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Teaching-Learning-Based Optimization Algorithm 
for the Combined Dynamic Economic Environmental 

Dispatch Problem  

Badr M. Alshammari 

College of Engineering 
University of Ha’il 
Ha’il, Saudi Arabia 

 

 

Abstract-The Dynamic Economic Environmental Dispatch 

Problem (DEEDP) is a major issue in power system control. It 

aims to find the optimum schedule of the power output of 

thermal units in order to meet the required load at the lowest cost 

and emission of harmful gases. Several constraints, such as 

generation limits, valve point loading effects, prohibited 

operating zones, and ramp rate limits, can be considered. In this 

paper, a method based on Teaching-Learning-Based 

Optimization (TLBO) is proposed for dealing with the DEEDP 
problem where all aforementioned constraints are considered. To 

investigate the effectiveness of the proposed method for solving 

this discontinuous and nonlinear problem, the ten-unit system 

under four cases is used. The obtained results are compared with 

those obtained by other metaheuristic techniques. The 

comparison of the simulation results shows that the proposed 
technique has good performance. 

Keywords-dynamic economic environmental dispatch; 

teaching-learning-based optimization; prohibited operating zones; 

ramp rate limits 

I. INTRODUCTION  

With the growing demand for electricity and rising fuel 
prices, electricity companies are constantly working to ensure 
continuous and reliable electrical power supply to their 
customers. In order to achieve this, system operators need to 
constantly adjust the control variables of power networks. This 
extremely difficult task is performed by the resolution of the 
Economic Dispatch Problem (EDP), which aims to determine 
the production levels of all thermal units which guarantee a 
balance between production and consumption at the lowest 
cost. Unfortunately, today network loads are dynamic, which 
means that it is required to plan the generation of units in real 
time to guarantee continuous power balance. The resolution of 
such Dynamic EDP problems (DEDP), considers the 
constraints imposed by generator Ramp-Rate Limits (RRL). 
Along with DEDP, the emission dispatch problem, which aims 
to minimize the emissions of fossil fuels, has emerged. The 
combination of the two problems in one single problem called 
Dynamic Economic Environmental Dispatch Problem 
(DEEDP) has become attractive. DEEDP aims to minimize 
simultaneously the total production cost and the emission of 
harmful gases. Thus, it can be considered as a multi-objective 
problem with conflicting objective functions [1]. In the past, 

several operating constraints have been taken into account in 
the DEEDP mathematical formulation, such as power balance 
constraint, Valve-Point Loading Effects (VPLE), Prohibited 
Operating Zones (POZ), and RRLs. During the past decades, 
several techniques have been proposed to solve this kind of 
problems, including linear programming [2], dynamic 
programming [3], and gradient algorithms [4]. Unfortunately, 
in these techniques, the cost function has been approximated by 
quadratic functions and VPLEs have been ignored in the 
problem formulation. This frequently leads to inexactitude of 
the optimal solutions. Moreover, those techniques may be 
trapped in local optima due to the non-convex and nonlinear 
characteristics of the cost function. In recent years, various 
meta-heuristic techniques have been suggested in the literature 
to overcome the limitations of the traditional methods.  

In [1], a differential evolution-based technique has been 
used to solve the DEEDP where a fuzzy-based method has 
been employed to extract the optimal solution. Authors in [5] 
utilized the artificial bee colony algorithm to solve the EDP 
with VPLEs. Unfortunately, the environmental impact of 
thermal units has not been considered. Particle swarm 
optimization (PSO) has also been used to solve power dispatch 
problems [6-8]. Basu [9] has solved the DEEDP by applying 
the second version of the Non-dominated Sorting Genetic 
Algorithm (NSGAII) proving that such technique may provide 
promising results. Another technique based on NGSAII has 
been developed in [10] to handle the DEEDP incorporating 
POZ constraints. An optimization method based on Simulated 
Annealing (SA) algorithm has been implemented in [11] in this 
regard, the cost function has been approximated by a cubic 
function and the problem has been converted into mono-
objective problem by using price penalty factors. Within this 
context, other metaheuristic techniques, such as Gravitational 
Search Algorithm (GSA) [12], Biogeography-Based 
Optimization (BBO) [13], Bacterial Foraging Algorithm (BFA) 
[14], and Harmony Search (HS) algorithm [15] have been 
developed and implemented for various complex dispatch 
problems. The main advantage of the aforementioned 
techniques is that they expand the entire search space for the 
optimal solution to avoid getting trapped in a local optimal. In 
addition, these techniques are not concerned with the nature 
and the shape of the objective functions. However, the 

Corresponding author: Badr M. Alshammari 



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www.etasr.com Alshammari: Teaching-Learning-Based Optimization Algorithm for the Combined Dynamic Economic … 

 

convergence of most of these techniques depends on their 
parameters and their computational time is quite large. 

The Teaching-Learning-Based Optimization (TLBO) 
algorithm [16] is a powerful algorithm which can provide 
promising results in single objective and multi-objective 
optimization. It is a population algorithm inspired from the 
teacher/learner relationship. The TLBO algorithm is based on 
two basic methods of learning: (i) through the teacher, known 
as the teacher phase, and (ii) through interaction with other 
students, called student phase. In this optimization algorithm, a 
group of students is considered as a population and the 
different subjects offered to the students are considered to be 
the feasible solutions and a student's result is considered to be 
the value of the fitness function [16]. The best solution in the 
whole population, which corresponds to the best value of the 
objective function, is assigned to the teacher. It has been shown 
that TLBO has the advantage of only requiring a few control 
parameters, such as the number of students in the class and the 
number of subjects presented for students, for its operation [17, 
18]. 

In this regard, a TLBO-based method is proposed for 
dealing with the problem of DEEDP. In the DEEDP 
formulation all operating constraints, such as generation limits, 
energy balance, VPLEs, RRLs, and POZ constraints are 
considered. To render the problem more practical, total real 
power losses are taken into account. To assess the effectiveness 
of the proposed optimization method, a ten-unit system is 
employed. The simulation results obtained by the proposed 
method are compared with other metaheuristic techniques.   

II. MATHEMATICAL FORMULATION OF THE DEEDP 

The DEEDP is a principal problem in power network 
operation. It aims to determine the optimum allocation of 
power outputs of all thermal units to minimize simultaneously 
the total fuel cost and total emission according to the predicted 
load demands, over entire dispatch periods generally of one 
hour. Taking VPLEs into account, the total fuel cost can be 
expressed by: 

( ) ( ){ }
2

min

1 1

sin
T N

t t t

T i i i i i i i i i

t i

C a b P c P d e P P
= =

= + + + −∑∑     (1) 

where , , ,  and  are the cost coefficients of unit i, 

t
iP  is the output power in MW of unit i at time t, T is the 

number of hours, and N is the number of units. 

The second objective function considered in this study, 
which is the total emission of harmful gases, is described as: 

( ) ( )
2

1 1

exp
T N

t t t

T i i i i i i i i

t i

E P P Pα β γ η λ
= =

= + + +∑∑     (2) 

where , , ,  and  are the emission coefficients. 

In this work, the two objective functions are combined in a 
single objective function by integrating the price penalty factor. 
The combined function is: 

( )1T T TF C Eδ δ λ= + −     (3) 

where ( )0,1randδ =  and λ  is the average of the price 
penalty factors of all units. The price penalty factor for unit i 
can be determined as: 

max

max

i
i

i

C

E
λ =     (4) 

where max
iC  and 

max
iE  are the maximum fuel cost and the 

maximum emission of unit i respectively. 

In order to find the optimal Pareto solutions, the objective 
function FT is minimized for various values of δ subject to the 
constraints (5)-(9). Equation (5) describes the power balance 

constraint where the real power losses 
t
LP  at time t are 

calculated by (10) [19]. As given in (6), the output power of 

each generator i should be within its lower 
min
iP  and upper 

max
iP limits. The RRLs of the thermal units are shown in (7) 

and (8) while POZs constraints are given in (9).  

1

0, 1,...,

N
t t t
i D L

i

P P P t T

=

− − = =∑
  

  (5) 

where, 
t
DP  is the load at time t.  

    (6) 

1t t down
i i iP P R
− − ≤

    
(7) 

1 upt t
i i iP P R

−− ≤
    
(8) 

where 
down
iR  and 

up
iR  are the down-ramp and up-ramp limits 

of unit i. 

min
,1

,, 1

max
,

, 2,...,

i

t down
i i i

upt t down
i i i k ii k

up t
i ii z

P P P

P P P P k z

P P P

−

 ≤ ≤



∈ ≤ ≤ =

 ≤ ≤
     

(9) 

where ,
down
i kP  and ,

up
i k

P  are the down and up bounds of POZ 

number k and iz  is the number of POZ for unit i. 

1 1 1

N N N
t t t t
L i ij j oi i oo

i j i

P P B P B P B

= = =

= + +∑∑ ∑
    

(10) 

where, , ,  are the loss coefficients of B-loss matrix. 

III. THE TLBO ALGORITHM 

TLBO algorithm, developed in [16], is a population-based 
optimization algorithm that mimics the teaching and learning 
phenomenon in a class. It is inspired by the transmission of 
knowledge from teacher to students and the mutual interaction 
between classmates. In TLBO algorithm, students in a class 

ia ib ic id ie

iα iβ iγ iη iλ

min max
, 1,...,≤ ≤ =ti i iP P P i N

ijB oiB ooB



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www.etasr.com Alshammari: Teaching-Learning-Based Optimization Algorithm for the Combined Dynamic Economic … 

 

constitute the population and a student is considered as a 
feasible solution for the optimization problem. Subjects offered 
to students constitute the decision variables and student’s result 
is the fitness function evaluated at the feasible solution. TLBO 
method is divided into two phases which are teacher phase and 
student phase. 

A. Teacher Phase 

In this phase, the teacher is the main interfering where his 
job is to improve the knowledge level of learners (students) and 
helps them to get high grades. However, grades or marks of 
students depend on teaching quality and student’s quality. For 
simulation, consider there are ‘n’ subjects offered to Npop 
students. Therefore, variable ‘n’ is equivalent to the number of 
problem design variables and Npop is the population, in TLBO 

algorithm. Let 
k
jM  be the mean result of learners in a 

particular subject j where { }1,2, ,j m∈ … , at the k-th teaching-

learning cycle ( { }max0,1,2, ,k I∈ … ). Since the teacher is the 
most highly learned and experienced person in the class, thus, 
he is considered the best learner in the entire population or 

class. Let 
*k

X  be the best solution in the entire population at 
the k-th iteration. The difference between the teacher’s results 
and the mean result of students in the j-th subject is calculated 
as [18]: 

( )*k k kj j F jD r X T M= −     (11) 
where [ ]0,1r ∈ is a random number. TF is the teaching factor 
that is selected randomly from { }1,2 . It is used to choose 
which value of mean should be changed. 

At the k-th teaching-learning cycle, the i-th feasible solution 
is updated according to the following expression. 

, ,
k k k
ij new ij old jX X D= +

    
(12) 

If ,
k
ij newX  gives better results compared to ,

k
ij oldX , it is 

accepted, otherwise, it is rejected. All accepted solutions will 
be used as input for the student phase. 

B. Student Phase 

In this phase, students acquire knowledge through mutual 
interaction. The learning phenomenon is simulated as follows. 

Two feasible solutions, 
k
uX  and 

k
vX  withu v≠ , are randomly 

selected from the population. If 
k
uX  is better than 

k
vX , then 

update 
k
vX  as given in (14) otherwise update 

k
uX  as given in 

(13). If the new solution is better than the old solution, then, the 
new solution will be accepted in the population and the old 
solution will be rejected, otherwise the new solution will be 
rejected and old solution will be kept in the population.   

( ),k k k kuj new uj uj vjX X r X X= + −     (13) 

( ),k k k kvj new vj vj ujX X r X X= + −     (14) 
The TLBO algorithm’s steps are shown in Figure 1. 

 

 
Fig. 1.  Steps of the TLBO algorithm. 

IV. TLBO ALGORITHM IMPLEMENTATION FOR THE DEEDP 

To verify the effectiveness of the proposed method in 
solving the DEEDP, numerical experiments are carried out 
employing the ten unit system. The TLBO algorithm was 
firstly applied for static economic emission dispatch for total 
demand power of PD=2000MW, and then for the dynamic case. 
All system data are taken from [20]. In this paper, TLBO and 
PSO algorithms are implemented in Matlab R2018B on a PC 
intel(R) Core i7, 1.5GHz, 64 bits. Population size and 
maximum number of iterations are both 200. The B-loss matrix 
of the studied system is shown in (15). 

0.49 0.14 0.15 0.15 0.16 0.17 0.17 0.18 0.19 0.20

0.14 0.45 0.16 0.16 0.17 0.15 0.15 0.16 0.18 0.18

0.15 0.16 0.39 0.10 0.12 0.12 0.14 0.14 0.16 0.16

0.15 0.16 0.10 0.40 0.14 0.10 0.11 0.12 0.14 0.15

0.16 0.17 0.12 0.14 0.35 0.11 0.13 0.13 0.
10
4

B = −
15 0.16

0.17 0.15 0.12 0.10 0.11 0.36 0.12 0.12 0.14 0.15

0.17 0.15 0.14 0.11 0.13 0.12 0.38 0.16 0.16 0.18

0.18 0.16 0.14 0.12 0.13 0.12 0.16 0.40 0.15 0.16

0.19 0.18 0.16 0.14 0.15 0.14 0.16 0.15 0.42 0.19

0.20 0.18 0.16 0.15 0.16 0.15 0.18 0.16 0.19 0.44

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

(15)

 

 

A. Static Dispatch 

The convergence of the objective functions for the 
proposed algorithm and PSO is shown in Figure 2. It can be 
seen that TLBO provides cheaper electricity production and 
lowest emission compared to PSO. In fact, the minimum cost 



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and emissions are 132968.93$/h and 18832.63ton/h 
respectively for the TLBO algorithm and 133088.62$/h and 
19054.12ton/h respectively for the PSO algorithm. The Pareto 
front generated by the proposed algorithm is shown in Figure 3. 
It is clear that that the Pareto solutions are uniformly 
distributed in the objective space. Moreover, Figure 3 shows 
that cost and emissions are conflicting functions.  

 

(a) 

 

(b) 

 

Fig. 2.  Convergence of objective functions for PD=2000MW: (a) cost, (b) 
emission. 

 

Fig. 3.  Pareto solutions for PD=2000MW. 

B. Dynamic Dispatch 

Pure dynamic economic dispatch and pure dynamic 
environmental dispatch are solved separately. Then, they are 
dynamically combined for economic environmental dispatch. 
Table I shows the optimal variation of the generation for 
dynamic economic dispatch, according to the daily variation 

of the load (
t
DP ). It is clear that the optimal output powers of 

all units are within their limits. The minimum production cost 
is 2472116.66$ while the corresponding emission is at its 
maximum value which is 330411.81ton. The optimum 
schedule of all system units for the dynamic emission dispatch 
is depicted in Table II. It can also be seen that output powers of 
all units are within their limits. The minimum emission is 
294153.04ton while the total cost is at its maximum value 
which is 2594148.32$. 

 

TABLE I.  DYNAMIC ECONOMIC DISPATCH 

Hour  P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 

1 1036 150.1259 135.5687 73.0000 117.0485 175.4140 126.8733 130.0000 117.5441 20.0000 10.0000 

2 1110 150.0664 135.0000 73.0000 108.9781 225.4140 160.0000 130.0000 120.0000 20.0000 10.0000 

3 1258 150.2382 135.0000 153.0000 125.7599 223.8123 159.6342 129.5876 119.8081 49.7545 39.8977 

4 1406 150.5704 135.0000 206.7431 175.7599 243.0000 159.0079 129.5631 119.0141 79.6457 43.2159 

5 1480 150.5888 135.0000 255.5104 225.7599 221.4589 156.7358 130.0000 119.9033 78.9610 45.4764 

6 1628 150.2503 135.0000 335.5104 275.7599 243.0000 159.7044 129.6031 119.9085 79.8822 47.4658 

7 1702 150.1468 198.5926 331.5975 300.0000 241.5421 160.0000 130.0000 119.9352 79.8647 43.3868 

8 1776 210.1460 213.1343 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 38.2598 

9 1924 273.4194 293.1343 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 

10 2022 300.4154 373.1343 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 

11 2106 315.4490 453.1343 337.4498 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 

12 2150 344.5307 470.0000 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 

13 2072 331.2602 397.3814 340.0000 300.0000 242.9249 159.9539 130.0000 119.9397 79.9670 55.0000 

14 1924 251.3135 317.3814 338.7426 300.0000 242.6070 159.6948 129.9303 120.0000 79.9776 54.9429 

15 1776 171.7944 237.3814 339.7179 300.0000 242.9101 159.5908 129.9045 118.7763 79.9693 54.4079 

16 1554 150.0967 157.3814 296.4912 250.7445 238.3715 159.4043 129.3618 119.6965 53.0343 43.1300 

17 1480 150.9007 135.0000 240.7998 242.3687 242.1751 159.6100 129.7144 119.7307 55.0000 44.0521 

18 1628 150.3632 174.5376 300.0000 292.3687 242.2373 159.9336 129.4308 119.2750 54.7366 53.3392 

19 1776 217.4110 254.5376 300.0000 300.0000 243.0000 160.0000 130.0000 120.0000 55.0000 55.0000 

20 1972 284.3186 334.5376 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 

21 1924 259.9202 309.6601 340.0000 300.0000 243.0000 159.2709 129.8075 119.9798 79.9277 53.0288 

22 1628 180.1857 229.9838 291.1958 250.6165 223.4006 159.4022 126.6683 120.0000 51.6945 43.7541 

23 1332 150.2720 150.0578 211.4456 201.6378 174.2186 160.0000 130.0000 90.0000 52.0055 44.2729 

24 1184 150.5086 135.0000 131.4456 167.0485 175.3310 110.0000 130.0000 120.0000 50.0000 40.0000 

Cost ($) 2472116.66 

Emission 

(ton) 
330411.81 

C
o
st
 (
$
/h
)

E
m
is
si
o
n
 (
to
n
/h
)

E
m
is
si
o
n
 (
to
n
/h
)

t
DP



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TABLE II.  DYNAMIC EMISSION DISPATCH 

Hour 
 

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 

1 1036 150.3364 135.2479 88.8628 91.5246 133.1490 133.2677 96.0287 92.6589 79.7478 54.8723 

2 1110 150.4649 138.1099 101.9172 99.8572 143.6597 143.8590 105.5614 114.0802 79.9698 55.0000 

3 1258 164.2919 166.1639 117.3305 121.6243 172.9143 159.9093 129.7196 120.0000 80.0000 54.9823 

4 1406 199.0112 203.9786 147.0126 144.0633 204.0232 159.7183 129.9286 119.9410 79.9646 55.0000 

5 1480 216.9388 219.6330 157.4592 163.6519 218.2469 160.0000 129.9633 120.0000 79.9462 55.0000 

6 1628 253.4935 255.9774 190.1283 190.7046 242.9276 159.9049 129.9803 119.9825 80.0000 55.0000 

7 1702 275.2332 273.7700 209.7002 210.7657 242.8287 160.0000 129.9338 120.0000 79.9196 54.9987 

8 1776 291.1351 295.7189 229.4559 232.4257 242.9839 159.8865 130.0000 120.0000 80.0000 54.8400 

9 1924 324.3152 326.1564 277.5305 279.7439 243.0000 160.0000 129.9974 119.9869 79.9975 54.9994 

10 2022 348.6556 349.0595 321.7455 294.5092 243.0000 160.0000 130.0000 119.9751 80.0000 55.0000 

11 2106 383.1823 382.7515 339.9697 299.9955 243.0000 160.0000 130.0000 120.0000 80.0000 54.9992 

12 2150 397.8457 425.6329 340.0000 300.0000 241.7596 152.4816 130.0000 120.0000 80.0000 55.0000 

13 2072 364.1944 364.2761 339.9983 299.9967 243.0000 159.9968 130.0000 120.0000 79.9960 55.0000 

14 1924 327.2057 322.9324 278.8479 278.7852 243.0000 159.9789 130.0000 120.0000 79.9829 55.0000 

15 1776 292.5619 292.8412 230.3221 233.2478 242.7153 159.8868 129.8985 119.9561 80.0000 55.0000 

16 1554 234.6654 237.5412 181.0347 183.2478 243.0000 160.0000 129.7930 120.0000 55.0000 55.0000 

17 1480 224.4285 225.2253 162.6887 164.5307 224.1457 160.0000 129.9327 120.0000 54.9989 55.0000 

18 1628 262.2682 260.2198 197.1840 196.3723 242.4237 159.9493 129.8766 119.9320 55.0000 55.0000 

19 1776 298.9110 296.1538 240.5298 238.0002 243.0000 159.9865 129.9697 120.0000 54.9945 55.0000 

20 1972 337.0679 337.4869 297.2509 287.9121 242.9982 159.9977 129.9953 119.9968 79.9966 54.9965 

21 1924 328.1016 326.5158 278.6325 274.7016 243.0000 159.9165 130.0000 119.9709 79.9725 54.9936 

22 1628 248.1062 246.5158 198.6325 224.7016 215.3974 159.6594 130.0000 119.9354 79.8864 55.0000 

23 1332 176.4330 166.5158 127.4188 174.7016 174.6863 160.0000 129.7901 119.8400 80.0000 54.9865 

24 1184 154.0152 155.7069 100.8685 124.7016 168.9035 152.3155 107.1434 110.9206 80.0000 55.0000 

Cost ($) 2594148.32 

Emission 

(ton) 
294153.04 

TABLE III.  COMBINED ECONOMIC EMISSION DISPATCH 

Hour 
 

P1 P2 P3 P4 P5 P6 P7 P8 P9 P10 

1 1036 150.4594 135.3072 80.0281 120.0864 126.2070 124.4066 129.6379 86.1200 59.2616 44.0814 

2 1110 150.0709 135.0000 81.2516 102.8341 167.8358 125.3782 129.3292 116.1200 79.9973 44.7038 

3 1258 150.4932 135.0161 138.7766 129.6167 188.9086 160.0000 129.2388 120.0000 79.7994 54.6856 

4 1406 154.9053 161.9512 177.1730 179.6167 223.7618 159.9893 129.7067 119.9437 79.9075 54.7681 

5 1480 152.9466 217.8705 186.4596 185.1000 236.2579 159.5941 130.0000 119.8567 79.8784 52.1092 

6 1628 213.1264 236.4829 260.3624 203.1865 243.0000 136.3359 130.0000 120.0000 80.0000 55.0000 

7 1702 227.8217 221.6160 271.7060 246.9217 243.0000 160.0000 129.8277 120.0000 79.9719 55.0000 

8 1776 228.2304 242.9587 290.8592 286.3618 242.9531 159.9532 130.0000 119.4716 79.8240 54.3041 

9 1924 293.0721 293.5529 340.0000 280.7385 243.0000 160.0000 130.0000 120.0000 80.0000 54.5004 

10 2022 306.2281 368.3049 340.0000 300.0000 243.0000 160.0000 129.8569 120.0000 80.0000 54.1663 

11 2106 376.6213 389.3073 339.9899 299.9805 242.9987 159.9980 129.9979 119.9977 79.9869 54.9993 

12 2150 385.6214 428.8158 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 

13 2072 361.8808 397.2726 340.0000 300.0000 243.0000 160.0000 130.0000 90.0000 80.0000 55.0000 

14 1924 289.4585 317.2726 300.7884 300.0000 243.0000 159.9907 129.6966 119.8300 80.0000 55.0000 

15 1776 232.8384 281.4039 276.1673 257.2175 242.9575 159.8950 129.9781 120.0000 79.9478 55.0000 

16 1554 153.0008 218.8426 222.2456 241.2300 243.0000 159.9386 130.0000 119.8715 55.0000 55.0000 

17 1480 150.1175 217.9193 195.6985 194.4730 243.0000 159.8241 129.9954 119.9426 55.0000 54.0499 

18 1628 229.1932 233.6730 207.0696 244.4730 243.0000 160.0000 130.0000 120.0000 55.0000 55.0000 

19 1776 257.6630 290.2181 268.7446 256.2676 242.9809 159.9782 130.0000 120.0000 54.9739 54.9997 

20 1972 271.6633 347.2125 340.0000 300.0000 243.0000 160.0000 130.0000 120.0000 80.0000 55.0000 

21 1924 301.8759 308.5015 297.6986 299.7156 242.8737 159.9440 129.6663 119.8831 79.9622 54.9860 

22 1628 222.0018 228.5015 217.6986 249.7616 222.5752 159.8970 129.6350 119.9210 79.9730 47.2841 

23 1332 150.2022 148.5746 138.5624 200.3815 223.2994 159.5506 130.0000 89.9210 80.0000 43.5042 

24 1184 150.4527 135.1441 73.0000 170.0864 173.2994 127.6795 130.0000 114.8581 80.0000 55.0000 

Cost ($) 2519909.93 

Emission 

(ton) 
303338.20 

 

Table III depicts the best compromise solution obtained 
from the resolution of the combined DEEDP. Fuzzy-based 
method [9] is employed to extract the optimal best compromise 
solutions. The total cost is 2519909.93$ which is more than the 

cost obtained for the pure economic dispatch (2472116.66$) 
and less than the cost obtained for the pure environmental 
dispatch (2594148.32$). Similarly, the emission is 
303338.20ton which is less than the emission obtained for the 

t
DP

t
DP



Engineering, Technology & Applied Science Research Vol. 10, No. 6, 2020, 6432-6437 6437 
 

www.etasr.com Alshammari: Teaching-Learning-Based Optimization Algorithm for the Combined Dynamic Economic … 

 

pure economic dispatch (330411.81ton) and more than the 
emission obtained for the pure environmental dispatch. The 
comparison results shown in Table IV show that the proposed 
TLBO outperforms PSO, Improved Bacterial Foraging 
Algorithm (IBFA), and the second version of the Non-
dominated Sorting Genetic Algorithm (NSGAII) in finding the 
optimum generation schedule for the DEEDP.  

TABLE IV.  COMPARISON WITH OTHER META-HEURISTIC TECHNIQUES 

Method Minimum cost ($) Minimum emission (ton) 

TLBO 2472116.66 294153.04 

PSO 2497562.38 301539.82 

IBFA [21] 2481733.3 295833.0 

NSGAII [10] 2.5168x10
6
 3.1740x10

5 

 

V. CONCLUSION 

In this study, a new metaheuristic called Teaching-
Learning-Based Optimization (TLBO) algorithm was used for 
solving the DEEDP. The problem is described as an 
optimization problem. The decision variables of the problem 
are the output powers of units at the hours of a single day. 
Energy balance equation, generation limits, valve point loading 
effects, prohibited operating zones and ramp rate limits are 
considered as problem constraints. To assess the effectiveness 
of the proposed method, the ten-unit system is used. The TLBO 
is applied for the pure dynamic economic dispatch, the pure 
dynamic environmental dispatch and the combined dynamic 
economic environmental dispatch. The obtained results were 
compared with other techniques proposed recently in the 
literature, such as PSO, IBFA and NSGAII, and it was found 
that the proposed algorithm outperforms them. 

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