A holistic review on optimization strategies for combined economic emission dispatch problem

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Renewable and Sustainable Energy Reviews journal homepage: www.elsevier.com/locate/rser

A holistic review on optimization strategies for combined economic emission dispatch problem ⁎

Fahad Parvez Mahdia, Pandian Vasanta, , Vish Kallimanib, Junzo Watadab, Patrick Yeoh Siew Faib, M. Abdullah-Al-Wadudc a b c

Department of Fundamental and Applied Sciences, University Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia Department of Computer & Information Sciences, Universiti Teknologi PETRONAS, Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia Department of Software Engineering, College of Computer and Information Sciences, King Saud University, Riyadh, Saudi Arabia

A R T I C L E I N F O

A BS T RAC T

Keywords: Combined economic emission dispatch Computational intelligence Economic dispatch Emission dispatch Optimization strategy Fuzzy theory Literature review

Power generation system largely depends on fossil fuels to generate electricity. Due to various reasons, the reserves of fossil fuels are declining and will become too expensive in near future. At the same time, generation of power from fossil fuels causes hazardous gases and particulates to emit, which pollutes the air and causes significant and long term damages on the environment. For this reason, extensive research works have been conducted for last few decades from different perspectives to reduce both the fuel cost as well as the emission of hazardous gases in power generation system. This power generation problem is commonly referred to as the combined economic emission dispatch (CEED) problem. This paper provides a comprehensive review on the uses of different optimization techniques to solve CEED problem. Authors have found advanced natureinspired methods as the most suitable and successful, and have concluded combinational hybrid methods as the most prospective methods to solve CEED problem.

1. Introduction Electrical power generation system largely depends on fossil fuel powered thermal plants to generate electricity. The consumption of fossil fuels in the electrical power generation systems must be controlled and minimized. Fossil fuel reserves available in the nature are very much limited [1] and not always easily accessible to all as fuel reserves are concentrated into a small number of countries and those countries may influence or restrict the supply of fossil fuels. Environmental pollution due to the emission of large amount of pollutant gas-particulates is another fact that motivates researchers to work on minimizing the use of fossil fuel in the thermal plants during the process of electricity generation. Although various alternatives including hydroelectric power generation, nuclear power generation and recent renewable energy technology have been developed and implemented to produce electricity, fossil fuel still remains to be the mostly used [2] ingredient to generate electricity. Thus, the major problems of using fossil fuel in power generation systems are to find an optimal solution to minimize both the use of fuel (fuel cost) and emission of hazardous gases simultaneously. Economic dispatch (ED) deals with the minimization of fuel cost by considering optimal power generation in each power generating unit of the power generation system, while emission dispatch deals with the minimization of the

⁎

emission of hazardous gases and particulates from the system. Both the objectives are conflicting in nature and cannot be optimized simultaneously. This conflicting behavior of these objectives gives rise to a complex multiobjective optimization [3] problem known as combined economic emission dispatch (CEED) problem, where both the objectives are considered and optimize simultaneously. Over the past decades, many optimization methods have been used to solve CEED problem. These methods can be classified into three categories: (i) conventional methods, (ii) non-conventional methods and (iii) hybrid Methods as depicted in Fig. 1. Previously mathematical programming based conventional methods such as Lagrange relaxation [4,5], lambda iteration [6,7], Newton-Raphson [8], interior point method [9], weighted minimax [10] and quadratic programming [11] had been used to solve ED and CEED problems. Classical methods have some advantages like they don’t have any problem-specific parameters to specify [12], their optimality is mathematically proven [13] and some of them are computationally fast [14]. They have some major disadvantages like they can immaturely converge into local optimum, sensitivity to the initial starting points, many of the them are not applicable to some types of cost function i.e. non-smooth, non-convex, non-monotonically increasing cost functions etc. [15,16]. Artificial intelligence-based non-conventional methods have been frequently used to solve CEED problems which include artificial

Corresponding author.

http://dx.doi.org/10.1016/j.rser.2017.06.111 Received 9 March 2017; Received in revised form 23 June 2017; Accepted 24 June 2017 1364-0321/ © 2017 Elsevier Ltd. All rights reserved.

Please cite this article as: Mahdi, F.P., Renewable and Sustainable Energy Reviews (2017), http://dx.doi.org/10.1016/j.rser.2017.06.111

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IPSO Improved particle swarm optimization LP Linear programming MINLP Mixed integer nonlinear programming MDE Modified differential evolution MODE Multiobjective differential evolution NPGA Niched Pareto genetic algorithm NSGA Non-dominated sorting genetic algorithm NSGA-II Non-dominated sorting genetic algorithm-II PSO Particle swarm optimization PSO-FFA Particle swarm optimization-Firefly algorithm PSO-GA Particle swarm optimization-Genetic algorithm PSO-GSA Particle swarm optimization-Gravitational search algorithm QOTLBO Quasi-oppositional teaching and learning based optimization RCGA Real coded genetic algorithm RGA Refined genetic algorithm SA Simulated annealing SMO Spider monkey optimization SOHPSO_TVAC Self-organizing hierarchical particle swarm optimization technique with time-varying acceleration coefficients SPEA Strength Pareto evolutionary algorithm SPEA 2 Strength Pareto evolutionary algorithm 2 SCEED Static combined economic emission dispatch TS Tabu search TLBO Teaching and learning based optimization θ-TLBO Theta-Teaching and learning based optimization

Nomenclature ABC ABC-SA ACO BA BBO BFA BF-NM CDE CEED CRO CS DE DE-CRO DE-HS DE-SA DE-SQP DEED DGPSO ED EED FCPSO FFA FFA-GA GA GSA HS

Artificial bee colony Artificial bee colony-Simulated annealing Ant colony optimization Bat algorithm Biogeography based optimization Bacteria foraging algorithm Bacterial foraging-Nelder-Mead Chaotic differential evolution Combined economic emission dispatch Chemical reaction optimization Cuckoo search Differential evolution Differential evolution-Chemical reaction optimization Differential evolution-Harmonic search Differential evolution-Simulated annealing Differential evolution-Sequential quadratic programming Dynamic economic emission dispatch Deterministically guided PSO Economic dispatch Economic emission dispatch Fuzzy clustering particle swarm optimization Firefly algorithm Firefly algorithm-Genetic algorithm Genetic algorithm Gravitational search algorithm Harmonic search

researchers have developed many hybrid methods [32–35] by combining two or more algorithms to solve CEED problems. Sometimes researchers integrate classical method with non-conventional method to solve CEED problems [36] and in some cases two or more nonconventional methods are combined to create hybrid algorithm to solve CEED problems [37]. But, hybrid algorithm usually suffers from long computational time as two or more algorithms operate (either in parallel) to solve CEED problem, where each of the algorithms perform individually into the problem. Table 1 briefly shows optimization methods used to solve CEED problems by their classification as discussed earlier. More recently, researchers are gathering ideas from quantum computation and merging it with the existing state of the arts optimization techniques in order to find superior results. The quantum parallelism phenomena of quantum mechanics have been exploited to get more computationally powerful algorithms. So far, the quantumbased optimization has been successfully implemented in different applications [57–59] and also in CEED problem [60], achieving

intelligence (AI)-based artificial neural network (ANN) [17] and computational intelligence [18] (CI)-based methods like genetic algorithm [19], particle swarm optimization (PSO) [20], harmony search (HS) [21], simulated annealing (SA) [22], differential evolution (DE) [23], gravitational search algorithm (GSA) [24], biogeography based optimization (BBO) [25] and some nature inspired advanced CI methods like bacterial foraging algorithm (BFA) [25], ant colony optimization (ACO) [26], cuckoo search (CS) [27], bat algorithm (BA) [28], artificial bee colony (ABC) [29], firefly algorithm (FFA) [30], flower pollination algorithm (FPA) [31] etc. These advanced optimization methods play a pivotal role in alleviating the problems found in the classical approaches in solving CEED problem, for example, they can enable us to solve nonlinear and nonconvex cost functions and can achieve nearly global/global solutions. However, some of these methods suffer from many problem specific parameter selections and high computational time. In order to combine the best features of different algorithm and thereby achieve superior performance than the stand-alone methods

Fig. 1. Different optimization methods and their subsections.

2

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Table 1 Optimization methods used to solve CEED problems. Classical Methods

Year

Non-conventional Methods

Year

Hybrid Methods

Year

Goal programming [38] Han-Powell algorithm [41] Weighted minimax method [10] Linear pogramming method [44] Classical technique based on co-ordination equations [47] Lagrangian relaxation [48] Newton-Raphson [8,51] Evolutionary programming [53] Stochastic search technique [55] Quadratic programming [11]

1988 1992 1993 1994 1994 1994 1997, 2003 1998 1998 1998

Genetic algorithm [39] Particle swarm optimization [42] Simulated annealing [22] Bacterial foraging algorithm [45] Differential evolution [23] Firefly algorithm [49] Artificial bee colony [52] Teaching and learning based optimization [54] Bat algorithm [28] Cuckoo search [27]

1997 2003 2005 2010 2010 2011 2011 2011 2013 2014

DE-BBO* [40] PSO-GA [43] BF-NM [36] ABC-SA [46] DE-HS [35] PSO-GSA [50] FFA-GA [34] DE-SA [33] PSO-FFA [56] DE-CRO [32]

2011 2012 2012 2013 2014 2014 2014 2015 2015 2016

*

The full forms (elaborations) of these abbreviated terms are given in the Nomenclature and Acronyms section.

fuel cost coefficients of ith generating unit. Additionally, Pgi stands for the real power generation of the ith unit (in MW) and n refers to number of generating unit. Emission dispatch problem is also often formulated as quadratic function which can be described as below,

significant improvements in computational efficiency [61], faster and better convergence properties [62,63]. This review paper mainly studies recent nature-inspired nonconventional methods used for solving CEED problems to discover the trend of using different optimization strategies to mitigate the research gap found in handling CEED problems. This study uncovers different aspects of modelling CEED problem like consideration of different equality and inequality constraints and test systems, which will benefit the policy maker to implement more economic and environmental friendly power generation system. Often researchers apply their proposed techniques in different power generation systems (small and large) to optimize CEED problem and this study will help to choose suitable technique for small and large systems. Finally, this study shows that use of nature-inspired metaheuristic techniques performs better than other heuristic and classical techniques to solve CEED problem, while hybrid techniques are found to be computationally lengthy but more prospective. The remaining of this paper is organized as follows: (i) CEED formulation section describes different aspects and form of functions to define CEED problems with many practical equal and unequal constraints. (ii) Non-conventional algorithms section reviews some of the most renowned algorithms such as GA, PSO, CS, BA and TLBO to solve CEED problems with their flowcharts and working principle. (iii) Hybrid methods section elaborates the hybrid algorithms used for CEED problems with their pros and cons. (iv) Fuzzy compromised solution for CEED problems section discusses about fuzzy approaches to get compromised solution from set of Pareto-optimal solution. (v) Discussion section has given a general overview of the trend to solve CEED problems with different optimization strategies using graphs. (vi) Future direction section provides opinions of authors on future optimization strategy to solve CEED problems and finally (vii) Conclusion section summarizes the paper by providing overall gist of the paper and finishing remarks.

n

∑ di Pgi 2 + ei Pgi + fi

E (Pgi ) =

where E is emission function measured in kg/h, and di, ei and fi are emission coefficients of ith generating unit. Both the objectives are noncommensurable and conflicting in nature, and thus sometimes researchers converted the objectives into a single objective using a price penalty factor. The combined economic emission function FT in ($/h) using a penalty factor can be described as below, n

FT =

∑ {F (Pgi ) + hi E (Pgi ) }

where the penalty factor hi in ($/kg) described above can be defined as follows

hi = F (Pgi, max )/ E (Pgi, max )

(4)

F (Pgi, max ) = ai (Pgi, max )2 + bi (Pgi, max ) + ci

(5)

E (Pgi, max ) = di (Pgi, max

+ ei (Pgi, max ) + fi

n

FT = w ∑ F (Pgi ) + (1 − w )

(6)

n

∑ hi E (Pgi ) i =1

(7)

Finally, the objective function (OF), where the objective is to reduce both the fuel cost as well as the amount of emission, can be described as below

Combined economic emission dispatch (CEED) usually refers to the minimization of fuel cost and emission of hazardous gases and particulates while satisfying total load demand and all other equality and inequality constraints. But, some researchers also consider other objectives like reliability level, load adjusting time, reserve capacity and even transmission loss as their objectives with CEED problem [64–67]. Economic dispatch problem usually represented as a quadratic cost function by the researchers and described as,

OF = min(FT )

(8)

In power generation systems, many real-time and practical constraints exist and researchers have to consider these constraints in order to get accurate and reliable result of power generation, which can be practically implemented in power generation systems. Table 2 shows some of the objectives and constraints considered by the researcher to solve CEED problem. Description of some notable constraints are given below: (1) Power Balance Constraint: The total generated power in all the generating units must satisfy the total load demand. For that reason,

n

i =1

)2

However, some of the researchers also used cubic function to represent economic dispatch, emission dispatch and CEED problem [68,69]. Higher order polynomial function adds complexities but reduces nonlinearities of actual power generating system [69]. To handle CEED problems, weighted sum method is used as a mean of tradeoff between these two conflicting objectives [70,71], where each objective function is multiplied by a user-defined weight (range from 0 to 1) which is usually refers to the importance of the objective. CEED problem with weight vector (w) can be described as below,

i =1

∑ ai Pgi 2 + bi Pgi + ci

(3)

i =1

2. CEED formulation

F (Pgi ) =

(2)

i =1

(1)

where F is total fuel cost/generation cost in $/h, and ai, bi, and ci are 3

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operating zone of the generating unit i. PgiL, j and PgiU, j −1 are the lower limit of jth prohibited zone and the upper limit of (j-1)th prohibited operating zone of the generating unit i respectively. Table 3 summarizes some of the most recent techniques and methods used to solve the CEED problem with short remarks to give an idea to the readers about the current research trends of using different optimization strategies to counter CEED problem. From the table, it is worth mentioning that some of the techniques are completely new, few of them are modified and improved versions of the previous algorithms and the rest of them are hybrid method, where more than one method are utilized to handle CEED problem. The applications are almost same with some little difference in their definitions. For example, dynamic economic emission dispatch (DEED) problem is a version of CEED, where generator ramp rate limits are considered.

Table 2 Objectives and constraints considered in CEED problem. Objectives

Constraints

Cost reduction Emission reduction Reliability level Load adjusting time Reserve capacity Transmission Loss

Power balance Transmission loss Generator limit Prohibited operating zones Generators ramp rate limit Tie-line limit

total generated power must be equal to the summation of total load demand and total power loss, described as below, n

P=

∑ Pgi = PD + PL

(8)

i =1

3. Non-conventional methods

where P, Pgi, PD and PL stand for total generated power in all generating units, total generated power in generating unit i, total power demand and total loss respectively. (2) Transmission Loss: Generated electrical power in power generation system encounters loss during its transmission to grid due to energy dissipation in the conductors, transmission line, transformer, magnetic losses in transformers etc. This loss is known as transmission loss, which is one of the major constraints in combined economic emission dispatch problems and can be described using Kron's loss formula [72], N

PL =

N

In order to overcome the shortcomings of mathematical model based classical methods, AI-based ANN, and more recently CI-based GA, PSO, DE, SA, HS, BFA, BBO, ACO, ABC, BA, CS etc. have been proposed, exploited and utilized to solve CEED problem. Non-conventional methods based on AI and CI have been very successful in getting high quality solutions with robustness, faster convergence rate and powerful computational performance. Authors briefly discuss some of the most well-known and prospective methods and its’ variants to tackle combined economic emission problem below.

N

∑ ∑ Pgi Bij Pgj + ∑ Bi0 Pgi + B00 i =1 j =1

i =1

3.1. Genetic algorithm (GA)

(9)

where Bij, Bi0 and B00 are loss coefficient of George's formula, transmission loss constant of generating unit i and Kron's transmission loss constant respectively. (3) Generation Limit Constraint: For stable operation in power generating unit, total power generation of each generating unit must be within its maximum and minimum limits. It can be described as below,

Pgi, min ≤ Pgi ≤ Pgi, max

Genetic algorithm (GA), one of the most used optimization algorithms, was developed by John Holland in 1970 [97]. This algorithm was inspired by the theory adopted by some evolutionist which stated that only strong and fit species survive in the nature. GA algorithm operates with a set of chromosomes, known as population. It is randomly initialized and then it searches for the fitter and fitter solution, and ultimately converges to a single best solution. Fig. 2 illustrates GA algorithm. Some well-known advantages of GA [98] are it is comparatively less susceptible to the complex problem than other non-evolutionary methods, in the presence of many parameters it can achieve solutions rapidly by dealing with multiple solutions in a single run, can explore to a number of local optima etc. GA has some termination criteria [99] by which it decides whether to continue or terminate search. The most common stopping criteria are given below Generation number: This termination criterion stops the evolution when it meets the user-specified maximum number of evaluation. This termination criterion is always active in GA. Evolution time: When the elapsed evaluation time exceeds the userspecified maximum evaluation time, this termination criterion becomes active and stops the evaluation. By default, evaluation doesn’t stop until it completes the current generation; but, this nature of operation can be altered to stop it within a generation. Objective function threshold: If the best fitness value of current population becomes less than user-specified threshold fitness value when the objective is to minimize the fitness or the best fitness value of current population becomes greater than user-specified threshold value when the objective is to maximize the fitness, this termination method will stop the evolution. Objective function convergence: When the chance of achieving significant changes in the next generations is excessively low, the fitness value is deemed as converges. This termination criterion stops further evaluation when fitness value is deemed to converge. Population convergence: When the population will be deemed to converge, this termination method will stop further evaluation. The population can be deemed to converge when the average fitness value

(10)

where Pgi,min and Pgi,max are minimum and maximum power output limit of generating unit i respectively. (4) Generator Ramp Rate Limit: All the generating units are practically restricted to operate in certain operating range because of their ramp rate limits. Therefore, they have to operate in two adjacent specific operation zones. It is necessary to consider generator ramp rate limit in order to formulate CEED accurately. So, the power output of each generating unit considering ramp rate limit can be formulated as below,

Max (Pgi, min, Pgi0 − DRi ) ≤ Pgi ≤ Min (Pgi, max, Pgi0 + URi )

(11)

0

where Pgi refers to the previous operating point of generating unit i, and DRi and URi are down rate limits and up rate limits of the generating unit i respectively. (5) Prohibited Operating Zones: In practical power generation system, the whole operating range of generating unit is not always available for operation. Physical operational limitation can cause some units to have prohibited operating zones and operating in these zones may lead to instabilities. For that reason, the generation output must avoid operation in the prohibited operating zones. So, the generating unit i should operate in the feasible operating zones described as below, L ⎧P gi, min ≤ Pgi ≤ Pgi,1, ⎪ ⎪ U L Pgi = ⎨ Pgi, j −1 ≤ Pgi ≤ Pgi, j , j = 2.3...., Ki ⎪ ⎪ PU gi, K ≤ Pgi ≤ Pgi, max, ⎩ i

(12)

where Ki refers to the number of prohibited operating zones in the curve of generating unit i where j represents the index of prohibited 4

5

Khan et al. [87]

Hadji et al. [88]

Jubril et al. [89]

Roy et al. [90]

Rajkumar [91]

18

19

20

21

11

17

Shivaie et al. [81]

10

Mandal et al. [86]

Yang et al. [80]

9

16

Zhang et al. [33]

8

Muthuswamy et al. [85]

Secui [79]

7

15

Zong et al. [78]

6

Nwulu et al. [84]

Chiang [77]

5

14

Modiri-Delshad et al. [75] Daryani et al. [76]

4

Ozyon et al. [83]

Roy and Bhui [32]

3

13

Singh et al. [74]

2

Pandit et al. [82]

Rajan et al. [73]

1

12

Authors

No.

2014

2015

2015

2015

2015

2015

2015

2015

2015

2015

2015

2015

2015

2015

2015

2016

2016

2016

2016

2016

2016

Year

Economic emission dispatch for wind–fossil-fuel-based power system Combined economic emission dispatch

Stochastic Combined Heat and Power Environmental/ Economic Dispatch Problem

Multi-objective Economic Emission Dispatch Solution

Combined emission economic dispatch of power system including solar photo voltaic generation

Environmental and economic power dispatch of thermal generators using Non-convex emission constrained economic dispatch

Economic power dispatch problems with emission constraints Dynamic economic emission dispatch of electric power generation

Environmental economic dispatch in multi-area power system

Power system optimal dispatch strategy considering the flow of carbon emissions and large consumers Environmental/techno-economic approach for bidding strategy in security-constrained electricity markets

Dynamic economic emission dispatch

Multi-area economic/emission dispatch

Optimal environmental and economic load dispatch

Power economic emission dispatch

Multi-objective optimal power flow problem

Economic emission dispatch problem

Dynamic economic emission load dispatch

Multiobjective thermal power dispatch

Optimum economic emission dispatch

Application

Table 3 Recent optimization strategies used to solve CEED problems.

Modified multi-objective genetic algorithm

CRO

Dance Bee Colony with dynamic step size adjustment Semi-definite programming relaxation technique

Self-organizing hierarchical PSO technique with time-varying acceleration coefficients Mixed Integer Optimization Problem (MIOP)

Modified NSGA-II (MSGA-II) algorithm

Game theory based demand response programs

Opposition-based gravitational search algorithm

Improved differential evolution with fuzzy selection

Carbon Emission Flow Based Optimal Dispatch Strategy Self-adaptive Global-based Harmony Search Algorithm (SGHSA)

Multi-objective hybrid DE-SA

Improved PSO with the random black hole strategy Chaotic global best artificial bee colony (ABC)

Firefly Algorithm (FFA)

Adaptive group search optimization (AGSO)

Backtracking search algorithm (BSA)

Hybrid differential evolution-based Chemical Reaction Optimization (CRO)

Opposition-based greedy heuristic search (OGHS)

Exchange market algorithm (EMA)

Technique (s)

Convergence feature of conventional GSO algorithm is improved. Can be used in multi-objective OPF problem. Secure operation of the power system could be fulfilled. Ease of implementation; applicability to non-smooth fuel cost and emission level functions; better effectiveness than the previous method, and the requirement for only a small population in applying the optimal EED problem of the HPS. Can search the Pareto front of the multi-objective functions quickly, and the solutions have the diversity and uniformity. Performs better than the classical ABC algorithm, the GBABC algorithm and other optimization techniques like ABC, TLBO, DE, EP and PSO. Performs better than other optimization methods, and the obtained compromise scheme can offer a viable way for EED. Proposed strategy can significantly reduce both the operation cost of the power grid and the power utilization cost of large consumers Considered a new and coordinated approach for double-sided bidding strategy in a security-constrained electricity market and decreases the production of atmospheric emissions as a valuable short-term solution. Provides wide range of trade off choices, satisfies all the complex constraints, performs better than the weighted sum approach using classical DE and some previous methods like PSO, and can be tested for larger number of objectives without additional complexity. Converges to the solution with a higher speed compared to GSA. Gives better solution than GA, PSO, NSBF, MSBF, MDE etc. Minimizes fuel and emissions costs and simultaneously determines the optimal incentive and load curtailment customers have to perform for maximal power system relief. Effectively capable for appreciable performance than NSGA-II to solve the different power system non-smooth EEPD problem Provides superior results than fuzzy controlled GA, Newton–Raphson method and BBO techniques in terms of fuel cost, emission output and losses. SCEED and DCEED problem has been investigated for full and reduced solar radiation, and full radiation respectively with constraints of thermal generator limits, power balance and renewable energy limits. Confirms that higher solar radiations contribute larger solar shares in both the cases. Larger solar share for a given load demand results in higher solar cost and total cost as well as lower fuel cost, emission cost and emissions Robustness has been tested and verified. Capable of enhancing the solution of the CEED considering practical generator constraints. Reduces the clustering of solution points on the Pareto surface and provides a more uniform distribution. Improves the computational efficiency of the weighted sum method. This approach possesses very good convergence properties, and the diversity of its solutions can be greatly improved through non-linear weight selection. The simulation results show that the proposed algorithm gives comparatively better operational cost compared with other optimization techniques. The results show the effectiveness of MNSGA-II based on extreme solutions and the (continued on next page)

Computationally efficient and robust. Performed better when compared with most recently invented SMO technique. Simple, flexible, robust and easy to implement. Parameters are adaptive and don’t have the compulsion of tuning. Obtained results found to be competitive when comparing with other techniques. Applicable for both single and multi-objective dynamic load dispatch problems. Effective and superior than other recently published techniques in terms of solution quality. And also able to reach optimal with less computational time. Proved highly robust in solving the EED problems.

Remarks

F.P. Mahdi et al.

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Inverted Generational Distance (IGD) Combined economic and emission dispatch problem

Fig. 2. Flowchart of genetic algorithm.

across the current population is less than user-defined percentage away from the best fitness value of the current population. Different versions of GA like non-dominated sorting genetic algorithm-II (NSGA-II) [104], epsilon-dominance-based genetic algorithm [103], and genetic algorithm based on similarity crossover [105] have been used to solve CEED problems. Basu implemented his proposed NSGA-II in 10-unit system and compared it with real coded GA (RCGA) to demonstrate its performance. Later, he claimed that NSGA-II can obtain better solution with less computational time than the classical techniques [104]. Osman et al. compared their proposed method with non-dominated sorting genetic algorithm (NSGA), niched Pareto genetic algorithm (NPGA) and strength Pareto evolutionary algorithm (SPEA) to demonstrate the performance of their proposed method. These recent versions of GA showed better performance than classical GA in terms of quality solutions, avoiding local optima and computational time. Apart from these techniques some hybrid methods like lambda based hybrid genetic algorithm [106] and tabu search integrated genetic algorithm [101] have also been used to solve this multiobjective problems. Table 4 presents a summary of GA and its variants applied to solve CEED problem for different units and constraints. 3.2. Particle swarm optimization (PSO) Inspired by the social behavior of the animals and organism like fish schooling, herd of elephants, bird flocking etc., particle swarm optimization (PSO) technique was developed by Kennedy and Eberhart [107] in 1995. PSO provides a population-based search approach, where individuals called particles, can be deemed as bird, fly and change their position with time to find the optimum solution in a multidimensional search space [108]. These individuals or particles initialized randomly by their position and velocity at the beginning of the search and are the probable solutions of the fitness function. Each particle iteratively evaluates the fitness of the probable solutions and adjust its position. Fig. 3 describes the steps of PSO. The best solution obtained by the particle is known as pbest. They

Guvenc et al. [24]

Dhanalakshmi et al. [96]

27

28

2011

Gravitational Search Algorithm (GSA)

Shaw et al. [95] 26

2012

Liang et al. [94] 25

2012

Mousa et al. [62] 24

2012

Optimization for Environmental/Economic Dispatch Problem Combined economic and emission dispatch problems of power systems Combined economic and emission dispatch solution

Hybrid multi-objective quantum genetic algorithm Multi-objective dynamic multi-swarm particle swarm optimizer Gravitational search algorithm (GSA)

Ziane et al. [93] 23

2014

Ho et al. [92] 22

2014

Economic emission load dispatch

Cuckoo Search Algorithm (CSA)

Economic Emission Load Dispatch with Multiple Fuel Options Multi-objective economic dispatch solution

Multi-objective Simulated Annealing

performance metrics, and they confirm that the algorithm has potential to solve the CEED and DEED problems. The result comparisons have indicated that the proposed method is a highly effective method. Experimental results show a proficiency of Simulated Annealing over other existing techniques in terms of robustness. Applied successfully to both of the objectives simultaneously and can work for more than two objectives as well. Provides sound optimal power flow results. The standard IEEE 30-bus six-generator test system is used. Results showed that the proposed approach is efficient. The results obtained confirm the potential and effectiveness of the proposed algorithm compared to some other algorithms surfaced in the recent literatures. In order to see the effectiveness of the proposed algorithm, it has been compared with other algorithms in the literature. Results show that the GSA is more powerful than other algorithms. An approach based on Technique for Ordering Preferences by Similarity to Ideal Solution (TOPSIS) is used to decide the choice of a solution from all solutions. 2014

Remarks Technique (s) Authors No.

Table 3 (continued)

Year

Application

F.P. Mahdi et al.

6

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Table 4 Summary of GA techniques and its variants in optimizing CEED problem. No.

Author/year

Variants

Objective (s)

Units Considered

Constraint (s)

1. 2. 3. 4. 5. 6. 7.

Song et al. (1997) [39] Abido (2003) [100] Kumarappan and Mohan (2004) [101] Basu (2008) [102] Osman et al. (2009) [103] Dhanalakshmi (2011) [96] Basu (2013) [104]

Fuzzy logic-controlled GA NPGA GA-TS NSGA-II Epsilon dominance-based GA Modified NSGA-II NSGA

Single and multiobjective Multiobjective Multiobjective Multiobjective Multiobjective Multiobjective Multiobjective

6 6 6 10 6 5, 19 4, 6

2 3 3 3 3 2 3

optimal solution then the above mentioned methods. Basu et al. [110] presented goal attainment based PSO to solve CEED problems, where fuel cost and emission are treated as competing objectives. Goal attainment method was used to convert this multiobjective problem into a single objective optimization and then the problem was handled by PSO. Later, other versions of PSO like modified PSO [111], local search integrated PSO [112], quantum behaved PSO [63], refined PSO [113], fuzzy adaptive modified theta PSO [114], bare-bones multiobjective PSO [115], improved PSO [65], modulated PSO [116], enhanced PSO [117], gravitational enhanced PSO [118] and selfadaptive PSO [119] have been used to solve CEED problems. S Lu and C Sun proposed two versions of quantum behaved PSO (QPSO) in their papers [60,63], where they introduced quantum computing idea into PSO to solve CEED problems. Obtained results showed that QPSO can yield high quality solutions with good convergence properties. Zhang et al. [115] developed a new variation of PSO named bare-bones multi-objective PSO to solve CEED problems. This algorithm has three distinctive features like it has such a particle updating strategy that does not require control parameters tuning, a mutation operator that has time variable action range which expand the search capability and a particle diversity based approach in order to update the global particle leaders. The developed method was tested with several trials on the IEEE 30-bus test system and compared with total ten multiobjective optimization algorithms including three well known versions of PSO which validated it's capability to generate excellent results with certain superior characteristics. Description of all these versions of PSO for solving CEED problems is beyond the scope of this paper. However, references are given for the interested readers to learn more about them. A short summary of PSO and its variants for solving CEED problem is presented in Table 5

keep updating their positions according to their own experience and the experience of their neighbors. The particle, which has the best fitness value among all the particles is known as gbest. The velocity of each particle changes using the equation below,

Vi k +1 = wVi k + c1 rand1 × ( pbesti k − Xi k ) + c2 rand2 × (gbest k − Xi k )

(13)

where Vi stands for the velocity of individual i at iteration k, w stands for weight vector defined below in (14), c1 and c2 are acceleration constant, rand1 and rand2 are random numbers between 0 and 1, Xik stands for the position of individual i at iteration k, pbestik is the best position of individual i until iteration k and gbestk is the best position of the group until iteration k.

w = wmax −

wmax − wmin × Iter Itermax

(14)

Again, particles change their position in multidimensional search space by modifying velocity in (13) using the following equation,

Xi k +1 = Xi k + Vi k +1

(15)

PSO and its different variants are one of the most used optimization techniques to solve combined economic emission dispatch problem [109]. As per the investigations performed by the authors, Kumar et al. [42] at first proposed PSO to solve combined economic emission problem. They obtained results for a test system of six generating units and compared them with conventional methods, RCGA and hybrid genetic algorithm, which showed that PSO gave better global

3.3. Cuckoo search algorithm (CSA) Inspired by the brood parasitism of some cuckoo species and Levy flight [120] behavior of some birds and insects, Yang and Deb [121] developed cuckoo search algorithm in 2009. It's relatively a new nature inspired efficient algorithm with few controlling parameters and successfully used in solving many global optimization problems [122]. Recent literature reveals that CSA performs better than both particle swarm optimization (PSO) and GA by providing higher success rate of finding optimal solutions [121]. The inclusion of Levy flights in global search process makes it more efficient than other algorithms that uses standard random walks [123]. Cuckoo are wonder birds, they have mysterious and aggressive reproduction strategy. Cuckoo engage the obligate brood parasitism by laying their eggs in the nests of other host birds. However, if a host bird discovers the eggs in her nest are not of her own, it will either throw these intruder's eggs away from her nest or simply abandon its nest and build a new nest elsewhere [124]. The three idealized rules that CSA follows are: (i) each cuckoo lays only one egg in randomly chosen nest at a time, 2) the best nests that contain high quality eggs (solution) will carry over to the next generations, 3) the total number of host nests is fixed, and pa ∈ [0, 1] is the probability that an egg laid by cuckoo will be discovered by the host bird. Fig. 4 shows the flowchart of CSA.

Fig. 3. Flowchart of PSO algorithm.

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Table 5 Summary of PSO techniques and its variants in optimizing CEED problem. No.

Author/year

Techniques

Objective (s)

Units Considered

Constraint (s)

1. 2. 3. 4. 5. 6. 7. 8.

Kumar et al. (2003) [42] Basu (2006) [110] Wang and Singh (2008) [111] Wang and Singh (2009) [112] Bahmanifirouzi et al. (2012) [114] Zhang et al. (2012) [115] Jadoun et al. (2015) [116] Jadoun et al. (2015) [117]

PSO Goal attainment-based PSO Modified PSO PSO with local search Fuzzy adaptive modified theta PSO Bare-bones PSO Modulated PSO Enhanced PSO

Multiobjective Multiobjective Multiobjective Multi-area multiobjective Single and multiobjective Multiobjective Multiobjective Multi-area multiobjective

6 5 6 4 5, 10 6 6, 10, 40 40

2 3 2 4 3 2 3 4

CSA was used to solve CEED problems keeping reliability as third objective by Chandrasekaran et al. in 2014 [27]. This problem with many objectives was formulated as a non-smooth and non-convex multi-objective problem considering the valve-point effects of thermal units. Later, fuzzy set theory had been exploited to find a best compromise solution from the obtained Pareto-optimal set. The proposed method was validated by testing it on a benchmark of 6-unit test system, IEEE RTS 24 bus system, and IEEE 118 bus system.

algorithm was inspired by the echolocation or bio-sonar characteristics of bats and based on three idealized rules, (i) echolocation technique of bats to sense distance and to calculate difference between their prey (food) and background barriers, (ii) bats vary their wavelength (λ0) and loudness (A0) to search for their prey. They also regulate frequency and rate of their emitted pulses, depending on the distance of their prey, (iii) assuming that the loudness is varied from a large (A0) value to a minimum constant value (Amin). The positions (xi) and velocities (vi) of the virtual bats are updated using the following equations,

3.4. Bat algorithm (BA)

ni = n min + (n max − n min ) α

(16)

vit = vit −1 + (xit − xcgbest ) fi

(17)

Bat algorithm was pioneered by Xin-she Yang [125] in 2010. This

xit

=

xit −1

+

vit

(18)

where α, ni, nmin and nmax are random vector with range from 0 to 1, frequency of pulse, minimum and maximum frequency respectively. Again, vit , vit −1, xit , xit −1 and xcgbest stand for velocity of bats at time t, velocity of bats at time (t-1), position of bats at time t, position of bats at time (t-1)and current best global location found by the bats respectively. Fig. 5 illustrates the operation of bat algorithm. Bat algorithm is easy to implement and more powerful than its predecessor GA and PSO [125]. One of the reasons behind its superiority is that it utilizes some of the major advantages of these algorithm (GA and PSO) in structured way. Almost at the same time Ramesh et al. [28], Nikman et al. [126] and Azizipanah-Abarghooee [127] proposed bat algorithm for solving CEED problems. Ramesh et al. [28] tested proposed bat algorithm in two different system consisting of three and six units respectively and separately compared with Refined GA (RGA), NSGA-II, ABC and hybrid GA-TS. Compared result showed that bat algorithm is efficient, easy to implement and performs better in minimizing both the objectives simultaneously. Nikman [126] in his paper compared each objectives of CEED separately with a wide range of previously used methods from the literature which justified bat algorithms supremacy over other algorithms. However, authors don’t find any comparison with other methods considering both the objectives simultaneously. Azizipanah-Abarghooee [127] proposed an improved bat algorithm with a new mutation strategy to avoid local optima and improve convergence characteristics. An interactive fuzzy based technique had also been exploited to deal with this multiobjective problem. 3.5. Teaching and learning based optimization algorithm (TLBO) Teaching and learning based optimization (TLBO) is a newly invented nature-inspired population based metaheuristic algorithm developed by Rao et al. [128] in 2011. TLBO is basically based on the classical teaching and learning phenomena and thus has two phases, (i) teacher phase and (ii) learner phase. TLBO is gaining growing attentions in recent years for some of its notable advantages over other methods like it has simple structure, easy to implement, can provide faster convergence and doesn’t have algorithm-specific parameters [129]. The population in TLBO is considered as a group of students and different control variables are considered as different

Fig. 4. Flowchart of cuckoo search algorithm.

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and suitability to solve problems like combined economic emission dispatch. With several modifications in the original TLBO algorithm, Niknam et al. [130] proposed a highly modified theta-multiobjective TLBO (θ-TLBO) to solve CEED problems. Several modifications such as phase angles based optimization process had been considered instead of the design variables to handle the nonlinear characteristics of the problem more efficiently, a new learning technique had been adapted to avoid entrapping into local optima, a new approach of selecting the population had been employed to achieve uniformly distributed Pareto optimal and to guide the individuals to seek the lesser explore regions a niching strategy had been exploited. Furthermore, a fuzzy clustering technique was utilized to handle the size of the repository as well as to obtain compromised solutions. Obtained results demonstrated that θTLBO is capable of providing good quality, robust and well distributed solutions. Individual comparison for dynamic economic dispatch (DED) and emission dispatch showed θ-TLBO performed better than other well-known methods such as GA, PSO, DE etc. but interestingly authors don’t find any comparison where results of both the objectives are compared simultaneously with other methods to show θ-TLBO's superiority as a multiobjective method. On the other hand, PK Roy et al. [131] proposed a quasi-oppositional TLBO (QOTLBO), where they adopted oppositional-based learning (OBL) concept into TLBO to accelerate the convergence rate. This paper presented detailed comparison for combined economic emission problems with other state of the arts methods such as GSA, MODE, PDE, NSGA-II and SPEA 2, which demonstrated its superiority of yielding better results than these methods. Shabanpour-Haghighi and his fellow researchers [132] proposed modified TLBO (MTLBO), where a self-adapting wavelet mutation strategy was utilized during the modified phase. Furthermore, a fuzzy technique was exploited to avoid large repository size and to get compromised solution. This method was found to be more effective than conventional TLBO. 4. Hybrid methods Hybrid methods make use of two or more algorithms in order to utilize their strengths and mitigate their weakness in solving complex problems and thus are found to be effective to find global optimal solution for complex combined economic emission dispatch problems with different constraints. Gong et al. [133] presented a hybrid method combining PSO with DE and integrating several techniques such as time variant acceleration coefficients, crowing distance-based technique etc. to get global optimal result for CEED problems. Obtained results were found to be well distributed, efficient and superior to many other algorithms like linear programming (LP), NSGA, SPEA and fuzzy clustering PSO (FCPSO). A. Bhattacharya et al. [134] exploited hybrid DE-BBO method to solve complex economic emission dispatch problem considering power demand and operating limit constraints. This method was pioneered by Gong et al. [135] in order to utilize the exploration and exploitation capability of DE and BBO methods respectively and previously used for economic dispatch (ED) problem [136]. Three different test systems with different degree of complexities were considered to test the performance of this method. The important findings of the paper are DE-BBO method effectively eliminates premature convergence and offers robust solution with high level of computational efficiency. Two of the most well-known optimization methods i.e. GA and PSO were incorporated with each other by Roselyn et al. [43] to tackle CEED problems. GA was combined with PSO to enhance the effectiveness of this method. Elitism technique was utilized before updating population in the algorithm, while position of the particles and velocity were updated by GA based mutation strategy to attain the global best position (solution). PSO has the ability to converge quickly and has found not to be affected much by initial population, whereas GA is more efficient in fine tuning although it is affected much by initial population. Thus, to overcome each other's drawbacks and take

Fig. 5. Flowchart of bat algorithm [126].

subjects offered to the students. The result of a student is somewhat analogous to the fitness function of the problem. This optimization technique mimics the teaching-learning ability of teacher and students where teacher is a highly qualified person with profound knowledge and he always tries to improve the average knowledge of his students. Students also interact with themselves to learn and improve their knowledge. The basis of evaluation of their knowledge will be their obtained result. Fig. 6 shows the flowchart of TLBO. Population, design/control variables and termination criteria should be defined at first. It will then evaluate the population and calculate the mean and difference in order to modify the solutions based on the best solution. It will continue to update, until and unless one of the termination conditions is met. Krishnanand and his colleagues [54] were the first group of researchers to apply teaching and learning based optimization (TLBO) method for solving combined economic emission dispatch problem. They tested the proposed method with a system of 40 thermal units and compared the results with DE, which verified its feasibility 9

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Fig. 6. Flowchart of TLBO algorithm [128].

(ERELD) considering a wide range of constraints such as power balance constraint, power generation limits, ramp rate limits, prohibited operating zones constraint, spinning reserve constraint, frequency deviation limit etc. Authors have found this paper as one of the most organized and well developed power generation system models to represent actual power generation system. The precision of NelderMead method and the power of BF method to cover a wide search area were simultaneously utilized to solve this many-objective problem. Hooshmand et al. [36] found that consideration of frequency constraint in the problem allowed them to solve the problem by controlling the

benefits from their advantages, PSO is usually utilized at the early stages, while GA is utilized at later stages [137] in PSO-GA hybrid algorithm. This proposed hybrid method was found to give better results with faster convergence and took less memory space. However, authors don’t find any comparison with other well-established standalone or hybrid methods except PSO to assert claim in its superior performance. Fig. 7 describes the flowchart of PSO-GA hybrid method. Hooshmand and his men [36] proposed a new hybrid bacterial foraging-Nelder–Mead (BF-NM) algorithm to solve tri-objective power generation, spinning reserve and emission load dispatch problem

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Fig. 8. Number of papers by methods/techniques used for solving CEED problem.

Fig. 9. Number of citations vs. methods/techniques used for CEED problem.

Fig. 7. Flowchart of PSO-GA hybrid algorithm [136]. Fig. 10. Number of papers published for solving CEED problems by years (2005–2016).

frequency within its permissible limit, which ultimately increase the social welfare for consumers. The superiority of this proposed hybrid method had also been verified after comparing with other stand-alone methods like GA, BFA and PSO. Recently, a new multiobjective hybrid evolutionary algorithm was proposed by Roy et al. [32], where they hybridize chemical reaction optimization (CRO) with differential evolution (DE) in order to have faster convergence and to avoid trapping into the local optima to solve dynamic economic emission dispatch (DEED) problem. The proposed algorithm

performed better in 10-unit system than improved bacterial foraging algorithm (IBFA), RCGA and CRO in terms of fuel cost and computational time but slightly outperformed by IBFA in terms of amount of emission. For a large 30-unit system, it outperformed a large number of methods such as IPSO, EP and chaotic DE (CDE) etc. in terms of cost function and computational time but again slightly outperformed by deterministically guided PSO (DGPSO). Table 6 is showing the summary of some hybrid techniques in optimizing CEED problem.

Table 6 Summary of hybrid techniques in optimizing CEED problem. No.

Author/year

Techniques

Objective (s)

Units Considered

Constraint (s)

1. 2. 3. 4. 5. 6. 7. 8. 9.

Gong et al. (2010) [133] Bhattacharya et al. (2011) [40] Hooshmand et al. (2012) [36] Arunachalam et al. (2013) [46] Sayah et al. (2014) [35] Younes et al. (2014) [34] Jiang et al. (2014) [138] Zhang et al. (2015) [33] Roy and Bhui (2016) [32]

PSO-DE DE-BBO BF-NM ABC-SA DE-HS FFA-GA PSO-GSA DE-SA DE-CRO

Multiobjective Multiobjective Manyobjective Multiobjective Multiobjective Single and multiobjective Multiobjective Multiobjective Multiobjective

6 3, 6 13 6, 10 6, 20, 40 6 6 5, 10 10, 30

2 2 10 2 2 5 4 3 3

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understandable as web of science is more selective research database than Scopus and authors have only access to the database of web of science from the year of 2005–2016. Authors have discussed about GA and PSO earlier in the paper. Total number of citations by methods graph as depicted in Fig. 9 also follow the same trend as PSO-based papers for solving CEED problems cited the most number of times. Fig. 9 also clarifies that researchers focus more on GA and its variant than DE based algorithms in their papers for solving CEED problems. However, many hybrid versions of DE to solve CEED problems make DE-based techniques ahead of GA-based techniques in the earlier graph (Fig. 8). The research trend to solve CEED problems has been depicted in Fig. 10, where it can be seen that research concentrating on solving CEED problems is on its peak in recent years. Although, this area of research is not new still researchers around the world are attracted to solve this problem with newer idea and techniques. From the research, authors have found that researchers are more interested to develop and use hybrid techniques to solve CEED problems to exploit and utilized benefits of different methods and overcoming each other's shortcomings.

5. Fuzzy compromised solution for ceed problem In multiobjective combined economic emission dispatch problem, there are two objective functions i.e. economic and emission dispatch functions to be considered in the same time and therefore it is difficult to compare two solutions. If solution vectors X1 and X2 are Paretooptimal, then neither set of vectors should be better than the other. It is because if X1 provides better result for one objective then X2 would provide better result for another objective. Both of the solution sets are competing or non-dominating solutions in nature. In multiobjective economic emission problem, it is difficult to find the best solution from many non-dominated solutions. In order to compare these solutions and get the best compromised solution some mechanism is needed to combine both the objectives in accordance with the decision maker's preference. Fuzzy set theory is often used by the researchers to get the best compromised solution from many non-dominated solutions. As both the objectives of fuel cost and emission are conflicting in nature, it is not possible to get the least fuel cost and at the same time least emission. But, it is desirable to get a dispatch option that can reduce both fuel cost and emission as much as possible. Degree of satisfaction (DoS) to each objective is assigned by fuzzy membership functions, where DoS reflects the merit of their objective in a linear scale of 0–1 (worst-best). If Fi is a solution in the Pareto-optimal set in the ith objective function and is represented by a membership function µi, which can be defined as [139],

⎧1, Fi ≤ Fi, min ⎪ ⎪ Fi, max − Fi , Fi, min < Fi < Fi, max μi = ⎨ F i, max − Fi, min ⎪ ⎪ 0, F ≥ F ⎩ i i, max

7. Future direction Authors want to give some future directions on solving this complex multiobjective problem before going to conclusion. The major factors that decide which optimization technique or combination of techniques would be suitable for multiobjective CEED problem are convergence characteristics, reliability and suitability of the solution, robustness and computational efficiency. Thus, the algorithm or combination of algorithm that addresses all the major factors could be considered as ideal optimization technique for this multiobjective problem. The idea of quantum computing could be used with existing well-established method like cuckoo search and bat algorithm to make it computationally efficient and robust. The reason we select cuckoo search and bat algorithm is that it has been proved that both of these techniques utilize some nature-inspired features (as discussed in the above section) that enable them to perform better than most of the techniques like PSO and GA. One improved version of bat algorithm i.e. novel bat algorithm (NBA) could be more realistic choice with the integration of quantum computing phenomena. Authors assume that more advanced features of NBA [140] with quantum computing phenomena will be very useful to achieve optimal exploitation and exploration capability to achieve global optimal solution for multiobjective CEED problem. Furthermore, it has also be found [141] that integration of quantum computing with self-adaptive probability selection and chaotic sequences mutation improve the convergence characteristics significantly. It also helps to avoid trapping into local optima. Future research should also be directed to use Levy flight feature instead of random walk in quantum integrated novel bat algorithm as it also improve global search process (as discussed earlier).

(19)

where Fi,max and Fi,min stand for the maximum and minimum values of ith objective function respectively. For each non-dominated solution R, the normalized membership function µR can be calculated as below, N

μR =

∑i =1 μiR M

N

∑ j =1 ∑i =1 μiR

(20)

where M stands for the number of non-dominated solutions. The solution that contains the maximum of µR is the best compromised solution. All solutions in Pareto-optimal set are arranged in descending order according to their membership function in order to guide the decision maker with a priority list of non-dominated solutions. 6. Discussion Authors have conducted an exhaustive and thorough search in two of the most well-known research databases, Scopus and Web of science. Many keywords were used in search with the help of their advanced search option that usually used to refer solving combined economic emission dispatch problem using optimization methods. Emission dispatch problem is also defined as environmental dispatch problem in some literatures. Traditionally, mathematical modelling based classical methods alone are not so successful in solving CEED problems. That is why in this paper, authors have focused on advanced non-conventional methods, especially nature inspired methods. Authors compile the results from these two research databases as updated up to 26 of August 2016. Fig. 8 shows the number of papers published to solve CEED problems by some notable methods such as ANN, GA, PSO, DE etc. From the above figure, it is clear that particle swarm optimization and its different variants are the most used techniques to solve CEED problems. Differential evolution and its variants along with genetic algorithm and its variants are the second and third most used techniques. We can see from the figure that papers published in web of science indexed journal is less than Scopus indexed journals, it is

8. Conclusion This paper presents a comprehensive review on recent advanced optimization strategies to solve CEED problems. Classification of different optimization methods have been shown with their advantages and disadvantages. Different formulation criteria of CEED problem such as quadratic and cubic function along with their major equality and inequality constraints have been presented to give a clear idea to the readers about actual CEED problem. This paper mainly focuses on nature-inspired advanced optimization methods for solving multiobjective CEED problem. Description of some well-known and promising methods have been given along with their flowcharts and working principle. Again, authors have discussed fuzzy set theory to find comprised solution from a set of Pareto-optimal solutions of CEED problems. Later, some graphical data has been shown to figure out the 12

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