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International Electrical Engineering Journal (IEEJ)

Vol. (2016) No. 1, pp. 2136-2147

ISSN 2078-2365

http://www.ieejournal.com/

2136 Fatma et. al., Solution of Economic Load Dispatch using Recent Swarm-based Meta-heuristic Algorithms: A Survey

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 swarm-

based 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:

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.

•Evolutionary Programming

•Genetic Algorithm

•Differential Evolution 1) Evolutionary

•Particle Swarm Optimization

•Ant Colony Optimization

•Firefly Algorithm 2) Swarm based

•Big Bang Big Crunch

•Gravitational Search Algorithm

•Simulated Annealing

3) Physics and chemistry based

•Flower Pollination Algorithm

• Invasive Weed Optimization 4) Nature based

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


https://en.wikipedia.org/wiki/Shoaling_and_schooling

https://en.wikipedia.org/wiki/Microbial_intelligence


Vol. (2016) No. 1, pp. 2136-2147

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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.

A. Cost objective function

Minimize

Where

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

If valve point effect is considered, the cost objective

function becomes:

Minimize

Where

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]

Where

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.

B. Constraints

1) Equality constraint- Energy balance equation

Where

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

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.

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

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Vol. (2016) No. 1, pp. 2136-2147

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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 valve-

point 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



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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.

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

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 non-

convex 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 HGA-

APO.

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.

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



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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, ICA-

PSO.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



Vol. (2016) No. 1, pp. 2136-2147

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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 multi-

objective EED problem. The proposed method uses a

Chaotic Local Search (CLS) to enhance the self-

searching 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



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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


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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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


various techniques and by those obtained by (CSA-

Gauss) 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 non-

smooth 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-to-

gr_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



Vol. (2016) No. 1, pp. 2136-2147

ISSN 2078-2365



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.

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


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 Advantages Disadvantages

Ant Colony Optimization

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

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

Particle Swarm

Optimization

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-

It gets trapped in local optima when

handling heavily constraint problems

due to limited local/global searching

capabilities

Updating is performed without

α

β

δ

ω

κ

γ



Vol. (2016) No. 1, pp. 2136-2147

ISSN 2078-2365



continuous optimization problem considering quality of solutions and the

distance between solutions

Bacterial Foraging

Optimization Algorithm

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

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

Shuffled Frog Leaping

Algorithm

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 gets trapped in local optima

The convergence to proper target is very

late

Artificial Bee Colony

It has few parameters

It is a global optimizer

Flexible

High computational time

Firefly Algorithm

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

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

Cuckoo Search Algorithm

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

It can get trapped into local optima

Bat Algorithm

Simple, flexible and easy implementation


Fast initial convergence

It can be easily applied to nonlinear non-

continuous optimization problem

If it switches from exploration to

exploitation stage rapidly, it may lead to

stagnation after some initial stage

Grey Wolf Optimization

Easy to implement due to its simple structure

Faster convergence


Avoids local optima

The algorithm is still under research and

development

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

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.



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ISSN 2078-2365



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