https://doi.org/10.31449/inf.v44i3.1969 Informatica 44 (2020) 349–360 349 
 
Performance Assessment of a Set of Multi-Objective Optimization 
Algorithms for Solution of Economic Emission Dispatch Problem 
 
Sarat Kumar Mishra 
Department of Electrical and Electronics Engineering, Padmanava College of Engineering, Rourkela, India 
E-mail: mishra.sarat@gmail.com 
 
Sudhansu Kumar Mishra 
Department of Electrical and Electronics Engineering, Birla Institute of Technology, Mesra, Ranchi, India 
E-mail: sudhansu.nit@gmail.com 
Keywords: differential evolution, economic emission dispatch, multi-objective optimization, non-dominated sorting, 
particle swarm optimization 
Received: October 30, 2018 
This paper addresses the realistic economic emission dispatch (EED) problem of power system by 
considering the operating fuel cost and environmental emission as two conflicting objectives, and power 
balance and generator limits as two constraints. A novel dynamic multi-objective optimization 
algorithm, namely the multi-objective differential evolution with recursive distributed constraint 
handling (MODE-RDC) has been proposed and successfully employed to address this challenging EED 
problem. It has been thoroughly investigated in two different test cases at three different load demands. 
The efficiency of the MODE-RDC is also compared with two other multi-objective evolutionary 
algorithms (MOEAs), namely, the non-dominated sorting genetic algorithm (NSGA-II) and multi-
objective particle swarm optimization (MOPSO). Performance evaluation is carried out by comparing 
the Pareto fronts, computational time and three non-parametric performance metrics. The statistical 
analysis is also performed, to demonstrate the ascendancy of the proposed MODE-RDC algorithm. 
Investigation of the performance metrics revealed that the proposed MODE-RDC approach was capable 
of providing good Pareto solutions while retaining sufficient diversity. It renders a wide opportunity to 
make a trade-off between operating cost and emission under different challenging constraints. 
Povzetek: Opisan je izvirni multi-kriterijski optimirni algoritem za energetske sisteme, ki kombinira 
kriterij onesnaževanja in kriterij energetske potrošnje. 
1 Introduction 
The Economic Load Dispatch (ELD) problem deals with 
the estimation of the scheduled real power generation 
from the committed units for best economic operation. 
Over the years the problem has become more complex 
due to the increasing effects of emissions from fossil fuel 
based power plants on the environment. The emission 
and fuel cost of each unit depend on the quantity of 
power to be generated. Both of them are nonlinear 
functions of power output. Minimum operating cost does 
not ensure minimum emission. Each operating condition 
must satisfy the power balance criterion and should obey 
the generating limits of the committed units. These can 
be considered as constraints. Generally, better quality 
fuel ensures less emission but it can be further reduced 
by proper scheduling of generation from different units. 
The cost coefficients and emission coefficients of these 
generating units do not match. Hence, achieving these 
two objectives, i.e. less cost and less emission is 
contradictory in nature. Thus, the EED problem has 
evolved as a modification of the ELD problem. 
Therefore, the EED problem is a multi-objective 
optimization problem with nonlinear constraints. 
In [1-2], the power engineers solved the ELD 
problem by scheduling of the generation of multi-unit 
systems using the derivative based Gauss-Siedel and 
Newton-Raphson algorithms along with the Lagrangian 
multiplier. These conventional methods suffer from the 
problem of getting trapped in local minima and also fail 
for system discontinuities due to prohibited zones. These 
techniques are inadequate to solve multi-objective 
problems with nonlinear constraints. Chang et al. [3] 
rehabilitated the inherently multi-objective EED problem 
to a single objective one by assigning weights to the 
operating cost and emission. This weighted sum 
approach requires many runs of the same algorithm to 
find the Pareto optimal front. The solutions arrived at by 
this method do not ensure a uniform Pareto front. The 
trade-off information is lost when the function is 
concave. To avoid this bottom-hole different 
evolutionary based heuristic approaches have been 
introduced by many researchers [4-5]. These 
evolutionary algorithms have considered the two 
objectives simultaneously and are shown to perform 
better as compared to the conventional ones. Chiang et 
al. [6] made a further refinement and proposed an 
improved genetic algorithm to speed up the search 
process. He used the ϵ-constraint technique for efficient 

350 Informatica 44 (2020) 349–360 S.K. Mishra et al. 
 
 
constraint handling and proposed a multiplier updating 
mechanism for better exploration of the search space. 
Deb et al. [7] proposed the non-dominated sorting 
genetic algorithm which utilized rank and crowding 
distance as parameters to arrive at a compromise between 
the two conflicting objectives. This was applied to the 
multi-objective environmental economic load dispatch 
problem in [8]. The Pareto optimal front could be 
obtained by a single run of the algorithm. But, this 
population based genetic algorithm depends upon 
biologically inspired factors like mutation and crossover 
parameters. It needs further improvement in terms of 
exploring a wider area in the search space. Brar et al. [9] 
made improvements in the search space by adding the 
fuzzy inference system. Muthuswamy et al. [10] 
modified the non-dominated sorting technique by 
incorporating a dynamic crowding distance to improve 
the diversity of solutions in the search space. These 
algorithms fail when there are discontinuities in the cost 
function. 
Nayak et al. [11] implemented another evolutionary 
algorithm, the artificial bee colony (ABC) optimization, 
and improved the convergence rate and reliability under 
the presence of the prohibited zones and ramp rate limits. 
Liang et al. [12] modified the ABC algorithm to form an 
improved artificial bee colony (IABC) by addition of a 
new skill called chaos ques in the search process. Mori et 
al. [13] made an excellent improvement in the 
exploration of search space through the implementation 
of the particle swarm optimization (PSO) for this 
multimodal problem. They also used adaptive parameter 
adjustment to improve the results. A significant 
improvement in search space exploration was made by 
Hadji et al. [14]. They incorporated a time varying 
acceleration of the particles to improve the robustness of 
the algorithm. Recently, a differential evolution (DE) 
algorithm came up which generates the next set of 
population of new particles by the addition of a 
differential vector obtained from the difference of the 
position vectors of two different particles other than the 
particle undergoing evolution [15]. This algorithm is still 
dependent on the bio-inspired parameters but is able to 
avoid premature convergence. Meza et al. [16] improved 
the algorithm by incorporating spherical pruning for 
better exploitation of the search space. Di et al. [17] 
introduced a marginal analysis correction operator to 
improve the constraint handling. 
 In [18], the particle swarm optimization algorithm 
has been developed which is based on the intelligence of 
flock of birds. The same has been improved and tested 
for multi-objective problems in [19-21]. The EED 
problem has been solved to decide the unit commitment 
of the power system by considering operational power 
flow and environmental constraints in [22]. But, it again 
utilized the method of conversion of the multi-objective 
problem to a single objective one. A new approach to 
optimization is proposed in [23] which hybridized 
adaptive PSO and DE for improvement of the search 
space. An improvement over ABC called as multi-
objective global best artificial bee colony (MOGABC) 
optimization is suggested in [24] for better constraint 
handling in EED problem. The EED problem has been 
further modified and applied to the micro-grid containing 
renewable sources along with the conventional thermal 
power stations in [25]. It also converts the problem to a 
single objective one by incorporating a h-index.  
In this paper, a new constraint handling mechanism 
has been implemented, and a new multi-objective 
optimization (MOP) algorithm, namely the multi-
objective differential evolution with recursive distributed 
constraint handling (MODE-RDC) has been proposed. 
The constraint handling mechanism is suitably 
incorporated in three multi-objective optimization (MOP) 
algorithms, and the effectiveness of the algorithms has 
been tested under various load conditions. 
2 Multi-objective optimization: a 
review 
The main aim of the multi-objective optimization 
technique is to optimize two or more conflicting 
objectives simultaneously. The MOP is denoted by a 
decision variable vector, each element of which 
represents the objective functions [21]. The solution to 
the MOP is the optimum value of the vector function by 
considering all the constraints. A multi-objective 
minimization problem can be generalized as follows: 
Minimize f (x ⃗ ) = (f
1
(x ⃗ ), f
2
(x ⃗ ), …, f
M
(x ⃗ ))        (1)   
Subject to constraints: 
g
j
(x ⃗ ) ≤ 0; j=1, 2, ⋯, J     (2) 
h
k
(x ⃗ ) = 0; k =1, 2, …, K                 (3)                                                   
where, x ⃗  is a vector with N decision variables 
x ⃗ =[x
1
, x
2
, …, x
N
]
T
 
The search space may be limited by lower and upper 
bounds 
lb
i
 ≤ x
i
 ≤ ub
i
;   i =1, 2, …, N   (4) 
A solution vector u ⃗ =[u
1
, u
2
, …, u
N
]
T
 dominates over 
another solution v ⃗ =[v
1
, v
2
, …, v
N
]
T
 if and only if 
f
i
(u ⃗ )≤f
i
(v ⃗ )∀ i∈[1,2,…,M]
f
i
(u ⃗ )<f
i
(v ⃗ ) for at least one i∈[1,2,…,M]
}  (5) 
         Solutions that are not dominated by other 
solutions within the given solution space are said to be 
non-dominated solutions. The front obtained by mapping 
such points onto the objective space is said to be the 
Pareto optimal front (POF) 
POF = f (x ⃗ ) = [{f
1
(x ⃗ ), f
2
(x ⃗ ), …, f
k
(x ⃗ )}; |x ⃗ ∈p] (6) 
where, p is the set of non-dominated particles. 
3 Economic emission dispatch 
problem 
The generation schedule for minimum operating cost is 
called ELD. This schedule is obtained when the 
committed units of the power system are able to supply 
the load demanded and the associated transmission losses 
by satisfying the generator limits. The thermal generating 
units are associated with emissions which are highly 
polluting in nature. Therefore, it is essential to minimize 

Performance Assessment of a Set of Multi-Objective ... Informatica 44 (2020) 349–360 351 
 
 
the emissions along with the fuel cost. The problem has 
been transformed to EED problem. It is considered as a 
multi-objective optimization problem as minimum 
operating cost does not ensure minimum emission [5]. 
The operating cost of thermal power systems depends 
mostly on the cost of fuel used. The quantity of fuel used 
by each unit depends on the generated power, efficiency 
of turbine etc. 
The fuel cost characteristics of the generating units 
are normally of the second order polynomial of the 
generated power. Thus, the operating fuel cost of the ith 
generator supplying a real power P
G
i
is given by 
F
i
 = a
i
P
Gi
2
 + b
i
P
Gi
 + c
i
                  (7)                                        
where, a i, b i and c i are the coefficients of cost function. 
The emission from the generator 𝑖 can be 
approximated as 
E
i
 = α
i
 + β
i
P
Gi
 + γ
i
P
Gi
2
                  (8)                                                                         
where, α i, β i, γ i are the coefficients of emission function. 
The aim of the ELD problem is to determine 
generation schedule for the minimum total fuel cost 
given by 
F
T
 = ∑ F
i
N
i=1
                                 (9)              
subject to the constraints. 
The total real power generation must be equal to the 
demand plus transmission losses 
∑ P
Gi
N
i=1
= P
D
 + P
L
                (10) 
where, P D is the load demand on the system and P L is 
the transmission loss. It is given by Kron’s formula 
P
L
=∑ ∑ P
Gi
B
ij
P
Gj
N
j=1
N
i=1
+ ∑ B
i0
P
Gi
N
i=1
+B
00
.          (11) 
The constants B ij, B i0 and B 00 are dependent on the 
line parameters. The generated real power of each unit 
must be within the feasible lower and upper bounds. 
P
Gi(min)
 ≤ P
Gi
 ≤ P
Gi(max)
; i =1, 2, …, N .                  (12) 
Thus, the sole objective of the EED problem is to 
optimize both the fuel cost and emission simultaneously. 
Hence, it is inherently a multi-objective optimization 
problem where these two objectives which are 
conflicting in nature need to be optimized. The set of all 
the potential compromised solutions is represented by the 
Pareto optimal front. 
The problem can be stated as: 
minimize
P
G
[F
T
(P
G
),E
T
(P
G
)]                            (13) 
Subject to: g(P
G
)=0; h(P
G
)≤0 
where, the equality constraint is represented by 
equation (14) and inequality constraint by equation (15).  
∑ P
Gi
-P
D
-P
L
=0
N
i=1
                             (14) 
P
Gi
-P
Gi
max
≤0;P
Gi
min
-P
Gi
≤0                            (15) 
4 Multi-objective optimization 
algorithms 
The multi-objective evolutionary algorithms can be 
categorized mostly into four types in accordance with the 
algorithmic framework, such as indicator based, 
convolution based, memetic based and non-dominated 
sorting based. In this paper, we have solved the economic 
emission dispatch problem using three different multi-
objective optimization algorithms that are based on non-
dominated sorting. 
4.1 Non-dominated Sorting Genetic 
Algorithm-II (NSGA-II) 
This algorithm was formulated by Deb et al. [7], [8] for 
solving the multi-objective optimization problems. It is 
initialized with a random population, and used some 
operators for covering the objective space uniformly on 
the Pareto set. For multi-criteria optimization it uses 
three strategies: non-domination sorting, ranking based 
on density and crowding comparison. The individuals are 
classified into several layers based on their rank and 
crowding distance. The diversity in the solutions is 
maintained by rejecting the solutions with lower 
crowding distance. The quality of solutions is ensured by 
selecting the individuals with lower ranks. The advantage 
of this algorithm is that the complexity of computation is 
lowered and elitism is maintained. 
4.2 Non-dominated Sorting Multi-
Objective Particle Swarm 
Optimization (NS-MOPSO) 
Kennedy and Eberhart proposed that any optimization 
problem can be solved by mimicking the movement of a 
flock of birds and school of fish [18]. The social behavior 
of the swarm is to change their position and velocity to 
maximize their chance of getting food and follow the 
best successful neighbor. This lead to the formulation of 
particle swarm optimization (PSO). In this method of 
optimization, a local best and a global best solution are 
identified. The i
th 
particle in the population having the 
best position (pbest) may be represented by p
i
, that gives 
the best fitness value represented as 
p
i
 = (p
i1
, p
i2
, …, p
iN
)   (16)                                                                                                                                                                                              
The old and new velocity of the particles will be shown 
in equation (17) and (18) respectively.   
V
i
 = (v
i1
, v
i2
, …,  v
iN
)               (17) 
v
id
(t) = wv
id
(t -1) + c
1
r
1
(p
id
- x
id
)(t -1)+c
2
r
2
(p
id 
-
x
id
)(t -1)                              (18) 
and the new position of the particle will be 
x
id
(t)=x
id
(t -1)+χv
id
(t)                            (19) 
where, d = 1,2,…,D is the dimension of the 
decision variables and i = 1,2,… ,N, andχ is the 
constriction factor which constricts and controls the 
velocity magnitude. w, c
1
 and c
2
are weight parameters 
and r
1
, r
2
are random numbers known as acceleration 
constants in the range [0, 1]. This method of 
improvement of position and velocity is applied to the 
non-dominating vectors to solve the multi-objective 
problem [14], [19] & [20]. 

352 Informatica 44 (2020) 349–360 S.K. Mishra et al. 
 
 
4.3 Multi-Objective Differential Evolution 
with Recursive Distributed Constraint 
handling (MODE-RDC) 
The differential evolution (DE) algorithm as developed 
by Stern and Price [15] is less dependent on bio-inspired 
mechanisms, and serves better for multivariable 
problems. The multi-objective optimization using 
differential evolution (MODE) proposed by Meza et al. 
[16] is an improvement of DE to solve multiple number 
of conflicting objectives simultaneously. The MODE is 
an evolutionary multi-objective optimization algorithm 
that retains the diversity of solutions on the Pareto front. 
This real coded stochastic algorithm uses an initial 
population to explore the search space by avoiding 
convergence to local optimal points. It uses two main 
operators: mutation and cross over. Each initial particle 
of the population is improved using these two operators. 
The mutation operator uses a differential vector selected 
from the particles other than the target particle. Three 
vectors x
r0,g
, x
r1,g
 and  x
r2,g
are selected randomly from 
the population and the first one is updated with the 
difference of the other two. It is done as follows: 
v
i,g
=x
r0,g
+F∙(x
r1,g
-x
r2,g
)                                        (20) 
where, v
i,g
 is the mutant vector created from the 
target vector x
r0,g
 and x
r1,g
, x
r2,g
 are two other vectors; 
F∈(0,1+) is the scale factor that controls the rate of 
evolution. 
A new trial vector (child) is created from the mutant 
vector and the target vector after cross over. 
u
i,g
=u
j,i,g
={
v
j,i,g
if(rand
j
(0,1)≤C
r
orj=j
rand
)
x
j,i,g
otherwise
           (21)            
where, the cross over probability C
r
∈[0,1]. The child 
and the parent are tested for their fitness. The one with 
the best fitness is selected for participation in the next 
generation. 
x
i,g+1
={
u
i,g
 if f(u
i,g
)≤f(x
i,g
)
x
i,g
otherwise
                             (22) 
This is done for all i =1, 2, ⋯, n where n = 
population size. The steps of the proposed MODE-RDC 
algorithm are summarized as follows: 
I. Initialize the number of individuals N and the 
population P(0) by random selection within the 
limits of the search space. Set the fitness function, 
constraints, maximum number of generations, 
mutation factor, cross over rate and tolerance. 
II. Evaluate P(0)using the fitness function and 
constraint 
III. If constraint violation is out of bounds call the 
recursive distributed constraint handler 
IV. Obtain the non-dominated solutions in P(0) and 
store in D(0) 
V. Update the populations till the maximum number of 
generations or the convergence criterion is reached 
1. Randomly select a subpopulation of N
s
(k)  with 
the proposed solution on P(k) 
2. Apply the DE operators on N s(k) to get the 
offspring O(k) : 
a) Perform the mutation operation. 
b) Apply the fixing rule for boundary constraint 
violations. 
c) Perform cross over operation. 
3. Evaluate offspring O(k) and determine 
constraint violations 
4. Call the recursive distributed constraint handler 
until constraint violation is within tolerable 
limits 
5. Compare the parent and offspring and select the 
best store in D(k) 
6. Apply dominance, 
VI. Modify D(k), perform non dominated sorting on 
D(k) and plot the Pareto front. Terminate the 
algorithm. Select the proper solution using the high 
level decision making rules. Here, we have used the 
allowable emission norms as the accepted solution. 
4.3.1 Constraint handling 
The main problem in finding the solution to the EED 
problem is that every new population evolved must 
satisfy the upper and lower bounds along with the 
nonlinear power balance constraint. The power balance 
constraint, being a polynomial of the individual 
solutions, makes it a complicated task to ensure 
convergence. Therefore, a continuous effort has to be 
made to restrict the solutions in the feasible area. Here, 
we propose a recursive distributed constraint handling 
method. The constraint c is the mismatch of power 
defined as 
c=∑ P
Gi
N
i=1
-P
D
-P
L
                              (23) 
if c≤ε , then P
Gi
=P
Gi
 
else P
Gi
=P
Gi
-
|c|
N
 
Start
Set the population size, maximum number of 
iterations, objective functions, limits, constraints, 
maximum constraint violation (tolerance), mutation 
factor, crossover rate and stopping criteria
Initialize the population within the lower and upper 
bounds
Evaluate the objective functions and the 
constraint violations
Constraint violations
 ≤ tolerance?
Update the population within the lower 
and upper bounds using the recursive 
distributed constraint handling
Perform non dominated sorting and plot the 
Pareto front
Stopping criteria/maximum 
iterations achieved?
Print results 
and stop
Perform mutation, 
crossover and selection
Yes
Yes
No
No Increment 
iteration
 
Figure 1: Flowchart of MODE-RDC algorithm. 

Performance Assessment of a Set of Multi-Objective ... Informatica 44 (2020) 349–360 353 
 
 
subject to P
Gi
min
≤P
Gi
≤P
Gi
max
 
where, ε is the maximum allowable constraint 
violation. The constraint violation is evaluated and 
distributed over the decision variables. The values of the 
N decision variables will change until the constraint 
violation is restricted within the permissible limits. Thus 
the solutions are confined within the feasible work space. 
The proposed algorithm is implemented using 
sequences shown in the flowchart (fig. 1). In the first 
block, the parameters including the limits are set. The 
second block initializes the population randomly between 
the upper and lower limits of the generating units. The 
population created is evaluated for the constraint 
violation; if the violation is high, then the population is 
updated using the constraint handler. The non-dominated 
sorting is performed, and Pareto optimal front is plotted 
from the updated population. This population represents 
the first iteration; subsequent iterations are performed to 
get further modified populations by applying equations 
(20), (21) and (22). This process is continued till 
convergence or the maximum number of iterations 
performed.  
5 Performance measures 
The following three performance metrics [21] have been 
applied to investigate the performance quality of the non-
dominated solutions obtained in the form of Pareto fronts 
using different algorithms. 
5.1 Generation Distance (GD) 
It is the estimated distance between the non-dominated 
solution vectors from the standard efficient front. It is 
mathematically expressed as 
GD= 
√∑ d
i
2 n
i=1
n
                 (24)                                                                                    
where, n is the number of solution vectors and d i is 
the minimum Euclidean distance between each of them. 
GD=0 indicates that all the solution vectors are present in 
the standard Pareto front. A smaller positive value of GD 
means the Pareto front obtained from the proposed 
algorithm is closer to the standard Pareto front. 
5.2 Spacing (S) 
Spacing is the measure of the spread of the solution 
vectors. It is expressed as 
S≜√
1
n-1
∑ (d
̅
-d
i
)
2
n
i=1
                (25)                                                                      
where,d
i
= min
j
(|f
1
i
(x ⃗ )-f
1
j
(x ⃗ )|+|f
2
i
(x ⃗ )-f
2
j
(x ⃗ )|) for all 
i, j=1, 2, …, n and d
̅
=mean of all d
i
 and n is the number 
of non-dominated solution vectors found so far. The 
lower the value of 𝑆 the better is the Pareto solution. 
5.3 Diversity metric (Δ) 
It measures how evenly the solution vectors are 
distributed in the search space, i.e. extent of the spread 
on the Pareto front. It is found from the Euclidean 
distances as follows 
 =
𝑑 𝑓 + 𝑑 𝑙 + ∑ |𝑑 𝑖 − 𝑑 ̅
|
𝑁 −1
𝑖 =1
𝑑 𝑓 + 𝑑 𝑙 + (𝑛 −1)𝑑 ̅
                             (26)                                                                                  
where, d i is the distance between the consecutive 
solution vectors in the non-dominated solution set. The 
average of these distances is d
̅
. Here,d
f
and d
l
are the first 
and last Euclidean distances. A low value of Δ indicates 
better diversity, and ∆=0 means the non-dominated 
solution vectors are uniformly spread on the Pareto front. 
6 Simulation study and results 
The EED problem was simulated for two different 
standard test cases i.e., IEEE 14 bus and IEEE 30 bus. 
The system data of these two test cases were obtained 
from the website www.ee.washington.edu/research/pstca. 
The cost and emission coefficients were also recorded 
from standard sources [22] and are presented in the 
Appendix along with the B coefficients. Each test case is 
solved for three different load demands. The solutions 
are obtained by applying three different algorithms e.g., 
NSGA-II, MOPSO and proposed MODE-RDC. The 
algorithms are run in a MATLAB environment with a PC 
running on Microsoft windows 8 platform having a core 
i3 processor with a clock speed of 1.3 GHz and RAM of 
4 GB.A maximum generation of 300 is taken with a 
population size of 100. The crossover rate is chosen as 
intermediate with the ratio set as 1.2 and mutation chosen 
as Gaussian with a scale of 0.1 and a shrink of 0.5 for 
NSGA-II. The velocity weight of MOPSO is selected as 
0.4 and position weights as 1 with a population size of 
100 and a maximum number of iterations of 100. The 
scaling factor of differential evolution is set as 0.5 and 
crossover rate as 0.5 with a population size of 100. 
6.1 Test case I: IEEE-14 bus system 
The algorithms were applied to this test case for three 
different load demands; i.e., for 200 MW, 259 MW and 
300 MW. The performance was compared with respect to 
Pareto optimal front, computational time, fuel cost, 
transmission loss involved and statistical performance 
metrics. 
6.1.1 IEEE-14 bus system: load demand 200 
MW 
The Pareto optimal fronts obtained by applying the three 
algorithms are compared and shown in Fig.2 for a load 
demand of 200MW. 

354 Informatica 44 (2020) 349–360 S.K. Mishra et al. 
 
 
The comparative generation schedule, fuel cost, 
emission and transmission loss are presented in Table 1. 
The Pareto front obtained by applying the proposed 
MODE-RDC algorithm and other two algorithms for 
different load conditions are depicted from Fig.2 to Fig. 
7. The fuel cost value (518.399$/hour) obtained is lowest 
among all the three competitive algorithms. The emission 
obtained from the proposed algorithm is also comparable 
with other two. Similarly, the algorithms were run for 25 
times, and the performance metrics were calculated 
which are presented in Table 2.  The average spacing 
obtained is 0.37959 which is the lowest among all the 
three algorithms. The average values of other two 
performance matrices show improved performance of the 
proposed algorithm. This indicates that the Pareto 
solutions obtained by the proposed algorithm are superior 
to the competing algorithms. 
6.1.2 IEEE-14 bus system: load demand 259 
MW 
Figure 3 shows the Pareto optimal fronts obtained for the 
test case with the load demand of 259 MW. 
 
Figure 2: Solution of IEEE 14 bus system for a load demand of 
200 MW. 
Algorithm NSGA-II MOPSO MODE-RDC 
PG1 (MW) 121.894 117.4404 121.1744 
PG2 (MW) 37.4252 41.0169 41.8528 
PG3 (MW) 19.3125 19.9156 20.4068 
PG4 (MW) 10.0000 13.9457 10.9482 
PG5 (MW) 15.6575 11.8954 10.0000 
Time (sec) 85.4620 0.963873 9.0003 
PL (MW) 4.2892 4.2230 4.3822 
Fuel Cost ($/hour) 518.569 518.6977 518.3990 
Emission(lb/hour) 244.963 241.1887 242.3576 
Table 1: Results of EED of EEE 14 bus system for a 
load demand of 200 MW. 
Algorithm NSGA-II MOPSO 
MODE-
RDC 
Generation 
Distance 
(GD) 
Minimum 0.0452 0.0714 0.0273 
Maximum 0.0819 0.0714 0.0772 
Average 0.051075 0.0714 0.050145 
Standard 
Deviation 
0.0144013 0.0000 0.0059599 
Spacing 
(S) 
Minimum 0.2266 0.5864 0.2659 
Maximum 0.7777 0.5864 0.5576 
Average 0.469715 0.5864 0.37959 
Standard 
Deviation 
0.135470 0.0000 0.0643687 
Diversity 
(Δ) 
Minimum 1.2497 0.7446 0.4843 
Maximum 1.6853 0.7446 0.7300 
Average 1.47758 0.7446 0.613785 
Standard 
Deviation 
0.134289 0.0000 0.0710588 
Table 2: Performance of algorithms for IEEE 14 bus 
system at load demand of 200 MW. 
 
 
Figure 3: Solution of IEEE 14 bus system for a load 
demand of 259 MW. 
Algorithm NSGA-II MOPSO MODE-RDC 
PG1 (MW) 150.416 150.6611 130.7742 
PG2 (MW) 51.3048 50.2912 53.0186 
PG3 (MW) 23.5338 23.7902 26.3320 
PG4 (MW) 23.5837 22.8592 30.7226 
PG5 (MW) 17.29 18.3925 24.2551 
Time (sec) 91.4121 2.380883 8.0020 
PL (MW) 7.1283 6.9942 6.1025 
Fuel Cost 
($/hour) 
720.3 720.1619 720.1591 
Emission 
(lb/hour) 
360 359.2373 359.1248 
Table 3: Results of EED for IEEE 14 bus system at 
load demand of 259 MW. 
Algorithm NSGA-II MOPSO MODE-
RDC 
Generation 
Distance 
(GD) 
Minimum 0.061130 0.1056 0.056818 
Maximum 0.247369 0.1056 0.215051 
Average 0.115768 0.1056 0.094455 
Standard 
Deviation 
0.052146 0.0000 0.037827 
Spacing 
(S) 
Minimum 0.531774 0.6438 0.527058 
Maximum 2.442706 0.6438 1.926600 
Average 1.099879 0.6438 0.641592 
Standard 
Deviation 
0.528886 0.0000 0.428131 
Diversity 
(Δ) 
Minimum 1.200668 0.5898 0.526846 
Maximum 1.702898 0.5898 0.825663 
Average 1.456543 0.5898 0.569785 
Standard 
Deviation 
0.124752 0.0000 0.077072 
Table 4: Performance of algorithms for IEEE 14 bus 
system at load demand of 259 MW. 

Performance Assessment of a Set of Multi-Objective ... Informatica 44 (2020) 349–360 355 
 
 
The generation schedule for this load is presented in 
Table 3, and the statistical performance metric values are 
shown in Table 4. The values of fuel cost and emission 
obtained by the proposed algorithm are better as 
compared to the other two algorithms. The generation 
schedule obtained by the former leads to less 
transmission loss. The proposed MODE-RDC algorithm 
shows lower average values of GD, S and ∆ as compared 
to the other two competitive algorithms. 
6.1.3 IEEE-14 bus system: load demand 300 
MW 
With a higher load of 300 MW the Pareto optimal fronts 
obtained using the algorithms are shown in Fig. 4. 
The generation schedule and performance metrics of 
the solution points are presented in Tables 5 and 6 
respectively. The fuel cost and emission obtained using 
proposed MODE-RDC algorithm is better in terms of 
emission and PL in MW. The transmission losses 
involved due to the schedule obtained by the proposed 
algorithm is also lower. The average value of GD, S and 
∆ metrics of the solutions arrived from the proposed 
algorithm are less than that of the other two. Thus the 
quality of solutions is maintained. 
6.1.4 IEEE-14 bus system: summary of results 
The summary of generation schedules obtained for the 
three load conditions using the three algorithms as 
presented in Tables 1, 3 and 5 show that the fuel cost for 
the proposed algorithm provides improved performance 
for the load conditions. For the IEEE 14 bus test case, the 
two-tailed Sign tests [21] is conducted for the pair-wise 
comparison of the algorithms by considering three 
different performance metrics, and are presented in 
Tables 7, 8 and 9. The tests were carried out for all the 
three load conditions and by repeated run of the three 
algorithms for 25 times. It is observed from Tables 7, 8 
and 9 that the proposed algorithm wins over the other 
two for all loads in terms of all the three performance 
metrics i.e. the generation distance, spacing and diversity 
metric as winning parameters. It can be pointed in Table-
10 that in Sign test, if more than 17 wins are recorded, 
then the algorithm is better with a detected difference 
α=0.1; and if more than 18 wins are recorded then, 
α=0.05.  
 
Figure 4: Solution of IEEE 14 bus system for a load 
demand of 300 MW. 
Load 
(MW) 
Algorithm MODE-
RDC 
Wins 
MODE-
RDC 
Losses 
Detected 
differences 
200 NSGA-II 17 8 α = 0.1 
MOPSO 13 12 - 
259 NSGA-II 18 7 α = 0.5 
MOPSO 13 12 - 
300 NSGA-II 18 7 α = 0.5 
MOPSO 13 12 - 
Table 7: Result of sign test on MODE-RDC algorithm 
for IEEE 14 bus system with GD metric as winning 
parameter. 
Load 
(MW) 
Algorithm MODE-
RDC 
Wins 
MODE-
RDC 
 Losses 
Detected 
difference
s 
200 NSGA-II 14 11 - 
MOPSO 13 12 - 
259 NSGA-II 16 9 - 
MOPSO 13 12 - 
300 NSGA-II 14 11 - 
MOPSO 13 12 - 
Table 8: Result of sign test on MODE-RDC algorithm 
for IEEE 14 bus system with S metric as winning 
parameter. 
 
Algorithm NSGA-II MOPSO MODE-RDC 
PG1 (MW) 158.385 159.5448 144.5312 
PG2 (MW) 59.5374 57.2405 61.6878 
PG3 (MW) 28.554 29.1715 30.9264 
PG4 (MW) 34.3464 36.9012 41.7176 
PG5 (MW) 27.8335 26.9604 29.1517 
Time (sec) 94.0921 2.303318 8.0025 
PL (MW) 8.6563 9.8184 8.0147 
Fuel Cost 
($/hour) 
880.909 879.916 880.4091 
Emission 
(lb/hour) 
440.116 440.862 440.234 
Table 5: Results of EED of IEEE 14 bus system for 
load demand of 300 MW. 
Algorithm NSGA-II MOPSO MODE-
RDC 
Generation 
Distance 
(GD) 
Minimum 0.056728 0.1245 0.055189 
Maximum 0.216685 0.1245 0.345505 
Average 0.123737 0.1245 0.120521 
Standard 
Deviation 
0.044166 0.0000 0.058929 
Spacing 
(S) 
Minimum 0.510125 0.7691 0.568051 
Maximum 2.065131 0.7691 1.644507 
Average 1.154852 0.7691 0.764450 
Standard 
Deviation 
0.428284 0.0000 0.666390 
Diversity 
(Δ) 
Minimum 1.269374 0.6529 0.491511 
Maximum 1.580342 0.6529 0.964161 
Average 1.426765 0.6529 0.648467 
Standard 
Deviation 
0.087880 0.0000 0.102660 
Table 6: Performance of algorithms for IEEE 14 bus 
system at load demand of 300 MW. 
 

356 Informatica 44 (2020) 349–360 S.K. Mishra et al. 
 
 
It is evident from the Table 7 and 8 that the proposed 
MODE-RDC algorithm shows better performance as 
compared to other two competitive algorithms. The 
algorithm is better with respect to NSGA-II a detected 
difference α=0.1 for load of 200 MW, and a detected 
difference of α=0.05 for load of 259MW and 300 MW. 
However, the proposed algorithm does not show much 
improvement as compared to MOPSO algorithm. 
6.2 Test case II: IEEE-30 bus system 
The algorithms were applied to this test case for three 
different load demands; i.e., for 200 MW, 283.4 MW and 
350 MW. The performance is compared with respect to 
Pareto optimal front, computational time, fuel cost, 
transmission loss involved and statistical performance 
metrics. 
6.2.1 IEEE-30 bus system: load demand 200 
MW 
The Pareto optimal fronts obtained by applying the three 
algorithms for the load demand of 200 MW are presented 
in Figure 5. 
From the simulation output it reveals that the Pareto 
curve obtained by applying the proposed algorithm 
covers a wider area of the search space. The generation 
 
Figure 5: Solution of IEEE 30 bus system for load 
demand of 200 MW. 
Load 
(MW) 
Algorithm MODE-
RDC 
Wins 
MODE-
RDC 
Losses 
Detected 
differences 
200 NSGA-II 25 0 0.05 
MOPSO 13 12 - 
259 NSGA-II 25 0 0.05 
MOPSO 13 12 - 
300 NSGA-II 25 0 0.05 
MOPSO 13 12 - 
Table 9: Result of sign test on MODE-RDC algorithm 
for IEEE 14 bus system with ∆ metric as winning 
parameter. 
No. of 
algorithm runs 
α = 0.05 α = 0.1 
5 5 5 
6 6 6 
7 7 6 
8 7 7 
9 8 7 
10 9 8 
11 9 9 
12 10 9 
13 10 10 
14 11 10 
15 12 11 
16 12 12 
17 13 12 
18 13 13 
19 14 13 
20 15 14 
21 15 14 
22 16 15 
23 17 16 
24 18 16 
25 18 17 
Table 10: Significant values for decision on two-tailed 
sign test. 
 
Algorithm NSGA-II MOPSO MODE-RDC 
PG1 (MW) 103.927 104.4705 100.8991 
PG2 (MW) 37.512 37.7012 41.8153 
PG3 (MW) 18.996 19.3131 19.4211 
PG4 (MW) 18.718 16.8090 14.9330 
PG5 (MW) 13.021 12.7445 14.9143 
PG6 (MW) 12.000 12.9950 12.0000 
Time (sec) 90.8698 1.5908 8.0285 
PL (MW) 4.1740 4.0333 3.9828 
Fuel Cost 
($/hour) 
524.966 523.9469 523.7250 
Emission 
(lb/hour) 
244.007 244.0324 244.9227 
Table 11: Results of EED of IEEE 30 bus system for a 
load demand of 200 MW. 
Algorithm NSGA-II MOPSO MODE-
RDC 
Generation 
Distance 
(GD) 
Minimum 0.018414 0.0457 0.013645 
Maximum 0.088774 0.0457 0.094384 
Average 0.034309 0.0457 0.032455 
Standard 
Deviation 
0.015609 0.0000 0.009311 
Spacing 
(S) 
Minimum 0.159507 0.2623 0.156047 
Maximum 0.870246 0.2623 0.807493 
Average 0.304470 0.2623 0.255573 
Standard 
Deviation 
0.157360 0.0000 0.099082 
Diversity 
(Δ) 
Minimum 0.975386 0.5672 0.547595 
Maximum 1.575610 0.5672 0.853479 
Average 1.223858 0.5672 0.558198 
Standard 
Deviation 
0.173773 0.0000 0.052061 
Table 12: Performance of algorithms for IEEE 30 bus 
system at load demand of 200 MW. 
Algorithm NSGA-II MOPSO MODE-
RDC 
PG1 (MW) 132.672 134.7225 111.077 
PG2 (MW) 53.443 50.2415 51.679 
PG3 (MW) 27.719 27.0213 31.856 
PG4 (MW) 29.870 31.4431 33.083 
PG5 (MW) 25.102 23.0641 30.000 
PG6 (MW) 21.916 24.2446 31.969 
Time (sec) 94.5415 2.0302 8.003 
PL (MW) 7.32 7.3371 6.264 
Fuel Cost 
($/hour) 
821.269 820.1034 822.0048 
Emission 
(lb/hour) 
380.213 380.7899 379.5462 
Table 13: Results of EED of IEEE 30 bus system for a 
load demand of 283.4 MW. 
 
 

Performance Assessment of a Set of Multi-Objective ... Informatica 44 (2020) 349–360 357 
 
 
schedule for an acceptable emission level is achieved, 
and is presented in Table 11. 
The quality of solutions is assessed by evaluating all 
the three performance metrics, and is presented in Table 
12. The cost of fuel obtained by employing the proposed 
algorithm is lower, and the corresponding schedule 
causes lower transmission loss. It surpasses the 
performance of NSGA-II in terms of computational time. 
The lower average values of all the three performance 
matrices imply superior performance of the proposed 
algorithm over other two. 
6.2.2 IEEE-30 bus system: load demand 283.4 
MW 
The test case is subjected to the rated load of 283.4 MW, 
and performance of the algorithms is assessed. The 
Pareto fronts obtained for this demand are presented in 
Figure 6. 
The Pareto curve corresponding to the proposed 
algorithm covers a wide area of the search space. The 
generation schedules obtained by applying the algorithms 
are shown in Table 13. The proposed algorithm yields 
lower values of fuel cost and emission. The transmission 
losses involved with this schedule is less than the other 
two algorithms. The quality of solutions is assessed by 
running the algorithms for 25 times; statistical values of 
the performance metrics thus obtained are presented in 
Table 14. The average diversity of the solutions using the 
proposed algorithm is less than that of the other two 
algorithms. It also requires less computational time as 
compared to the NSGA-II. 
6.2.3 IEEE-30 bus system: load demand 350 
MW 
The test case is further subjected to a higher load of 350 
MW, and performance of the algorithms is assessed. The 
Pareto optimal fronts are shown in Figure 7. The 
generating schedule for the system obtained for this 
demand is presented in Table 15. 
The statistical behavior of the performance metrics 
obtained for the solutions are shown in Table 16. It is 
observed that the proposed algorithm performs better 
than NSGA-II in terms of diversity of solutions, 
computational time, fuel cost and emission values. 
 
Figure 6: Solution of IEEE 30 bus system for load 
demand of 283.4 MW. 
Algorithm NSGA-II MOPSO MODE-
RDC 
Generation 
Distance 
(GD) 
Minimum 0.054373 0.1407 0.021384 
Maximum 0.116501 0.1407 0.233931 
Average 0.077291 0.1407 0.065103 
Standard 
Deviation 
0.017481 0.0000 0.029863 
Spacing 
(S) 
Minimum 0.383454 0.9516 0.339348 
Maximum 1.026579 0.9516 2.075391 
Average 0.621816 0.9516 0.621204 
Standard 
Deviation 
0.189580 0.0000 0.360044 
Diversity 
(Δ) 
Minimum 0.603026 0.6719 0.563586 
Maximum 1.229024 0.6719 0.767057 
Average 0.968746 0.6719 0.670803 
Standard 
Deviation 
0.163341 0.0000 0.066364 
Table 14: Performance of algorithms for IEEE 30 
bus system at load demand of 283.4 MW. 
Algorithm NSGA-II MOPSO MODE-RDC 
PG1 (MW) 159.003 163.500 162.974 
PG2 (MW) 68.918 66.800 65.864 
PG3 (MW) 46.060 32.600 36.256 
PG4 (MW) 25.070 35.000 33.083 
PG5 (MW) 30.000 30.000 27.768 
PG6 (MW) 31.711 33.300 33.351 
Time (sec) 89.7484 3.3319 8.03545 
PL (MW) 10.762 11.200 10.970 
Fuel Cost 
($/hour) 
1111.24 1082.10 1081.3329 
Emission 
(lb/hour) 
540.295 
 
539.90 539.1846 
Table 15: Results of EED of IEEE 30 bus system for 
load demand of 350 MW. 
Algorithm NSGA-
II 
MOPSO MODE-
RDC 
Generation 
Distance 
(GD) 
Minimum 0.064384 0.1329 0.056721 
Maximum 0.162268 0.1329 0.391057 
Average 0.094781 0.1329 0.093724 
Standard 
deviation 
0.025093 0.0000 0.056003 
Spacing 
(S) 
Minimum 0.474948 0.7443 0.403432 
Maximum 1.483643 0.7443 3.664206 
Average 0.789943 0.7443 0.741615 
Standard 
Deviation 
0.255086 0.0000 0.609410 
Diversity 
(Δ) 
Minimum 0.807397 0.5516 0.509509 
Maximum 1.353364 0.5516 0.958338 
Average 1.095059 0.5516 0.531211 
Standard 
deviation 
0.136457 0.0000 0.069968 
Table 16: Performance of algorithms for IEEE 30 bus 
system at load demand of 350 MW. 
Load 
(MW) 
Algorithm MODE-
RDC 
Wins 
MODE-
RDC 
Losses 
Detected 
differences 
200 NSGA-II 14 11 - 
MOPSO 13 12 - 
283.4 NSGA-II 13 12 - 
MOPSO 15 10 - 
350 NSGA-II 13 12 - 
MOPSO 13 12 - 
Table 17: Result of sign test on MODE-RDC algorithm 
on IEEE 30 bus system with GD metric as winning 
parameter. 

358 Informatica 44 (2020) 349–360 S.K. Mishra et al. 
 
 
6.2.4 IEEE-30 bus system: summary of results 
The summary of results for this test case with the three 
load demands by applying all the three algorithms is 
presented in Tables 11, 13 and 15. It shows that the fuel 
cost obtained using the proposed algorithm provides 
improved performance as compared to other two 
algorithms. The transmission loss involved with the 
generation schedule thus arrived is also lower. The 
quality of solutions arrived using the algorithms is 
further estimated from pair wise sign test [21] on 25 runs 
of the algorithms. The results are presented in Tables 17, 
18 and 19. Based on the number of wins and losses it is 
observed from Tables 17, 18 and 19 that the solutions 
obtained by applying the proposed algorithm yield lower 
average values in terms of all the three performance 
metrics. So, these solutions can be considered to be better 
than those from the other two algorithms. Also, the 
proposed MODE-RDC algorithm does not perform very 
well in terms of GD and S metric as in case of IEEE 30 
bus system for load demand of 350 MW as depicted in 
Tables 17 and 18. This is clear in these tables as it does 
not have a significant detected difference that needs at 
least 17 wins out of 25 runs. This is due to the reduction 
in the number of non-dominated solutions in the 
successive iterations in the proposed algorithm. 
Here, it can be pointed out that in most cases the 
average value of S metric has increased with rise in load 
demand for all the three algorithms this can be verified 
from Tables 2, 4 and 6 for test case I and Tables 12, 14 
and 16 for test case II. This is due to the fact that when 
the load demand on the system rises, the size of the 
feasible space decreases due to the generator limits. The 
situation is further limited by the power balance 
constraint as the transmission losses increase with 
increase in power generation. Thus, the feasible solutions 
fall apart causing increase in the spacing parameter. 
7 Conclusion 
A set of three multi-objective optimization algorithms 
have been applied to solve the EED problem for two test 
cases on three different load demands. The performance 
of the proposed MODE-RDC algorithm along with other 
two is assessed by considering three different 
performance metrics. The performances of these 
algorithms have been critically analyzed. The Pareto 
optimal fronts obtained by all the three algorithms 
incorporating the proposed recursive distributed 
constraint handling technique have sufficient diversity by 
exploiting the entire available range of search space. In 
particular, the Pareto front obtained by the multi-
objective differential evolution with the recursive 
distributed constraint handling (MODE-RDC) approach 
has a better diversity in most cases. The spacing between 
the Pareto solutions has found to be increased with rise in 
the load demand on the system for all the three 
 
Figure 1: Solution of IEEE 30 bus system for load 
demand of 350 MW. 
Load 
(MW) 
Algorithm MODE-
RDC 
Wins 
MODE-
RDC 
Losses 
Detected 
differences 
200 NSGA-II 16 9 - 
MOPSO 13 12 - 
283.4 NSGA-II 14 11 - 
MOPSO 16 9 - 
350 NSGA-II 13 12 - 
MOPSO 13 12 - 
Table 18: Result of sign test on MODE-RDC algorithm 
for IEEE 30 bus system with S metric as winning 
parameter. 
Load 
(MW) 
Algorithm MODE-
RDC 
Wins 
MODE-
RDC 
Losses 
Detected 
differences 
200 NSGA-II 15 10 0.05 
MOPSO 13 12 - 
283.4 NSGA-II 14 11 0.05 
MOPSO 13 12 - 
350 NSGA-II 23 2 0.05 
MOPSO 12 13 - 
Table 19: Result of sign test on MODE-RDC 
algorithm for IEEE 30 bus system with Δ metric as 
winning parameter. 
Gen no 1 2 3 4 5 
Max MW 250 140 100 120 45 
Min MW 10 20 15 10 10 
γ 0.0126 0.02 0.027 0.0291 0.029 
β -0.9 -0.1 -0.01 -0.005 -0.004 
α 22.983 25.313 25.505 24.9 24.7 
a 0.00375 0.0175 0.0625 0.00834 0.025 
b 2.0 1.75 1.0 3.25 3.0 
c 0 0 0 0 0 
Table 20: IEEE 14 bus system cost and emission 
coefficients. 
Gen 
no 
1 2 3 4 5 6 
Max 
MW 
200 80 50 35 30 40 
Min 
MW 
50 20 15 10 10 12 
γ 0.0126 0.02 0.027 0.0291 0.029 0.0271 
β -0.9 -0.1 -0.01 -0.005 -
0.0004 
-
0.0055 
α 22.983 25.313 25.505 24.9 24.7 25.3 
a 0.00375 0.0175 0.0625 0.00834 0.025 0.025 
b 2.0 1.7 1.0 3.25 3.0 3.0 
c 0 0 0 0 0 0 
Table 21: IEEE 30 bus system cost and emission 
coefficients. 

Performance Assessment of a Set of Multi-Objective ... Informatica 44 (2020) 349–360 359 
 
 
algorithms. Moreover, the time requirement to achieve 
the Pareto front by applying the proposed recursive 
distributed constraint handling based technique is 
satisfactory.  
Further research on this topic may include the 
inclusion of different evolutionary local search 
mechanisms into the approaches. It is expected to obtain 
lower computational speed and exploitation of the multi-
dimensional search space. There is a need for further 
investigation to explore the strengths and weaknesses of 
the proposed algorithm, so that it can be applied to other 
multi-objective problems in power systems, such as 
management of voltage profiles, reactive power 
compensation etc. The performance of the proposed 
algorithm can also be investigated by considering other 
real world constraints like ramp rate limits, power loss 
etc. 
Appendix 
The standard test cases taken for the solution are IEEE 
14 bus and IEEE 30 bus power systems. The parameters 
of the test cases have been adopted from standard 
sources. The cost and emission coefficients used for 
solution of the problem are shown in tables 20 and 21 
below. 
The values of B coefficients used for the IEEE 14 
bus test case are 
B= 
[
 
 
 
 
0.0208  0.0090 -0.0021  0.0024  0.0006
0.0090  0.0168 -0.0028  0.0035  0.0000
-0.0021 -0.0028  0.0207 -0.0152 -0.0179
0.0024  0.0035 -0.0152  0.0763 -0.0103
0.0006  0.0000 -0.0179 -0.0103  0.0476
]
 
 
 
 
 
B0= [-0.0001  0.0023 -0.0012  0.0027  0.0011] 
B00=3.1826×10
-4
 
The values of B coefficients used for the IEEE 30 bus 
test case are 
B=
[
 
 
 
 
 
0.0218  0.0103  0.0010 -0.0025  0.0007  0.0033
0.0103  0.0233  0.0001 -0.0043  0.0009  0.0032
0.0010  0.0001  0.0525 -0.0380 -0.0111 -0.0066
-0.0025-0.0043 -0.0380 -0.1011  0.0132  0.0045
0.0007  0.0009 -0.0111  0.0132  0.0163 -0.0001
0.0033  0.0032 -0.0066  0.0045 -0.0001  0.0270
]
 
 
 
 
 
 
B0=[-0.0002 0.0029 -0.0033 0.0035 0.00016 0.0048] 
B00=0.0025 
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