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International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
Solution of Economic Load Dispatch using Recent
Swarm-based Meta-heuristic Algorithms: A Survey
Fatma Sayed Moustafa*, N. M. Badra*, Almoataz Y. Abdelaziz**
*Department of Engineering Physics and Mathematics, Faculty of Engineering, Ain Shams University, Cairo,
Egypt
**Department of Electrical Power & Machines, Faculty of Engineering, Ain Shams University, Cairo, Egypt
Abstract- Economic load dispatch (ELD) in the operation of
electric power system is an essential task, since it is required to
determine the optimal output of electricity generating facilities,
supplying the power to meet load demand at minimum cost
while satisfying transmission and operational constraints.
Several techniques were applied to solve the economic load
dispatch problem, both conventional and intelligent methods.
Recently, researchers are paying more attention to intelligent
techniques such as Swarm- based algorithms and their
development in order to be used to successfully solve
complicated real life optimization problems. This paper
presents a survey on the novel modifications applied to swarmbased algorithms used in solving ELD problems and its
variants. Swarm optimization algorithms used in this paper
are: Ant Colony Optimization (ACO), Particle Swarm
Optimization (PSO), Bacterial Foraging Optimization
Algorithm (BFOA), Shuffled Frog Leaping Algorithm
(SFLA), Artificial Bee Colony (ABC), Firefly Algorithm (FA),
Cuckoo Search Algorithm (CSA), Bat Algorithm (BA) and
Grey Wolf Optimization (GWO).
Keywords: Economic load dispatch (ELD), Ant Colony
Optimization (ACO), Particle Swarm Optimization (PSO),
Bacterial Foraging Optimization Algorithm (BFOA), Shuffled
Frog Leaping Algorithm (SFLA), Artificial Bee Colony (ABC),
Firefly Algorithm (FA), Cuckoo Search Algorithm (CSA), Bat
Algorithm (BA) and Grey Wolf Optimization (GWO)
I. INTRODUCTION
Due to the increase in power demand and continuous
rise in fuel costs in the recent years, decreasing the cost
of operating and generating electrical power has
become a necessity.
The main objective of ELD is to meet load demand and
reduce total operating costs while satisfying operational
constraints of the generation resources available.
The variants of the ELD problem include: Combined
Heat
and
Power
Economic
Dispatch,
Emission/Environmental Economic Dispatch and
Dynamic Economic Dispatch. In practical, multiple fuel
options, valve loading effect, security constraints,
Prohibited Operating Zones and Ramp Rate Limit
Constraints should be considered in solving the ELD
problem [1, 2].
Many researchers have proposed and developed many
techniques to solve the ELD problem. Conventional
methods like Lambda iteration method and Newton’s
method are fast and reliable yet have limitations in
finding global optimum. To overcome such limitations,
intelligent meta-heuristics methods have been
developed. These state of the art algorithms could be
categorized based on their inspiration into:
1) Evolutionary
2) Swarm based
3) Physics and
chemistry based
4) Nature based
• Evolutionary Programming
• Genetic Algorithm
• Differential Evolution
• Particle Swarm Optimization
• Ant Colony Optimization
• Firefly Algorithm
• Big Bang Big Crunch
• Gravitational Search Algorithm
• Simulated Annealing
• Flower Pollination Algorithm
• Invasive Weed Optimization
Swarm Intelligence (SI), defined as “The emergent
collective intelligence of groups of simple agents” by
Bonabeau et al, [3] has drawn the attention of many
researchers in different fields. SI is based on the
mimicking of social behavior exhibited in nature such
as: foraging of bees, bird flocking, nest building,
fish schooling, hunting and microbial intelligence.
The two principles in swarm intelligence are:
1- Self-organization which is based on: activity
amplification/ balancing by positive/ negative feedback,
random fluctuations and multiple interactions.
2- Stimulation by work which is based on: work being
independent on specific individuals and division of
labor amongst individuals.
2136
Fatma et. al.,
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
Initially, SI algorithms suffered from premature
convergence and getting trapped in local optima.
However, these algorithms were continuously improved
and modified to help in solving various optimization
problems with high quality solutions, better
convergence and less computational time.
II. PROBLEM FORMULATION
The Economic Load Dispatch problem is an
optimization problem with the objective of minimizing
fuel cost which is subject of some equality and
inequality constraints.
1) Equality constraint- Energy balance equation
Where
Ng
P  P
i 1
i
D
 PL
Ng Ng
PL   Pi Bij Pj
i 1 j 1
PD= Load demand
PL= Power transmission losses
Bij= Loss coefficients (constants)
Pi, Pj = Real power injection at the ith and jth busses
2) Inequality constraint- Generating limits
Pi min  Pi  Pi max
A. Cost objective function
Ng

 Minimize F 
ai  bi Pi  ci Pi 2 $/hr
T
Where
i 1
Fт: Total Quadratic cost function; it could be also a
cubic function
Pᵢ: Real power generated
Ng: Number of generation busses
aᵢ, bᵢ, cᵢ: Fuel cost coefficients for ith unit

B. Constraints
If valve point effect is considered, the cost objective
function becomes:
Minimize
III. META-HEURISTIC ALGORITHMS
This paper outline nine SI-based algorithms and the
modifications applied to them in order to solve the
economic load dispatch problem and its variants
A. Ant Colony Optimization
Ant Colony Optimization (ACO) was proposed by
Marco Dorigo in 1992 in his Ph. D. thesis [4]. It is
inspired by the foraging behavior of ants constructing
the shortest path between their colony and food source
using pheromone trails as shown in Fig. 1.
Ng
FT   ai  bi Pi  ci Pi 2  ei * sin( f i ( Pi min  Pi )) $/hr
Wherei 1
eᵢ, fᵢ: Fuel cost coefficients for ith unit considering valve
point effects

If Combined Emission Economic Dispatch, the
problem becomes a multi-objective problem:
Min [Fт, Eт] Ng
Where E 
   P   P 2   e i Pi $/hr
T



i 1
i
i i
i i
i
Eт: Total Emission cost function
αᵢ, βᵢ, γᵢ, δᵢ, ᵢ : Emission coefficients for ith unit
In Combined Heat and Power Economic dispatch, the
objective is to find optimum power and heat operation
with minimal fuel cost. Heat and power demand must
be satisfied and operation is bounded in a heat – power
plane.
In Dynamic Economic Dispatch problem, the objective
is to find optimum power and minimize fuel cost over a
dispatch period. All dynamic constraints should be
satisfied such as: prohibited operating zones and ramp
rate limits are included in the inequality constraints and
valve point effects are also considered.
Fig. 1. Ants will choose the shortest path between nest
and food source [5]
In reference [6], I. Karakonstantis and A. Vlachos
developed an Ant Colony Optimization for Continuous
Domains (ACOR) algorithm approach. The proposed
method will solve the Economic Load Dispatch problem
(ELD), the Minimum Emission Dispatch problem
(MED), the Combined Economic and Emission Dispatch
problem (CEED) which is a multi-objective optimization
problem and the Emission Controlled Economic
Dispatch problem (ECED). The effectiveness of the
proposed method was tested on 6 generators for
2137
Fatma et. al.,
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
demands 500 MW, 700MW, 900MW and 1100 MW
while taking into consideration the power losses. These
test systems results were compared to those obtained by
Genetic Algorithm, Hybrid Genetic Algorithm and
Quadratic Programming showing that the proposed
method can handle complex problems producing feasible
and high quality solutions.
In reference [7], D. C. Secui successfully implemented a
method based on ACO (MACO) in solving the DED
problem with inequality and equality constraints and
with cost functions which take into consideration the
valve-point effects is proposed. The efficiency of the
proposed method was tested on 10, 13 and 30 thermal
generating units and the results were compared to those
obtained by MDE, HDE,DE , MHEP– SQP , DGPSO ,
PSO–SQP(C), IPSO, GA, PSO, ABC , AIS and other
techniques. The numerical results show that the
proposed method has better convergence and shows
superiority over the other techniques in term of the
quality of the solutions in solving the DED problem with
valve-points effects.
In reference [8], A. Vlachos, I. Petikas and S. Kyriakides
developed a Continuous Ant Colony (C-ANT) algorithm
to solve the ELD Problem. The proposed method will be
used in continuous workspaces to obtain high quality
solutions. It will be able to work quickly with
complicated
problems,
thus
achieving
global
optimization and avoiding local optima. The efficiency
of the proposed method was tested on 4 generators and
was compared to those obtained by conventional Particle
Swarm Optimization (PSO) algorithms. The numerical
results show that the proposed method obtains high
quality solutions in less time.
In reference [9], N. A. Rahmat, I. Musirin, and A. F.
Abidin solved weighted economic load dispatch problem
using a Differential Evolution Immunized Ant Colony
Optimization (DEIANT) technique. The effectiveness of
the proposed method was tested on IEEE 30-Bus
Reliability Test System (RTS) with 6 generators.
Comparison with the results obtained by ACO and
Evolutionary Programming (EP) technique show that the
proposed method outperforms ACO and EP in achieving
lower operating cost, power loss, and emission level and
computation time.
B. Particle Swarm Optimization
Particle Swarm Optimization (PSO) is a population
based search procedure developed by Kennedy and
Eberhart in 1995 [10]. It was inspired by cognitive and
social behavior of swarms of birds, school of fish etc, to
maximize the survival of the species. Particles adjust
their position according to their own best performance
and their neighbors’ best performance according to the
model in Fig. 2.
Fig. 2. Particle Swarm Model [11]
In reference [12], J. Lin, C. L. Chen, S. F. Tsai, and C.
Yuan combined an intelligent PSO (INPSO) with a
direct search method (DSM) to solve ED with valvepoint effect. The developed method will help increase
the possibility of exploring the search space where the
global optimal solution exists. Local optimization will
be done by DSM and global optimization will be done
by INPSO, where the starting points are current INPSO
solutions. The efficiency of the proposed method was
tested on two test systems where valve-point effects are
considered, one with 13 generators and another with 40
generators. These test systems results were compared to
different variants of PSO: conventional PSO, PSO with
inertia weight, PSO using common another particle
behavior, CNPSO with a diversity-based judgment
mechanism and INPSO with local optimization. The
numerical results show that the proposed method is
superior to other existing techniques in term of the
quality of the solutions.
In reference [13], M. Basu developed a modified
particle swarm optimization where Gaussian random
variables in the velocity term are used. The proposed
method will improve search efficiency and guarantee
obtaining the global optimum with a good speed of
convergence. The efficiency of the proposed method
was tested on 15-unit system with prohibited operating
zones and transmission losses, 40-unit system with
valve-point effects, 10-unit system considering multiple
fuels with valve-point effects and 140-unit Korean
power system with valve-point effects and prohibited
operating zones. These test systems results were
compared to those obtained by self-organizing
hierarchical particle swarm optimizer with time varying
acceleration coefficients (HPSO-TVAC) and particle
2138
Fatma et. al.,
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
swarm optimization with time-varying inertia weight
(PSO-TVIW). Hence, showing that the proposed
method overcomes premature convergence, thus
obtaining better results compared to other methods.
In reference [14], S. Duman, N. Yorukeren and I. H.
Altas proposed a novel modified hybrid Particle Swarm
Optimization (PSO) and GSA based on fuzzy logic
(FL) method. The proposed method will control ability
to search for the global optimum and increase the
performance of the hybrid PSOGSA. The proposed
method was validated using the well-known 23
benchmark test functions and its efficiency tested on
IEEE 5-machines 14-bus, IEEE 6-machines 30-bus, 13
and 40 unit test systems; with and without the losses.
Comparing these test systems results to those obtained
by PSO, GSA and PSOGSA show that the proposed
method can converge to the near optimal solution, thus,
improving the performance of the standard hybrid
PSOGSA approach.
In reference [15], V. K. Jadoun, N. Gupta, K. R. Niazi
and A. Swarnkar developed a Modulated Particle
Swarm Optimization (MPSO) that will enhance
exploration and exploitation of the search space. The
efficiency of the proposed method was tested on 6
generators, 10 generators and 40 generators systems
considering several operational constraints like valve
point effect, and prohibited operating zones (POZs) and
compared to those obtained by PSO, BBO, DE/BBO,
LMPSO and SMPSO. Linearly Modulated PSO
(LMPSO), Sinusoidal Modulated PSO (SMPSO)
The numerical results show that the proposed method is
superior to other existing techniques in term of
searching capability and convergence rate.
systems. The numerical results illustrate that the
proposed method is superior to EP, conventional PSO,
GA, DSPSOTSA, BBO, HHS, HIGA and PSO-GSA.in
term of the quality of the solutions; therefore, it could
be useful in solving non-linear economic dispatch
problems. The proposed method will be capable of
finding the most optimal solution for the non-linear
optimization problems, since the best features of PSO
and EP are combined.
In reference [18], N. Yousefi developed a particle
swarm optimization with time varying acceleration
coefficients. The proposed method can solve nonconvex ELD problems with different constraints like
transmission losses, dynamic operation constraints, and
prohibited operating zones. The efficiency of the
proposed method was tested on 3-machines 6-bus,
IEEE 5-machines 14-bus, IEEE 6-machines 30-bus
systems and 13 thermal units power system. The
numerical results show that the proposed method has a
faster convergence rate reaching global optimum
solutions and avoid premature convergence when
compared to those obtained by GA, APO and HGAAPO.
C. Bacterial Foraging Optimization
Bacterial Foraging Optimization Algorithm (BFOA)
was introduced by Passino in 2002 which was inspired
by the foraging behavior of the E. Coli bacteria living
in the human intestine [19]. Bacteria search for
nutrients (chemotaxis) to maximize energy obtained per
time communicating with each other using signals. The
movement of bacteria is achieved by swimming or
tumbling as illustrated in Fig.3.
In reference [16], Z. Yu and F. Zhou proposed a new
index, called iteration best, is incorporated into particle
swarm optimization, and chaotic mutation with a new
Tent map approach. The proposed method will balance
global and local search of particles avoiding premature
convergence and being trapped into local optimal. The
efficiency of the proposed method was demonstrated
for test cases of 6 and 15 generators systems. These test
systems results were compared to those obtained by
IPSO, CPSO, PSO and SOH-PSO to confirm that the
proposed method has high convergence rate reaching
more accurate global optimal solution.
In reference [17], S. Prabakaran, V. Senthilkumar G.
Baskar proposed a new Hybrid Particle Swarm
Optimization (HPSO) method that integrates the
Evolutionary Programming (EP) and Particle Swarm
Optimization (PSO) techniques. The efficiency of the
proposed method was tested on 3, 6, 15 and 20 units
Fatma et. al.,
Fig. 3. Movement of bacteria [20]
In reference [21], E. E. Elattar proposed a hybrid
genetic algorithm and bacterial foraging (HGABF)
approach. For larger constrained problems, bacterial
foraging (BF) optimization algorithm has poor
convergence characteristics. To overcome such
2139
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
shortage, BF algorithm and genetic algorithm (GA) are
integrated together. The efficiency of the proposed
method was assessed on 5, 10, and 30-unit test systems
and compared to those obtained by adaptive particle
swarm optimization (APSO) algorithm, simulated
annealing (SA) algorithm, artificial immune system
(AIS), Maclaurin series-based Lagrangian (MSL)
method, GA, PSO, artificial bee colony (ABC)
algorithm time varying acceleration coefficients
improved particle swarm optimization (TVAC-IPSO)
and hybrid immune-genetic algorithm (HIGA). The
numerical results show the efficiency and superiority of
the proposed method to determine the global or near
global solutions for the DED problem over other
methods.
In reference [22], M. S. Li, Y. Hu and X. Zhang
proposed an improved Bacterial Swarm Algorithm
(BSA) which has an increased computational
complexity compared to other conventional dispatch
methods. When tested on an IEEE 30-bus system with
uncertain load, which represents a portion of the
American Electric Power System; consisting of 30
buses, 6 generators, and 40 branches, it showed
excellent convergence performance compared to most
Evolutionary Algorithms (EAs) such as GA and PSO.
D. Shuffled Frog Leaping Algorithm
Shuffled Frog Leaping Algorithm (SFLA) is population
based cooperative search simile introduced by Eusuff
and Lansey in 2003 [23]. SFLA was motivated by the
memetic evolution of a group of frogs seeking food. It
is a combination of PSO and memetic algorithm
shuffling and generating virtual frogs (Fig. 4).
Fig. 4. Shuffled behavior of leaping frogs in search of
food [24]
In reference [25], M. K. Karimzadeh proposed an
improved shuffled frog leaping algorithm for solving
combined heat and power economic dispatch problem
that is robust and will help global exploration. The
effectiveness of the proposed method was tested on the
4 units system which consists of a conventional unit,
two co-generation units and ahead alone unit with
power demand PD and heat demand HD as 200 MW
and 115 MW respectively. The numerical results
showed the efficiency and superiority of the proposed
method in terms of CPU time and solution precision
compared to PSO, ABC and DE.
In reference [26], M. R. Narimani proposed a Modified
Shuffle Frog Leaping Algorithm for Non-Smooth
Economic Dispatch which will help reduce
computational time and avoid being trapped in local
optima by generating mutant vectors; thus, improve the
quality of solutions. The effectiveness of the proposed
method was tested on of 6 and 40 thermal units and was
compared to those obtained by conventional approaches
such as Genetic Algorithm (GA), Tabu Search
Algorithm (TSA), PSO and others in literatures. The
numerical results revealed the capability of the
algorithm to reach a reliable and superior solution in a
faster computational time.
In reference [27], P. Roy, et al., developed a hybrid
modified shuffled frog leaping algorithm (MSFLA)
with genetic algorithm (GA) crossover approach for
solving the economic load dispatch problem of
generating units considering the valve-point effects.
The proposed method will help to overcome the slow
searching speed of the shuffled frog leaping algorithm
(SFLA) in the late evolution and easily being trapped in
local optima. The proposed method was tested on four
test systems: IEEE standard 30 bus test system, a
practical Eastern Indian power grid system of 203
buses,264 lines, and 23 generators, and 13 and 40
thermal units systems whose incremental fuel cost
function take into account the valve-point loading
effects. These test systems results were compared to
those obtained by CEP, FEP, BBO, DEC-SQP, ICAPSO.MFEP, IFEP, and QPSO demonstrating the
superiority of the proposed method in terms of solution
quality, computational efficiency and robustness.
In reference [28], Y.N. Vijayakumar and Dr.
Sivanagaraju combined the benefits of shuffled frog
leaping algorithm and differential evolution by
proposing a hybrid shuffled differential evolution
(SDE) algorithm approach for the economic load
dispatch problem. The SDE algorithm integrates a
novel differential mutation operator specifically
2140
Fatma et. al.,
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
designed for effectively addressed the problem. The
efficiency of the proposed method was tested on three
standard test systems having 3, 13, and 40-units. The
numerical results showed that the proposed approach
gives more accurate solution and converges better in
less computation time compared to the GA and MPSO
methods.
E. Artificial Bee Colony
Artificial Bee Colony (ABC) is a population based
search procedure proposed by Dervis Karaboga in 2005
[29]. It was motivated by foraging behavior of
honeybees to find food sources and communicate the
information amongst other bees in the hive. The
artificial agents are classified according to their tasks
into employed bees, the onlooker bees, and the scout
bees, as shown in Fig. 5.
Fig. 5. Foraging behavior of honeybees to find food
sources [30]
In reference [31], D. C. Secui proposed a new modified
artificial bee colony algorithm (MABC) to solve the
economic dispatch problem, taking into account the
valve-point effects, the emission pollutions and various
operating constraints of the generating units. To avoid
premature convergence and find stable and high quality
solutions, a new relation for the solutions update within
the search space. The MABC is endowed with a chaotic
sequence generated by both a cat map and a logistic
map to enhance its performance. The effectiveness of
the proposed method was tested on 6, 13, 40 and 52
units systems. Also it is assessed when it is endowed
with three modalities for generating random sequences
(Cat, Log and Random) and two selection schemes of
the solutions (disruptive selection and classical
proportional selection). These test systems results were
compared to those obtained by ABC, PSO, HS, DE,
BBO, FA, GA etc. The numerical results showed that
the proposed methods obtain high quality solutions,
meeting all of the equality and inequality constraints
with high accuracy.
In reference [32], A. N. Afandi and H. Miyauchi
developed a Harvest Season Artificial Bee Colony
algorithm to improve performance in terms of the
search mechanism and convergence speed. The
effectiveness of the proposed method was tested on
IEEE-62 bus system and compared to those obtained by
ABC, SFABC, SBABC, MOABC and IABC. The
numerical results showed that the proposed method
reduced the number of iterations.
In reference [33], S. Arunachalam, R. Saranya and N.
Sangeetha combined the faster computation of ABC
and robustness of SA algorithm to improve global
search capability, thus creating a hybrid ABC and SA
algorithm for solving the combined economic and
emission dispatch problem including valve point effect.
The effectiveness of the proposed method was tested on
IEEE 30 bus six generator systems and a 10 generating
unit system. When compared to numerical results
obtained by ABC, SA and Hybrid ABCPSO method,
the proposed method provided better solution with
reasonable computational time.
In reference [34], H. Shayeghi and A. Ghasemi
improved modified ABC based on chaos theory
(CIABC) and effectively applied it for solving a multiobjective EED problem. The proposed method uses a
Chaotic Local Search (CLS) to enhance the selfsearching ability of the original ABC algorithm for
finding feasible optimal solutions of the EED problem.
Also, many linear and nonlinear constraints, such as
generation limits, transmission line loss, security
constraints and non-smooth cost functions are
considered as dynamic operational constraints.
Moreover, a method based on fuzzy set theory is
employed to extract one of the Pareto-optimal solutions
as the best compromise one. The effectiveness of the
proposed method was tested on standard IEEE 30 bus 6
generators, 14 generators and 40 thermal generating
units, respectively, as small, medium and large test
power system. The numerical results showed that the
proposed method surpasses the other available methods
in terms of computational efficiency and solution
quality.
In reference [35], M. S. Rathinaraj and P. Prakash
developed an artificial bee colony algorithm with
dynamic population size (ABCDP) algorithm from the
ABC algorithm inspired by the foraging behavior of
honey bee swarm giving a solution procedure for
solving economic dispatch problem. The effectiveness
of the proposed method was tested on IEEE 30 bus 6
generators unit system having total load of 283.4 MW
considering power loss. The numerical results
2141
Fatma et. al.,
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
demonstrated that the proposed method has a faster
convergence rate, less computational time, consistent,
simple and easy to implement with high quality
solutions and is applicable on large scale systems when
compared to those obtained by with PSO, GA, IABC,
IABC-LS algorithms
F. Firefly Algorithm
Firefly Algorithm (FA) was developed by Yang in 2008
which was inspired by the behavior of fireflies using
flashing light to attract each other [36, 37]. Fireflies are
unisex, their attractiveness is proportional to their
brightness which is inversely proportional to distance
and with no brighter firefly, it will move randomly
(Fig. 6).
Fig. 6. Brighter fireflies attract less bright ones [38]
In reference [39], G. Chen and X. Ding proposed an
improved firefly algorithm (FA) to solve economic
dispatch (ED) problem that will help overcome the
highly nonlinear characteristics, such as prohibited
operating zone, ramp rate limits, and non-smooth
property. The effectiveness of the proposed method was
validated by six benchmark functions, which include
Sphere, Schwefel, Rosenbrock, Rastrigin, Ackley and
Griewank and then applied on ELD system with 3, 13,
and 40 thermal units. These test systems results were
compared to those obtained by GA, PSO, EP, BBO and
FA etc. The numerical results revealed that the
proposed method was capable of improving the search
ability, achieving higher quality solution with high
diversity and avoiding premature.
In reference [40], A. Jalili, A. Noruzi, M. Yazdani and
M. Mirzayi presented a hybrid method based on Firefly
Algorithm (FA) and Fuzzy Mechanism (FM) for
solving Economic Load Dispatch (ELD) problem by
considering the valve point in power system. The
efficiency of the proposed method was tested on six
and forty generating units, considering the ramp rate
limits and prohibited zones of the units. These test
systems results were compared to those obtained by
PSO, IPSO, Hybrid GAPSO, Chaotic PSO (CPSO),
self-organizing hierarchical PSO (SOH-PSO), New
PSO and BBO and the proposed method was found to
efficiently reach optimum with a rapid convergence
rate with high accuracy.
In reference [41], T. Malini used the Firefly Algorithm
(FA) to solve the multi objective optimization for
Economic and Environmental Dispatch (EED) problem
considering security constraint described by Voltage
Profile Index (VPI). The proposed method algorithm is
capable of solving and determining the exact output
power of all the generating units and minimizes the
total cost function of the generation units. The
efficiency of the proposed method was tested on IEEE
30 bus system 6 generators, 41 lines and 24 load buses
and compared to those obtained by GA. The numerical
results demonstrated that the proposed method is very
efficient and accurate in obtaining global optima with
high success rates for the given constrained
optimization problem.
In reference [42], G. Maidl, D. S. de Lucena and L. dos
Santos Coelho proposed a modified firefly algorithm
(MFA) based on the situational knowledge source
(memories of successful solutions) and used to solve
non-convex ED optimization problem including
practical aspect like valve-point. The effectiveness of
the proposed method was tested on a 13 thermal units
whose incremental fuel cost function takes into account
the valve-point loading effects. These test systems
results were compared to those obtained by improved
evolutionary programming, Hybrid genetic algorithm,
Particle swarm optimization, improved genetic
algorithm, Self-tuning hybrid differential evolution,
improved particle swarm optimization; thus revealed
that the proposed method has the ability to converge to
a better quality near-optimal solution and possesses
better convergence characteristics and robustness.
In reference [43], M. M. Loona, M. S. Mehta and M. S.
Prashar introduced a new metaheuristic nature-inspired
Hybrid algorithm called DE-Firefly Algorithm (FFA) is
to solve ELD problem. The efficiency of the proposed
method was validated on a 3 unit test system and
compared to the results obtained by Firefly Algorithm
showing that it is efficient and robust reaching a more
optimal solution than FFA.
G. Cuckoo Search Algorithm
Cuckoo Search Algorithm (CSA) was introduced by
Yang and Deb in 2009 which was inspired by a special
species of bird called cuckoo [44]. Each cuckoo lay an
egg in a host bird’s nest chosen randomly. Eggs that
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Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
aren’t discovered by host bird (high quality) continue in
the iterations with a probability [0, 1]; whereas
discovered eggs are thrown or the host abandons the
nest, as illustrated in Fig. 7.
Fig. 7. Representation of a nest solution in the Cuckoo
Search Algorithm [45]
In reference [46], C. D. Tran, T. T. Dao, V. S. Vo and
T. T. Nguyen proposed two modified versions of CSA,
where Gaussian and Cauchy distributions generates
new solutions and impose bound by best solutions
mechanism. The (CSA-Gauss) and (CSA-Cauchy) has
fewer parameters and fewer equations than CSA with
Lévy distribution. The effectiveness of the proposed
method was tested on two 10-unit systems: System with
Multiple Fuel Options (2400, 2500, 2600 and 2700
MW) and without Valve Point Effect and another
System with Multiple Fuel Options (2700 MW
neglecting losses) and Valve Point Effect. These test
systems results were compared to those obtained by
various techniques and by those obtained by (CSAGauss) and (CSA-Cauchy). The numerical results
revealed that the proposed method is highly effective
and faster for solving ELD problem with multiple fuel
options with/without valve point effect.
In reference [47], K. Chandrasekaran, S.P. Simon and
N. P. Padhy used the CSA to solve the ERED
(Emission
Reliable
Economic
Multi-objective
Dispatch) problem, which is formulated as a nonsmooth and non-convex multi-objective ED problem
incorporating valve-point effects of thermal units. The
fuzzy set theory is used to find a best compromise
solution from the healthy distributed Pareto-optimal set.
The efficiency of the proposed method was tested on a
benchmark of 6-unit test system, IEEE RTS 24 bus
system, and IEEE 118 bus system solving both EED
and ERED problems. These test systems results were
compared to those obtained by PSO and ABC showing
that the proposed method provided a better compromise
solution that is both feasible and robust.
In reference [48], N. T. P. Thao and N. T. Thang
implemented a Cuckoo Search Algorithm for solving
environmental economic
load
dispatch. The
effectiveness of the proposed method was tested on
three and six thermal units with different loads and
dispatches. Compared to Tabu Search, variants of GA
and BBO the proposed method was very efficient
obtaining lower fuel cost, emission and computation
time.
In reference [49], E. Afzalan and M. Joorabian
proposed a modified CS algorithm employing a new
mutation scheme inspired by the DE/current-togr_best/1 and applied to determine the feasible optimal
solution of the economic load dispatch problem
considering various generator constraints. The
efficiency of the proposed method was tested on 3, 6,
15, and 40 thermal units with generator constraints,
such as: ramp rate limits, prohibited operating zones in
the power system operation, and transmission losses.
The numerical results revealed that the proposed
method enriches the searching behavior and solution
quality; thus, avoid being trapped into local optimum.
H. Bat Algorithm
Bat Algorithm (BA) was introduced by Yang and
Gandomi in 2012 and is inspired by echolocation
behavior of bats to recognize direction and differentiate
between food and prey [50]. This algorithm shows
similarity to PSO in terms of velocity and position
equations (Fig. 8).
Fig. 8. Echolocation behavior of bats [51]
In reference [52], S. S. S. Hosseini, X. S. Yang, A. H.
Gandomi and A. Nemati used a newly developed Bat
Algorithm (BA), based on the echolocation behavior of
bats to determine the feasible optimal solutions of the
ED problems under different nonlinear constraints such
as transmission losses, ramp rate limits, multiple fuel
options and prohibited operating zones. The
effectiveness of the proposed method was tested on 3,
13, 15 and 40 generating unit ED test systems with
non-convexity. When compared to results obtained by
2143
Fatma et. al.,
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
PSO, GA, SQP, and BF, it can be concluded that the
proposed method is a promising alternative to existing
techniques in obtaining better solutions.
In reference [53], T. K. Dao, T. S. Pan and S. C. Chu
developed an evolutionary based approach Evolved Bat
Algorithm (EBA) to solve the constraint economic load
dispatched problem of thermal plants. The effectiveness
of the proposed method was tested on six units and
fifteen units of thermal plants and compared to those
obtained by GA and PSO. The numerical results
showed that the proposed method reaches better quality
solution with higher efficiency, superior accuracy and
less computational time.
In reference [54], P. S. K. Reddy, P. A. Kumar and G.
N. S. Vaibhav used the bat algorithm to obtain the
optimal solution of economic load dispatch (ELD). The
effectiveness of the proposed method was tested on 3
and 6-unit system and compared to PSO and IWD
confirming its superiority in terms of convergence,
accuracy and computational time.
I. Grey Wolf Optimization
Grey Wolf Optimization (GWO) is the most recent
algorithm introduced by Seyedali Mirjalili in 2014
which was inspired by the grey wolf (Canis lupus)
hunting behavior [55]. Privileged wolves are alpha
wolves – decision makers, then beta wolves – alpha
assistant, and then delta wolves – lowest ranking and
omega are inferior wolves preceded by scoffed kappa
and lambda as in Fig. 9.
α
β
δ
ω
κ
γ
Fig. 9. The hierarchy of the grey wolves
In reference [54], Dr. S. Sharma, S. Mehta and N.
Chopra proposed to solve convex economic load
dispatch problem using a new meta-heuristics inspired
by grey wolves Grey Wolf Optimization GWO. The
proposed method mimics the hunting mechanism and
leadership hierarchy of the grey wolves. The efficiency
of the proposed method was tested on three and six unit
systems. These test systems results were compared to
those obtained by Lambda Iteration Method,
Conventional Method, PSO and Cuckoo Search
Algorithm. The numerical results showed that the
proposed method is simple, reliable and efficient.
In reference [56], L. I. Wong, M. H. Sulaiman and M.
R. Mohamed applied the newly developed Grey Wolf
Optimizer to solve economic load dispatch ED
problems. The proposed method mimics the hunting
mechanism and leadership hierarchy of the grey
wolves. The effectiveness of the proposed method was
tested on 6 units and 15 units systems. These test
systems results were compared to those obtained by
DS, BBO, GA and variants of PSO which proved that
the proposed method is superior to other methods in
terms of convergence, accuracy and computational
time.
Table 1. Advantages and disadvantages of Swarm-based meta-heuristic algorithms [57]-[64]
Meta-heuristic
Ant Colony Optimization
Particle
Optimization
Swarm
Advantages
 Applicable to a broad range of optimization
problems, such as: Traveling Salesman
Problem
 Since ants move simultaneously and
independently without supervision, it can be
used in dynamic parallel applications
 Positive feedback favoring most taken path
leads to discovering good solution rapidly
 Distributed computation avoids premature
convergence
 Simple concept and easy implementation
 Robust in controlling the few parameters,
computationally efficient and requires less
memory
 It can be easily applied to nonlinear non-
Disadvantages
 Theoretical analysis is difficult so
research is experimental instead of
theoretical
 Although convergence is guaranteed,
the time it takes is uncertain
 Only applicable for discrete problems
 It gets trapped in local optima when
handling heavily constraint problems
due to limited local/global searching
capabilities
 Updating
is
performed
without
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Fatma et. al.,
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
continuous optimization problem
Bacterial
Foraging
Optimization Algorithm
Shuffled Frog
Algorithm
Leaping
Artificial Bee Colony
Firefly Algorithm
Cuckoo Search Algorithm
Bat Algorithm
Grey Wolf Optimization
 Self-adaptive
 Global convergence avoiding premature
convergence
 Less computational time
 Requires less memory
 It can be widely applied to non-linear
optimization problems and can handle more
number of objective functions
 Robust, accurate, efficient and fast
 It combines the profits of the local search tool
of PSO and the idea of mixing information
from parallel local searches to move toward a
global solution
 It has few parameters
 It is a global optimizer
 Flexible
 It doesn’t only include self-improving process
with the current space but also include
improvement among its own space
 Less computational time to reach optima or
near optima
 It has a higher convergence rate and much
simpler
 Few parameters to control
 It possesses a fine balance of intensification
(local search) and randomization (exploration
of whole search space)
 Convergence rate is insensitive to one of the
parameters
 Simple, flexible and easy implementation
 Few parameters to control
 Fast initial convergence
 It can be easily applied to nonlinear noncontinuous optimization problem
 Easy to implement due to its simple structure
 Faster convergence
 Few parameters to control
 Avoids local optima
IV. CONCLUSION
 Economic load dispatch (ELD) problem play a
vital role in the operation of power system. This paper
presents important variants and considerations of the
ELD problem. First, the formulation for the ELD
problem was outlined. The main objective of ELD is to
determine optimum power generation and minimizing
the fuel cost. Then a review of the swarm optimization
algorithms was presented. Although these algorithms
have successfully solved the ELD problem, yet further
considering quality of solutions and the
distance between solutions
 Due to its biased random walk ,
swarming effect is not satisfactory for
the ELD problem which is a complex
problem in huge multi-dimensional
space with constraints
 It gets trapped in local optima
 The convergence to proper target is very
late
 High computational time
 It can get trapped into local optima
 Firefly algorithm parameters are set
fixed and they do not change with the
time
 No memory or history of better
solutions of previous iterations

It can get trapped into local optima
 If it switches from exploration to
exploitation stage rapidly, it may lead to
stagnation after some initial stage
 The algorithm is still under research and
development
improvements to the algorithms were needed. Thus,
updates and modifications were introduced to these
algorithms. This paper reviewed the work reported in
literature in the field of using swarm optimization
algorithms and their recent updates to solve economic
dispatch problems. A comparison is made to
demonstrate the advantages and disadvantages of each
meta-heuristic algorithm as shown in Table 1.
2145
Fatma et. al.,
Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey
International Electrical Engineering Journal (IEEJ)
Vol. (2016) No. 1, pp. 2136-2147
ISSN 2078-2365
http://www.ieejournal.com/
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