in each cluster.
if
(pre-determined probability),
set the best individual in each cluster as
the cluster center in each cluster,
Otherwise,
one individual is randomly generated in
each cluster, and the generated individual
is set as the cluster center.
4.3.2 New Individual Generation
New equations for new individual generation is
proposed in MBSO considering diversification of
individuals:
,
1,0
1,0
1,0
1,…,,
1,…,
(13)
where, is a probability utilized to determine the
utilized equation,
is the lower bound of decision
variable ,
is the upper bound of decision variable
, and
are randomly selected
individuals.
Total Optimization of Smart City by Global-best Modified Brain Storm Optimization
105
4.4 Total Optimization of SC
Algorithm by GMBSO
The proposed algorithm of total optimization of SC
by GMBSO is shown below:
Step.1 individuals are randomly generated.
inside the search space which is reduced
using the method proposed in Sato, M., and
Fukuyama, Y., 2016a, b. The random
decision variables of individuals are changed
to operational variables by the cut-out
transformation function (Suzuki, et al., 2012)
and calculate the object function value of all
individuals using equation (1).
Step.2 individuals are divided into
clusters by FbG.
Step.3 Select
by four conditions explained
in 4.1.2. When the condition (11) is satisfied,
is modified using (12). New
individuals are generated using (13).
Step.4 Calculate the objective function values of
individuals with operational variables
which is changed by the cut-out
transformation function. Compare the new
individuals with the current individuals of the
same individual number. Then, if the new
individual is better than the current individual,
the new individual is set as the new current
individual.
Step.5 Calculate the objective function values of all
new individuals using (1). Compare the
values with the objective function value of
gbest individual. The gbest is updated when
the objective function value of the current
individual is better than pre-t.
Step.6 Proceed to step. 7 if the current number of
iteration reaches the maximum number of
iteration which is pre-determined. Otherwise,
proceed to Step.2 and repeat the procedures.
Step.7 Finally output the best solution with the
objective function value and operational
variables.
5 SIMULATIONS
5.1 Simulation Conditions
The proposed GMBSO based method is applied to a
typical mid-sized smart city model in Japan. The
number of each model of each sector is set
considering the typical mid-sized smart city and
shown below:
Drinking water treatment plant: 1, Waste water
treatment plant: 1, Industry model: 15, Building
model: 50, Residential model: 45000, Railroad: 1
These number are set considering that a load ratio of
each sector is almost the same as the load ratio of each
sector in Toyama city (Kanno, et al., 2015). In the
paper, DEEPSO, BSO, MBSO, and GBSO based
methods are utilized as conventional methods and the
results of the conventional methods are compared
with the results of the proposed GMBSO based
method.
Many countries have developed various SCs and
the SCs have their goals. Hence, the simulation deals
with three cases. Case 1 considers a SC such as
industrial parks and the goal is set as minimization of
energy cost. Case 2 considers a SC such as local
governments and the goal is set as minimization of
CO
2
emission. Case 3 considers all terms of the
objective function almost equally.
Case 1:
∶1
，
∶0,
:0
Case 2:
∶0
，
∶0,
:1
Case 3:
:0.00001,
:0.99998,
:0.00001
As shown in the cases, appropriate weighting
coefficients can be set and it is practical to utilize one
weighted function as an objective function instead of
multi-objective functions.
Parameters for DEEPSO are set as follows:
: 0.2,
: 0.006, : 0.75, initial weight
coefficients of each term of update equations: 0.5,
the number of clones: 1.
Parameters for BSO, GBSO, MBSO, and the
proposed GMBSO method are shown as follows:
:0.5,
:0.5,
:0.2,
:0.2,: 0.2, : 0.2 (for MBSO, and
GMBSO),
:0.7,
:0.2(for GBSO, and
GMBSO).
Common parameters are set as follows:
The number of individuals: 80, the number of
trials: 50, the maximum iteration numbers for
BSO, GBSO, MBSO, and GMBSO based
methods: 4000, the maximum iteration number
for DEEPSO based method: 2000 (Two
evaluations are done for one individual in
DEEPSO. Hence, the number is set in order to set
the same number of the objective function
evaluations.), Initial searching points are set
randomly.
C language (gcc version 4.92 on Cygwin) has been
utilized for development of simulation software on a
PC (Intel Core i7 (3.60GHz)).
IJCCI 2018 - 10th International Joint Conference on Computational Intelligence
106
5.2 Simulation Results
Table 1 shows comparison of average, the minimum,
the maximum, and standard deviation values of the
objective function values for three cases among
conventional DEEPSO, BSO, GBSO, MBSO and the
proposed GMBSO based methods. The results in the
table are calculated when the average objective
function value by one of the conventional methods,
DEEPSO based method, is set to 100 %. It can be
observed that the proposed method can reduce the
most for average, the maximum, the minimum, and
standard deviation values among all conventional
methods, which are DEEPSO, BSO, GBSO, and
MBSO, and the proposed GMBSO based method at
all cases. It is considered that about one million US$ a
year can be reduced for reduction of energy cost when
1 % of the objective function is reduced (case 1). It
can be said that GBSO can focus on more
intensification and MBSO can focus on divesification.
Hence, the proposed GMBSO can effectively work in
order to keep a balance between diversification and
intensification. In addition, the problem is one of
large-scale optimization problems. Hence, the
balance between diversification and intensification is
important and the proposed GMBSO can effectively
work for the SC problem.
Table 1: Comparison of average, the minimum, the
maximum, and standard deviation value of Case 1, 2, and 3
among DEEPSO, BSO, GBSO, MBSO, and the proposed
GMBSO.
Case
Ave. Min. Max. Std.
1
DEEPS
O
100.00 98.75 101.63 0.57
BSO 97.13 96.46 97.96 0.30
GBSO 95.94 95.55 97.03 0.26
MBSO 97.20 96.75 97.66 0.20
GMBSO 95.06 94.90 95.29 0.09
2
DEEPS
O
100.00 99.53 100.58 0.20
BSO 99.28 98.98 99.60 0.14
GBSO 98.29 98.22 98.42 0.04
MBSO 99.38 99.15 99.50 0.06
GMBSO 98.26 98.17 98.36 0.04
3
DEEPS
O
100.00 99.44 100.88 0.32
BSO 99.64 99.38 99.87 0.09
GBSO 99.36 99.12 99.53 0.10
MBSO 98.37 98.30 98.46 0.04
GMBSO 98.10 98.05 98.16 0.03
*) All of values are rates when the average of the objective
function value is set to 100 %.
Table 2 shows comparison of the optimal
operation for reduction of energy cost (case 1) among
conventional DEEPSO, BSO, GBSO, MBSO and the
proposed GMBSO based methods. As an example,
the table shows operation of industrial sector. In the
table, column A expresses output of electric power
from GTG, and column B expresses electric power
which is purchased by industrial sector. In the model,
output of electric power from GTG is inexpensive.
Electric power which is purchased by the sector is
expensive at 8 to 22 hours. Hence, output of electric
power from GTG should be increased and electric
power which is purchased by the sector should be
reduced from 8 to 22 hours for reduction of cost of
electric power and natural gas which are purchased.
It is observed that output of electric power from GTG
is increased and electric power which is purchased is
reduced from 8 to 22 hours the most by the proposed
GMBSO based method.
6 CONCLUSIONS
This paper proposes a new evolutionary computation
method, called, GMBSO which is a combined method
of GBSO and MBSO in order to keep a balance
between diversification and intensification. In
addition, it also proposes a total optimization method
of a smart city by GMBSO. The better results can be
obtained by the proposed method than the
conventional DEEPSO and BSO, GBSO, and MBSO
based methods.
Applications of novel evolutionary computation
methods which work effectively for large-scale
optimization problems such as the SC problem will
be conducted to the problem as one of future works.
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Total Optimization of Smart City by Global-best Modified Brain Storm Optimization
107
Table 2: Comparison of the best facility operation for case 1 among DEEPSO, BSO, GBSO, MBSO, and the proposed
GMBSO in an industrial model.
DEEPSO BSO GBSO MBSO GMBSO
A B A B A B A B A B
1 0.00 8.21 0.00 7.85 0.00 7.59 0.00 7.00 0.00 7.25
2 0.00 5.13 0.00 5.09 0.00 5.22 0.00 7.07 0.00 7.16
3 0.00 8.08 0.00 7.97 0.00 8.03 0.00 7.22 0.00 7.15
4 0.00 8.08 0.00 8.25 0.00 8.22 0.00 7.17 0.00 7.00
5 0.00 8.29 0.00 9.22 0.00 9.23 0.00 9.17 0.00 9.17
6 0.00 8.90 0.00 9.09 0.00 8.91 0.00 8.90 0.00 9.25
7 0.00 9.03 0.00 8.58 0.00 9.18 0.00 9.24 0.00 9.12
8 6.00 1.09 6.00 1.15 6.71 0.30 7.46 1.84 8.98 0.12
9 10.65 2.15 12.26 0.81 12.36 0.55 8.98 1.99 10.74 0.22
10 10.92 2.24 10.48 2.48 11.63 1.37 13.85 0.95 14.71 0.33
11 14.06 3.81 17.47 1.35 16.68 2.20 18.32 0.61 18.80 0.17
12 14.32 8.67 7.73 15.71 18.45 4.91 20.00 4.67 19.72 4.98
13 14.99 2.61 14.12 5.13 18.54 0.59 15.48 2.31 17.06 0.88
14 13.02 9.20 18.21 3.91 18.81 3.49 19.40 2.78 20.00 2.00
15 13.86 9.32 17.22 6.03 19.05 4.14 20.00 3.08 20.00 3.07
16 18.84 6.07 16.77 6.51 18.55 4.55 16.14 4.96 20.00 1.10
17 10.88 13.03 16.30 6.68 18.48 4.43 18.27 4.51 20.00 2.79
18 18.16 3.84 20.00 2.17 18.55 3.44 20.00 1.97 20.00 1.99
19 20.00 3.11 18.96 3.77 18.37 4.07 20.00 3.04 19.15 3.85
20 19.44 1.96 16.53 3.97 17.14 3.66 17.25 4.09 20.00 1.23
21 17.26 0.09 13.74 3.93 16.79 0.87 16.33 0.93 17.12 0.08
22 7.26 4.97 8.73 3.27 10.84 1.16 11.56 0.59 12.13 0.09
23 0.00 13.03 0.00 12.84 0.00 12.97 0.00 13.05 0.00 12.92
24 0.00 10.38 0.00 10.45 0.00 10.45 0.00 10.45 0.00 10.20
209.65 72.15 214.50 66.88 240.97 39.72 243.02 38.32 258.43 22.90
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