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The Nucleus 50 , No. 2 (2013) 99-115

Application of evolved evolutionary algorithms for the solution 99

P a k i s t a n

T h e N u c l e u s

The NucleusA Quarterly Scientific Journal of Pakistan

Atomic Energy Commission

N C L E A M , I S S N 0 0 2 9 - 5 6 9 8

APPLICATION OF EVOLVED EVOLUTIONARY ALGORITHMS FOR THE SOLUTIONOF DIFFERENT ASPECTS OF HYDROTHERMAL SCHEDULING

A COMPREHENSIVE OVERVIEW

M. IQBAL, F. KARIM, *S. HAROON, M. ASHRAF, I. AHMAD, T. NADEEM and A. AHMAD

Department of Electrical Engineering, University of Engineering and Technology, Taxila, Pakistan

(Received February 22, 2013 and accepted in revised form May 02, 2013)

Hydrothermal Scheduling (HTS) presents highly complicated, non-linear and multi-constrained optimization problem.

Usually very turbulent and non-convex search space is linked with Hydrothermal (HT) Scheduling problem. So rather arobust and powerful optimization tool is required to optimize this problem efficiently. In literature, so far, many powerfuland robust optimization algorithms have been employed for the solution of HTS problem. Genetic Algorithm (GA)represents one of the most established while Bacterial Foraging Algorithm (BFA) represents one of the newestEvolutionary Algorithms. Both GA and BFA are being actively deployed to solve non convex optimization problems,where conventional approaches have rather failed to provide acceptable results. The aim of this research paper is toprovide a comprehensive survey of literature related to both GA and BFA as effective optimization algorithms for thesolution of various aspects of HTS problem. The outcomes alongwith both strengths and weaknesses of individualalgorithms are also discussed.

Keywords: Hydrothermal Scheduling, Optimization Algorithms, Heuristic Algorithms, Bacterial Foraging Algorithm,Genetic Algorithm, Search Space

1. Introduction

HTS is an important aspect of not onlydetermining the optimal usage of both hydro andthermal resources economically so as to meet theload demand alongwith minimization of netoperational cost as much as possible but alsosatisfying a large number of coupling constraintsrelated to both hydro and thermal power plants likegeneration limits, rate of water discharge,inequality constraints representing water reservoirand hydraulic continuity limitations etc. [1]. On thebase of time intervals for which HTS has been

performed, the problem can be classified as shortterm HTS (STHTS), mid term HTS (MTHTS) andlong term HTS (LTHTS). Since energy productionfrom water is the cheapest one and below minimaloperational cost is usually related to hydro powergeneration so, minimizing the utilization of fossilbased fuels in thermal power plant while exploitingthe maximum amount of water resource for energyproduction is the main idea of problem.

In the nutshell, alongwith all constraints andlimits HTS problem presents highly complicated

and nonlinear search space for which our objectiveis the minimization of net operational cost. Withoutquestions HTS problem is one of the mostchallenging and complicated problem of PowerSystem Operation [1].

2. Mathematical Modelling of HTS Problem

The generalized mathematical modeling of HTSproblem consists of defining both objective functionand constraints related to thermal and hydropowerplant [2].

2.1. Objective Function

The optimization of HTS problem includes theminimization of electric energy cost for thermalgeneration during predefined time intervals [3].

Here, M defines the total no. of thermal powerplants; T defines the scheduling intervals;

defines the fuel cost function ofthermal power plant in respective time interval and

Corresponding author : [email protected]
mailto:[email protected]:[email protected]


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100 M. Iqbal et al.

represents the total operational cost of allthermal power plants overall intervals.represents power generation of i th thermal powerplant in respective time interval. Here fuel costcurve with valve point loading effect is a non-smooth, non-differentiable rectified sine model [4].

Here, a i, b i, c i, d i and e i are machine constants.represents the lower limit of i th thermal

power plant.

2.2. Constraints

2.2.1. Load Balance

Out of all important equality constraints is thesuccessful fulfillment of load demand [1].

Here, is the load demand; definesthe line losses and defines hydro powerrelated to j th hydro power plant in t interval, Ndefines the total number of hydro power plants.Here, the hydro plant power can be obtained by anonlinear relation between water discharge,

volume of water and hydro power generation [5].

Here, V is the respective volume; Q is thehydraulic parameter representing water dischargerate in corresponding time interval t and C is thecoefficient related to hydro power plant.

2.2.2. Generation Capacity

The corresponding generation capacities ofthermal as well as hydro power units have ofcourse some limits [1].

Have to be satisfied as well. Hererepresents lower limit of i th thermal power plant.

represents upper limit of i th thermal powerplant. is lower limit of jth hydro power plantand is upper limit of jth hydro power plant.

2.2.3. Hydraulic Continuity Equation

Hydraulic continuity equation has to be satisfied

for hydro power plants in case of interconnected orcascade network [2].

Here shows the scheduling intervals; isthe volume for corresponding hydro power plant incorresponding time; I(j,t) is the inflow; Q(j,t) is thedischarge and is the spillage.

2.2.4. Physical Limitations on ReservoirParameters

There are some sort of physical limitations onboth water discharge and volume of water that can

be accommodated in reservoir [1].

Here represents lower limit ofdischarge for j th hydro power plant.represents upper limit of discharge for j th hydropower plant. is the lower limit of volume for

jth hydro power plant and is the upper limitof volume for j th hydro power plant.

2.2.5. Initial and Final Reservoir Storage Volumes

Usually there is some sort of boundary on howmuch volume of water can be accommodated inreservoir before and after the production of energyfrom water so, on base of that the initial and finalstorage volumes are defined from [1].

Here represents starting or initialvolume of j th hydro power plant andrepresents ending or final volume of j th hydro

power plant.It is very clear that HTS problem is a very

complicated and multi-constrained generationscheduling problem so rather a very robust andpowerful optimization algorithm is required tooptimize this problem successfully.

3. Adoptation of Various OptimizationMethodologies for the Solution ofDifferent Aspects of Hts Problem inLiterature

Adaptation of huge number of optimizationtechniques to solve various aspects of HTS


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Figure 1. Categorized optimization techniques being used to solve HTS problem

problem manifests the importance and broadnessof respective research area. Various categories ofdifferent optimization algorithms have beenmodified and hybridized to continuously reduce theoperational cost of coordinated operation of HTpower system. The roots of both HTS problem andadaptation of different basic optimizationtechniques for solution of HTS problem can beguessed by historical survey based research articlebeing presented [6]. The earliest optimizationmethods were the base load procedures, bestpoint loading and incremental cost criterion.Nowadays different optimization methods andalgorithms are in use especially, in the recentyears, Evolutionary Search Algorithms (EA) havearoused intense interest due to their flexibility,versatility and robustness in seeking a globallyoptimal solution for HTS problems [7-9] .

Overall, the popular and mostly usedoptimization methods for the solution of differentaspects of HTS problem can be further classified

as below. Figure 1 shows the exactly similarcategorized division of different methodologiesbeing adopted in literature to solve complicatedHTS problem. A very popular and efficient surveybased research article regarding solution ofSTHTS problem has been presented [2]. Theemphasis of our research article is to provide anenhanced and comprehensive survey of how HTSproblem has been solved using different evolvedEvolutionary optimization techniques. Theadaptation of different algorithms, their merits anddemerits regarding HTS and test systems beingadopted alongwith outcomes being obtained are

also discussed in this article (Most of the data

being collected is based on IEEE/IET/Elsevier/Springer/Taylor and Francis databases).

Classical Simplex and Derivative basedTechniques

Deterministic Methodologies

Heuristic Algorithms

3.1. Classical Simplex and Derivative Based

TechniquesClassical category contains Gauss-Siedel and

Newton-Raphson based simplex and derivativebased mathematical optimization techniques whichusually make use of single and multiple stepsDerivative and Hessian operators. Conventionaloptimization techniques have usually been foundto be suitable for relatively simpler, convex,differentiable and linear optimization problems withsmooth search space.

For the solution of HTS problems the classicaltechniques although have proved to be very

simpler to apply but were only suitable andproductive for differentiable and smooth fuel costcurves for thermal production facilities [1] and alsohave the problem of trapping to local optima whilenever reaching global optimum for non smoothsearch space [6]. However, they have shown onegreat strength, that is to find the local optimum indue time. This particular strength of classicalderivative based techniques has motivateddifferent researchers to modify and coverweaknesses of other Heuristic and mathematicaloptimization algorithms by merging them withclassical approaches. A very simple HTS problem

with smooth fuel cost curves and limited energy


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[10] has been solved via derivative based NewtonRaphson (NR) method. Here due to nativeweakness of algorithm a smooth, differentiable andlinear model has been optimized using NRapproach while not considering the valve pointloading effects. In [11] Gauss-Newton andStationary Newton algorithms have been adoptedalongwith Interior points (IP) based methodology toperform economical generation scheduling of HTpower system using Jacobian Operator. Accordingto authors the results being obtained have showedthe accuracy of proposed hybrid approach.

For more realistic problems like HTS problemhaving non-smooth, non-differentiable fuel costcurves, classical techniques have usually been

failed so the application of these techniquesnowadays is limited to theory.

3.2. Deterministic Approaches

Deterministic approaches present a wide classof optimization search techniques based ondeterministic transition rules and mathematicalbackground, mostly optimizing the problem bydecomposing it in sub problems and solving subproblems while relaxing or using multipleregression or bundled technique. Either way theysolve the problem by linking sub problems inmultiple iterative processes. Deterministic

approaches can be further divided in LagrangianRelaxation (LR), Benders Decomposition (BD),Integer and Mixed Integer programming (MIP),Dynamic Programming (DP), Linear and Nonlinearprogramming (NLP) techniques.

Solution of HTS problem using differentdeterministic approaches will be discussed herealong with merits and de-merits of each techniqueagainst their application on HTS problem.

3.2.1. Lagrangian Relaxation (LR)

Probably the most used and well establishedmathematical programming approach fromDeterministic algorithms to solve HTS problem isthe LR technique. It is iterative baseddecomposition technique where multipleconstraints are congested in main objectivefunction using Lagrangian multipliers then mainproblem is divided in sub problems and each subproblem is solved individually while relaxing othersub-problems (constraints) to obtain dual solution.The corresponding difference between primal anddual solution triggers the termination criteria of LRtechnique [1]. The deficiencies related toLagrangian based techniques are mainly trappingto local optima [1] and oscillations around global

optima [12], so different modifications have beenadopted to tackle with this flaw of LR technique likeaugmentation of multipliers in LR method andhybridization of LR based techniques with otherEvolutionary and Deterministic algorithms [13] thusimproving efficiency of LR based algorithmsagainst complicated optimization problems.

For HTS problem different flavors of LR basedalgorithms have been adopted like in [13] newmultiplier updating augmented LR based hybridapproach has been adopted to optimize systemcontaining HT and natural gas generation units.Hybrid approach not only nullified the nativeproblems of LR but very efficient results have beenobtained against HTS problem. In [14] LR has

been adopted as hybrid approach together withExpert Systems (ES) to optimize STHTS problem.Results have shown the general accuracy ofalgorithm against complicated optimizationproblems like HTS itself.

In the nutshell LR based modified and hybridalgorithms performs at par with other robustalgorithms being adapted for HTS problemoptimization. The only problem which has to becontrolled relating to LR based techniques is thesevere oscillations around global optima.

3.2.2. Benders Decomposition (BD)

Just like LR based method of dual optimization,BD is another Deterministic approach. It also workson same principle as LR based techniques do i.e.dividing main problem in different sub problemsthen solving each sub problem individually whilerelaxation other sub-problems. It is basically adecomposition strategy for Lagrange based dualproblem. Alongwith same working philosophy asLR based techniques the problems related to BDtechnique are also same like oscillations aroundglobal optimum, never quite reaching it. BDactually works by linking different stages ofproblem while discretizing each stage and solvingusing forward and backward iterative methodology.Sometimes, BD is also known as Dual DynamicProgramming (DDP) approach.

For HTS optimization problem BD technique isusually modified or adopted as hybrid approachlike in [15] Multistage Benders Decomposition(MSBD) has been adopted to solve complicatedHTS problem. MSBD is actually DDP basedapproach where problem is solved using iterativebackward and forward recursion process. Resultsbeing obtained have shown strength of thistechnique against other programming techniques

to solve HTS problem. In [16] Nested Benders


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Decomposition (NBD) approach has been adoptedto optimize HTS problem. The main problem hasbeen decomposed in small sub problems and eachsub problem has been further divided in smallnano problems. Each nano problem has beensolved using Benders approach. Thus wholetechnique has worked like a cage of NBDapproach. Results being obtained have shownpromising characteristics of correspondingalgorithm against complex HTS problem. Theadaptation of BD technique as hybrid approach isto cover problems like oscillations around globaloptima, never quite reaching optimum against thesolution of complicated HTS problems [15, 16] .

3.2.3. Integer and Mixed Integer Programming

This category of mathematical programmingtechniques present a wide class of Mixed Integerbased optimization methodologies that are used asoptimization algorithms for many complexproblems like HTS problem. Integer basedprogramming techniques usually work on variableswhich only take integer values. Linkage of presentand past value is also one of the main steps ofInteger Programming techniques. Theseoptimization algorithms are further divided in thetwo parts

Branch and bound Mixed Integer programming

techniquesCutting plane Integer Programming techniques

Although problems like trapping to local minimaand poor convergence are not related to MixedInteger Programming techniques but due to hugedimensions of HTS problem programming basedtechniques take high computational times like in[17]. Mixed Integer Programming has been used tosolve complicated HTS problem. To avoidpremature convergence and long computationaltime taken by Mixed Integer Programming some ofthe constraints have been relaxed. In [18] Mixed

Integer based Non-Linear Programming has beenadopted to cope with native problems of MixedInteger Programming against complex HTSproblem. The main objective function has beenoptimized by Mixed Integer Programming alongwith satisfaction of constraints using Non-LinearProgramming. Likewise the same Mixed IntegerNon-Linear Programming approach has beenadapted in [19] to solve more realistic HTSproblem based on Portuguese network. Resultsbeing obtained are quite satisfactory.

3.2.4. Dynamic Programming (DP)

DP is one of the most popular Deterministic

mathematical programming approaches for non-convex and very complicated optimizationproblems. DP has been extensively used for HTSproblem solution. It divides main problem indifferent small sub problems, solving each problemin parallel with other problems and checking eachpossible state. As problem increases in size,states, due to increase in the dimensions ofproblem DP takes exceptionally high time which isalso known as dimensionality curse [20] . DP isusually considered as an effective mathematicaltechnique to resolve the complex optimizationproblems since its first formulation by Bellman in

1954. The long computation time and storagememory requirements are the main drawbacks ofconventional DP, but with the course of time usingStochastic programming instead of conventionalDeterministic programming they are reduced.

For HTS problem, which is very complexDynamic problem, DP although have shown goodresults but takes exceptionally large computationaltime due to dimensionality curse so in [21] extended DP has been adapted to optimize HTSproblem. The main problem has been divided insub thermal and hydro problems. Then each subproblem has been further divided in nanoproblems. The algorithm has been further assistedby mixed coordination methodology between sub-problems to cope with the native problem of DPagainst complicated HTS problem. In [22] multi-pass DP has been used to solve HTS problem andto cover the problem of DP, EvolutionaryProgramming has been integrated in DP to solveHTS problem.

3.3. Heuristic Algorithms

The limitations and a bag of mix resultsregarding usage of Conventional searchtechniques against optimization of highlycomplicated and nonlinear problems have openeda wide research area toward more optimal androbust class of optimization algorithms. Heuristiccomputational methods represent the largestbranch of optimization algorithms representingsimulated nature inspired intelligent algorithms.Most of the algorithms from Evolutionary andHeuristic category follow Darwins theory (naturalselection or only fitter one will survive) thuscopying some sort of natural process to seek theperfection in the process of optimization. Heuristicalgorithms have found application in almost everyfield of science. From simpler mathematical


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problems to real time weather simulations,Evolutionary Heuristic algorithms have shownexcellent results and robustness. In this article, wewill only discuss the adoptability of most renownedHeuristic algorithms for optimization of HTSproblem. Thus against HTS problem most usedHeuristic algorithms are categorized as naturesinspired Evolutionary and Knowledge basedalgorithms from Artificial Intelligence (AI) category.These algorithms are basically divided in to twoparts.

One part containing evolutionary algorithmslike Genetic Algorithm (GA), DifferentialEvolution (DE), Evolutionary Programming(EP), Particle Swarm Optimization (PSO),

Simulated Annealing (SA), Honey Bees Algorithm (HBA) and Bacterial Foraging Algorithm (BFA).

Second part shadowing Fuzzy-Logic (FL),Neural Networks (NN) and Expert Systems.

Most of algorithms from Heuristicmethodologies have been adopted to optimizeHTS problems [23]. Heuristic algorithms followpath of nature to solve complex problems asnature does itself. Algorithms usage foroptimization of HTS problems and their merits anddemerits will be discussed one by one.

3.3.1. Simulated Annealing (SA)SA is a very popular and well established

Evolutionary algorithm based on the principle ofmetallurgical annealing process and has found tobe suitable for optimization of complex problems.

Annealing is the process where materials likeglass, ceramics and different crystals are cooledgradually after heating them at very temperaturesto attain perfected states. It follows the law ofthermodynamics as when any metal is slowly icedin its melted state it attains the state of perfectionbut sometimes if non-perfected state is achieved

whole process is restarted again to achieveperfection [24] . So if SA is not able to achieveglobal optimum, it takes exceptionally high time.For the perfect state to be achieved, cooling rate isan important decision. The algorithm wasintroduced by Metropolis in 1950 [25] based onMonte Carlo annealing process. Thecorresponding algorithm is also sometimes termedas probabilistic hill-climbing and stochasticrelaxation [25] . Although SA has found numerousapplications regarding optimization in differentfields but the algorithm shows excellent results forpower system operation like SA has been adopted

in literature to perform HTS in [26, 27] . Overallalgorithm consists of the following steps

Production of candidate solution: Initializationof both temperature and solution. Next solutionis found by perturbation of last solution.

Acceptance criteria: The algorithm continueson the principle that next solution must havelower energy.

Cooling schedule: The proper mathematicalmodel is adopted for cooling criteria of nextsolution like exponential cooling selection(ECS).

Stopping criteria: How the algorithm wouldstop i.e. either based on repetition of solution

or fixed number of iterations etc.For HTS problem SA has been used mainly

with some modifications or as hybrid approacheslike in [28] a comprehensive comparison betweenSA and GA has been performed against solution ofcomplex medium term HTS problem. Bothtechniques have been found to be equally suitablefor HTS problem. The prime reason to use hybridapproach is to cope with native problems of SAand to support SA against complex problems likeHTS problem.

3.3.2. Particle Swarm Optimization (PSO)

PSO is probably the most popular populationbased Evolutionary algorithm optimizing nonconvex and nonlinear problems using social,cultural and intelligent swarming behavior ofdifferent animals like flock of birds and school offish. It was first introduced by Kennedy andEberhart in 1995 [29] for continuous mathematicaloptimization problems. Perhaps it represents thesimpler algorithm having small number ofparameters. PSO basically belongs tomathematical background where it is consideredas a very poor technique but for power systemoptimization problem this algorithm is very suitabledue to its random nature [23] .

In PSO algorithm, a particle is accelerated insearch space. The particle moves toward globaloptimum by evaluating both its own and othersfavorable paths in each next iteration. From wholeclass of Heuristic algorithms, PSO is the mostsuccessful algorithm for HTS problems [7]. A broadresearch area is linked with PSO like reactivepower and voltage control [30] , voltage stabilizer[31], economic dispatch (ED) with valve pointloading effects [32] and short term HTSscheduling. The whole algorithm works as follows


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Initialization of particles velocity and positionin nth dimensional space.

Update the velocity and position using Pbestand Gbest in each subsequent generation.

Termination criteria.

However, PSO needs some tuning related toparameters so as to perform optimally particularlyfor HTS problems. So far HTS problems, PSO ismostly used in modified form like in [7] smallpopulation based PSO has been used to optimizeSTHTC problem. Here small population has beentaken to help PSO to find global optima inminimum time and to cope with the problemsrelated to small population different operators havebeen used. In [33] modified PSO has beenadapted to optimize HTS problem and the resultsbeing obtained have found to be better than SA.Hybrid approach has been applied in [34] whereDifferential Mutation operator has been used toassist PSO to find optimum best against HTSproblem thus quantum behaved PSO (QPSO) hasbeen found to be suitable against both PSO andDifferential Evolution (DE) individually.

3.3.3. Evolutionary Programming (EP)

EP presents a huge class of Evolutionaryoptimization algorithms applied directly to solvemany complex optimization problems like HTSproblem. Works on same philosophy as GA likerandom initialization of strings of solutions acrosssearch space and modifying strings in each nextiteration but EP based techniques e.g. infamousDifferential Evolution (DE) differs in operators used[35]. The whole algorithm can be described asfollows:

Initialization

Mutation

SelectionTermination

EP has been adopted to optimize HT powersystem like in [36] where EP has been modified byinserting Cauchy mutation in basic EP to showacceptable results against HTS problem. Generallyboth EP and DE have merits and demerits similarto GA like taking exceptionally high computationaltime to solve complex problems like HTS. So, tocope with these problems DE is used as hybridapproach alongwith other Heuristic andDeterministic approaches to solve HTS problemse.g. in [37] Chaotic Local Search (CLS) has beenused to cover problems like long computationaltime and poor convergence of DE against complex

STHTC problem. The results being obtained arecomparable to both PSO and DE individually. In[38] Sequential Quadratic Programming (SQP) hasbeen adapted to assist DE to cover its poorconvergence characteristics and tracking to localoptima against complex STHTC problem.

3.3.4. Honey Bee Algorithm (HBA)

HBA is the newest social behavior basedHeuristic algorithm converting both foraging andsocial behavior of honey bees in excellentoptimization methodology.

Despite the young age of HBA, it is well-definedalgorithm and has found to be suitable foroptimization of complex problems like economic

dispatch (ED) and HTS. In [39] BA has found to bebetter than modern Heuristic algorithms for thesolution of ED problem which is much similar toHTS problem. If we compare this algorithm with oldand famous nature inspired Evolutionaryalgorithms like GA, PSO and SA, HBA has showedmore promising results for complex power systemoptimization problems [39].

3.3.5. Neural Networks and Fuzzy Logic BasedTechniques

Neural Networks (NN) is basically a hugedistributed processor just like human brain which

has the ability of learning, storing, linking andgeneration of some sort of information. Learning isspecialized through weight-tune procedurealongwith storing and linking of inputs-information.Once learning is done, processor has the ability todevelop outputs i.e. Generation. This algorithm hasno limitations just like most other techniquesexcept the difficulty of designing NN processoritself and then training it for specific problem. Forpower system optimization problems especiallyHTS problem although NN shows itself as verypowerful tool but has seldom used primarily due todifficulty in application of NN to solve HTS

problem. In [40] Hopfield Neural Network has beenused alongwith LR methodology to solve STHTCproblem. Test system being adopted containedmultiple pumped storage hydro and thermalmachines. The results being obtained have beencompared with both LR and QuadraticProgramming (QP) based approaches and thisparticular technique has been found to be suitablefor STHTC.

Alongwith NN, Fuzzy-Logic (FL) basedtechnique is also another popular technique fromartificial systems. It has found to be suitableforvery complex problems having inaccurate data and


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Figure 2. Survey on application of BFA to solve various engineering problems.

stochastic nature. It basically operates on somedefinite rules and rules are operated based onfuzzy membership functions and fuzzy logic data. It

works on fuzzy variables (not clearly defined) i.e.set of variables like between 1 and 0. If eachmember of fuzzy set is well defined it contains allthe necessary information of solution set and if it isnot, problems related to huge computational timeand poor convergence occur. The process usuallycontains following three steps.

Fuzzification of data structure.Conversion of data structure to solution set.Defuzzification of solution set.

FL has been adopted to optimize HT powersystem operation like in [41] to solve complicatedand non-linear LTHTC problem open loopfeedback controller using Neural Fuzzy basedforecasting system has been used. The algorithmhas been tested on test system containing 19hydro power plants with cascaded reservoirs.Results being obtained are found to becomparable to those obtained after the applicationof DP on similar test system. Fuzzy-systems hasalso been applied as hybridization approach tosolve HTS problem like in [42] Fuzzy basedhybridized PSO based approach has been used tosolve HTS system to cover prematureconvergence related to PSO against complex

problems. Results have showed that respectivealgorithm is fast with respect to convergencespeed against both PSO and DP individually.

4. Bacterial Foraging Algorithm (BFA)

4.1. Working Philosophy

BFA is one the newest natures inspiredoptimization algorithm. It uses the foraging activityof bacteria, E. coli, as an optimization process.Bacterial foraging process was presented as anefficient optimization process in [43] where it wasused to optimize distributed controller. It has alsobeen used in the harmonic estimation [44] , optimalpower flow [45] and optimal design of powersystem stabilizers [46] . However for very complexdynamic optimization problems, BFA shows poorconvergence characteristics due to very highamount of randomization in the algorithm. Likewisefor HTS problem this algorithm again showed poorconvergence results so some sorts of modificationswere adopted in this algorithm [47] . BFA can beused as hybrid approach with other suchalgorithms like PSO [48] . The whole foragingprocess is divided in

Chemo-taxisReproduction

Elimination and Dispersal

0

10

20

30

40

50

60

70

2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012

N o .

o f P a p e r s

b e

i n g

P u

b l i s

h e

d

Years

Solution of Various Engineering Problems uing BFA in

Recent Years


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Chemo-taxis is the main part of foragingbehavior of E. coli bacteria where the bacteria firsttumbles (A very small step) checking whichdirection is most suitable for him based onconcentration of edible materials and thenswimming in same direction thus maximizing theamount of food in the end of foraging. Swim isusually performed in the form of steps and at eachstep concentration of food is checked so swimcontinues on the base of increasing concentrationof food. The chemo-taxis process is applied onwhole amount of bacteria in population. Forengineering and science problems, a brief surveyof usage of BFA from 2002 to 2012 is presentedbelow in Figure 2.

On base of food collected bacteria divideskeeping the population constant thus wholealgorithm from [43] can be plotted as below

4.2. BFA as an Optimization Algorithm

Step-1

To initialize the main parameters

P// Dimensions of search area (Population)

S// Amount of bacteria in each population

// Chemo-taxis steps of each bacteria

// Swim length in the form of steps

// Number of reproduction events

// Number of elimination-dispersal loops

// Probability of elimination-dispersal

// Swim-step length

// initialized location of bacterium (random)

//parameters for swarming

xrepellant // Height of repellant effect

z repellant // Width of repellant effect

xattractant // Depth of attractant effect

zattractant // Width of attractant effect

//Initialization of events loop

Step-2

// Elimination/dispersal loop

Step-3

// Reproduction loop

Step-4

// Chemo-taxis loop

//Start Chemo-taxis

for

Evaluate the cost function of eachbacterium at initialized random position using

(1)

Here,

Let = so that the cost can beminimized by moving to new locations.

Generate a random vector in [-1; 1] range.

Compute which shows direction and smalldisplacement to check concentration of foodusing

Tumble using

(2)

Compute at new position using(1)

Start swimming, let w = 0 (swim step counter)

While w < (until steps of swim are not over)

Let w =w + 1

For each step w, position of bacteria willchange using (2)

At each new position after swim, calculate costfunction using (1)

If < // Reducing strategy

Let =

Continue swimming in same direction (at eachstep cost gets lowered) and calculate new

using (1) in the end of swim

else let w= //stop counter for swim

Repeat the whole process for each bacterium(i=i+1 if i s)

Compute best (lower) cost obtained ( )


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If j go to Step-4 ( ). Else endchemo-taxis loop

//Start ReproductionStep-5

Evaluate the total health of each bacterium inthe end of chemo-taxis loop as follows

(3)

The health of bacterium notifies us about theamount of nutrients it has got over its entirelifespan. On base of this collection bacterium willeither reproduce or destroy in reproduction loop.

Sort bacteria according to amount of nutrientsthey have collected i.e. on the base of theirhealth .

The bacteria having higher number of nutrientswill pass through reproduction where they willsplit and other bacteria having lower number ofnutrients will die out eventually.

Step-6

If r < , go to Step-3 ( )

Else end reproduction loop

//Start Elimination/Dispersal

Step-7

On the base of probability , either eliminateor disperse selected amount of bacteria tokeep the population constant.

Step- 8

If ed < , go to Step-2 ( ),otherwise end algorithm.

5. Hydrothermal Scheduling Using BFA

BFA has showed satisfactory results againstoptimization of complicated HTS problems likeoptimization of short term variable head HTproblem and multi-objective optimization of HTS

problem [47], although some modifications arealways adopted to optimize these complexproblem. Mostly chemo-taxis step has beenmodified as decreasing function with respect totime. Beside HTS problem, BFA is also used tosolve complex ED problems where efficiency ofthis algorithm has been found to be on par withother such nature inspired Meta-Heuristicalgorithms [49]. Brief review of stances when BFAhas been used for HTS problem is describedbelow. Figure 2 contains graph representing no. ofpapers published relating to BFA application tosolve different aspects of HTS problem in recent

years. Here data being collected mostly belongs toIEEE, IET, Science Direct, Taylor & Francis andSpringer.

I.A. Farhat and M. E. El-Hawary in [50] havedevised nature inspired Enhanced BacterialForaging (EBFA) optimization algorithm to solvedynamic, highly nonlinear and multi-constrainedvariable head short term HT coordination(VHSTHTC) problem. The variable nature of headof water in this problem has made correspondingproblem even more beefy and complex. Authorsalso have considered real-time constraints relatedto both hydro and thermal power plants. Onlysmooth fuel cost curves for thermal machines havebeen considered here. According to authors, raw

BFA technique has showed poor convergencecriteria along with long computational time requiredto solve STHTC problem so some type of criticalchange in infrastructure of BFA (in the form ofchange in chemo-taxis step ) has been usedto show optimum results for STHTC problem. Theaccuracy of proposed enhanced BFA has beentested by applying EBFA on two test systems. Onetest system contained two thermal and two hydromachines and other test system contained fivethermal and four hydro machines. According toauthors EBFA has showed promising resultsagainst solution of complex VHSTHTC problem.

I.A. Farhat and M. E. El-Hawary in [51] havesolved a system containing 4 hydro units and 3thermal units. The test system presented highlynonlinear, complicated and dynamic multi-reservoircascaded short term HT coordination (STHTC)problem (scheduling from 1 day to 1 week). Real-time constraints from both hydro and thermalpower plants have been realized and non-smoothfuel cost curves for corresponding thermalgeneration units have been considered. Theproblem has been optimized by authors usingmodified Bacterial Foraging Algorithm (MBFA)where according to authors basic BFA has failed toconverge and been trapped in local minima. Herethe critical change in algorithm of raw BFA(dynamically decreasing chemo-taxis step) hasmanaged to show good results for the solution ofSTHTC problem.

I.A. Farhat and M. E. El-Hawary in [52] havemodified BFA which they then have termed asImproved Bacterial Foraging Algorithm (IBFA), tosolve complicated, dynamic and highly nonlinearSTHTC problem considering environmentalaspects. As a bi-objective optimization problem,


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Figure 3. No. of Papers using BFA to solve HTS problem in corresponding years.

one has to minimize both cost and pollution in thisproblem. So this flavor of STHTC problem haspresented dual objectives and multiple constraintswhich have made this problem very unique of itsown nature. Basic BFA has been modified byauthors, an improved BFA to solve this bi-objectiveproblem successfully. Real-time constraints andsmooth fuel cost curves for thermal machines have

been considered here. Algorithm has been testedon test system containing two thermal and twohydro machines. According to authors IBFA hasshowed promising results while optimizing bi-objective STHTC problem.

I.A. Farhat and M. E. El-Hawary in [53] havedevised a strategy to perform simultaneous unitcommitment (UC) and ED of highly nonlinear anddynamic fixed head short term hydrothermalcoordination (FHSTHTC) problem using natureinspired BFA algorithm to obtain optimum cost ofnet unit of electric energy alongwith satisfactorysolution of constraints. In fixed head problem,virtually a large reservoir has been presented sono effect on head of water hence constant head.

Although here authors have approximated fixedhead opposed to [50] but still system is complexone because real-time constraints have beenconsidered alongwith smooth fuel cost curves.BFA has showed excellent characteristics to solvethis type of multi-constrained complex problemexcept some deficiencies like trapping to localminima and poor convergence. To cope with thisproblem of raw BFA authors have modified thechemo-taxis step of BFA to solve FHSTHTCproblem, they have termed this version of BFA as

modified Bacterial Foraging Algorithm, MBFA. Totest the accuracy of algorithm, MBFA has appliedon two fixed head test systems. First systemcontained one thermal power plant and two fixedhead hydro machines while second test systemcontained one fixed head hydro and three thermalmachines. Results being obtained fromimplementation of algorithm on actual test systems

have showed accuracy of modified BFA.I. A. Farhat and M. E. El-Hawary in [54] have

proposed a modified bacterial foraging algorithm,an Improved Bacterial Foraging Algorithm, IBFA tosolve dynamic, nonlinear and multi-constrainedmulti-objective STHTC problem. Criticalimprovements have been introduced in basic BFAlike changes in chemo-taxis step to optimize thisbi-objective STHTC problem where both fuel costsand pollution have been minimized at the sametime. Weighting factors have been adapted to havean acceptable compromise between both objectivefunctions. Real-time constraints alongwith smoothfuel cost curves have been considered here. Thealgorithm has been tested on test system of twothermal and two hydro machines. According toauthors this improved flavor of BFA has showedpromising results against complex bi-objectiveoptimization problems like MOSTHTC problemitself.

I. A. Farhat and M. E. El-Hawary in [47] haveoptimized very complicated, highly non-linear andmulti-constrained scheduling of HT power systemfor 1 day to one week, short term hydrothermalcoordination (STHTC) problem. STHTC problem

presents highly non-linear search space where

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both UC) and ED problems have been performedsimultaneously. In the nutshell successfuloptimization of STHTC problem requires veryrobust algorithm. BFA is one of the newest andefficient Evolutionary algorithms. In literature it hasbeen used to solve complex optimization problems[54]. However for multi-dimensional problems likeSTHTC, this algorithm has shown poorconvergence characteristics so some sort of criticalimprovements have been introduced by authorsand they termed that improved version, an IBFA.STHTC problem has been solved using IBFA andaccuracy of algorithm has been proved by applyingthis algorithm on test system having one hydro andone thermal machine.

6. Genetic Algorithm6.1. Working Philosophy

Genetic algorithm (GA) is rather mostestablished and popular population basedHeuristic optimization algorithm. GA was firstintroduced by Goldberg (2000) as a tool for globaloptimization of complex, non-differentiable andnon-linear problems with turbulent search spaceand multiple constraints [55] . The trapping to localminima is no longer a problem for GA as thealgorithm randomly takes the set of solutions allover search space and optimize those sets with

each next iteration (generation) using differentoperators.

If we have a look at the brighter side, GA is verysuitable for the optimization of complex problemsbut if we have a look at darker side of GA, it suffersfrom high computational time and repetition ofsolution sets in large no. of iterations [56] . To solvethese problems related to GA, it is mostly used inmodified form like real coded GA [57] , hierarchicalGA or as hybrid approach. Just like otherstochastic Evolutionary algorithms GA is a globaloptimizer and performance of GA is mainlyassociated with the configuration of followingoperators

Initialization

Random generation of population

Fitness evaluation

Selection

Cross-over

Mutation

Termination

7. Hydrothermal Scheduling Using GA

In case of HTS problem GA has shown

excellent performance [58] . However it is not acomplete algorithm like it takes exceptionally highcomputational time once reaching optimum region.So to solve this problem related to GA,hybridization of GA with other optimizationtechniques like classical derivative basedtechniques has proved to be very favorable forHTS problems optimization like in [59] both GA andclassical lambda iterative technique have beenhybridized to optimize short-term orientedcomplicated problem consisting of HT powersystem and results obtained are quite fruitful. HTSusing different flavors of GA as optimization

methodologies will be discussed here. Figure 4represents a survey on adaptation of GA as anoptimization algorithm to solve HTS in recentyears.

In [60] Carneiro, A. A. F. M., P. T. Leite, et al.have adapted GA based approach as analternative to classical methods for the optimizationof operational planning of HT power system.Previous work on the same problem suffered fromconvergence, over simplification andapproximation of the problem. The results beingobtained from GA based approach have showedthat this approach can be one of the bestalternative to classical techniques in terms of itsparallelize operation, simplicity, less processingtime, dealing various plants of different behaviors.

Orero and M.R. Irving in [55] have suggestedthe solution of HTS problem using GA frameworkconsidering various constraints. The problem beingconsidered here is a multi reservoir cascadedhydro system having complex relationshipsamongst various variables of the function. Theproblem under consideration has beensuccessfully implemented using GA due to itscapability of handling such a multi-constraint

problem, simplicity, and robustness.In [61] STHTS problem has been solved using SAand GA and two hybrid techniques. All equality,inequality constraints have been taken intoaccount. The advantage of the proposed algorithmis that unlike other algorithms, the thermalgenerators have not been considered as singleunit and the proposed algorithm has reflected thecharacteristics of individual generator. The resultsbeing obtained have shown that the new proposedalgorithms can be more efficient and reliable.


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Figure 4. No. of Papers using GA to solve HTS problem in recent years

Xiangping, M., Z. Huaguang, et al. in [62] haveaddressed the main drawbacks of the GA that areslow speed and premature convergence and havetried to avoid these drawbacks using newlyproposed algorithm called Fast Synthetic Genetic

Algorithm (FSGA). The new algorithm has theadvantages like fast speed of convergence, higherprecision and most important one is reduction inpopulation size. A hybrid algorithm has beendeveloped by combining FSGA with Backpropagation (BP) and applied for short termeconomic dispatch of HT power system. Hybridalgorithm also has solved the problem of longtraining time of BP. The proposed algorithm hasbeen tested using three units and six buses testsystem. The results being obtained have beencompared with classical methods and comparisonshave shown that run time has reduced.

In [56] GA based model has been proposed forSTHTS problem. The proposed algorithm hasdivided the problem into two sub problems whichare UC and ED. Future cost curve has been usedto optimize the hydro energy required during thatspecific period. The performance of the proposedmodel has been improved by new technique usedfor representations of candidate solution andapplying a set of expert operators. Results beingobtained have been compared with the resultobtained previously from the same problem whensolved with LR, Mimetic algorithm, and GA and the

results being obtained are competitive with theprevious results.

Zoumas, C. E., A. G. Bakirtzis, et al. in [8] havesolved HTS for economic dispatch using Enhanced

Genetic Algorithm (EGA) and Priority List method.HTC problem is divided into two sub problems,Hydro part has been solved using EGA and isformulated as nonlinear, mixed integer optimizationproblem. Where thermal part has been solvedusing priority list method. Hydro as well as thermalconstraints have been taken into considerationwhile applying the proposed algorithm. Forimproving GA performance problem specificgenetic operators have been adapted. The mainadvantage of EGA over simple GA beingdemonstrated is the flexibility in modeling.

Leite, P. T., A. A. F. M. Carneiro, et al. in [63] have used a hybrid GA for the optimal operation ofBrazilian HT power system. In this paper acomparison has been presented between Gradientmethod and GA based on Gradient method (Hybridmethod). All equality and inequality constraintshave been taken into account. Two new geneticoperators, gradient mutation and gradient directmutation have been used in the proposed newhybrid algorithm. Results being obtained fromhybrid technique are quite promising and it hasbeen shown that the proposed method can beused for planning also.

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Kumar, S. and R. Naresh in [64] have solvedSTHTS problem with continuous and non smooth/non convex cost function using an efficient realcoded Genetic Algorithm (RGA) techniqueconsidering travel time between cascadedreservoirs and valve point effect in addition to allequality and inequality constraints. A comparisonbetween real coded and binary coded GA (BGA)has been demonstrated when implemented for thesame multi chain, cascaded HT power system. Thecomparison has shown that RGA is better thanBGA in its simplicity, ease of implementation,efficiency, small population size and effectiveconstraints handling without penalty parameters.

In [65] STHTS has been solved using

decomposition and GA based optimal power flow(OPF). The problem has been divided into two subproblem, Hydro sub problem has been solvedusing Discharge Proportional to Demand Method(DPDM), and Lambda iteration technique has beenused to solve the thermal sub problem includingline losses. To control line losses GA basedoptimal power flow has been used. Results beingobtained from DPDM have been compared withthat obtained from Average Inflow method (AIFM)and it has been found that DPDM is simple,reliable and efficient.

Ozyon, S., C. Yasar, et al. in [66] haveproposed GA based solution to environmentaleconomic power dispatch problem of a HT powersystem. The paper aims to reduce NOx emissionbesides the reduction of total thermal cost.Weighted Sum Method (WSM) has been adaptedto convert the multi objective environmental EDproblem into single objective optimization problem.GA has been then used to solve the singleobjective ED optimization problem.

In [67] Basu, M. has proposed Non Dominatedsorting Genetic Algorithm-II for the economicenvironmental dispatch of fixed head hydro thermal

(FHHTS) power system. Non Dominated SortingGA-II has been used to handle the problem asmulti objective problem as the said problem isnonlinear, constrained multi objective problem. TheGA been implemented here is the real coded andall constraints have taken into account. Theobjective of the paper is to reduce SOx and NOxemission alongwith the reduction of fuel cost.Results being obtained are compared with theresults obtained from previously used techniques;strength Pareto Evolutionary algorithm 2 and multiobjective DE and some others and found betterthan previous results.

Sasikala, J. and M. Ramaswamy in [58] haveintroduced a new Optimal Gamma basedtechnique using GA for the improvement of thecomputational speed, robustness and accuracy inscheduling of large HT power system problems.The simulation results being obtained from theproposed technique have showed that thistechnique is fast, has lower population size and isaccurate as compared to previously usedtechniques.

In [68] Mid-Long term hydrothermal schedulinghas been solved using a Hybrid GA consideringthe final water storage and effects of water headalso. The problem has been decomposed into twosub problem thermal and hydro as usual. The GA

has been used only to solve Hydro problem wherethe mathematical programming algorithm has beenused for thermal problem. Results and comparisonshow that Hybrid GA is much better than GA incase of large non linear system and is because inlarge system GA technique solves both hydro andthermal sub problem using GA so the searchbecome more stochastic. Hybrid GA has highercomputational speed and accuracy.

Kumar, V. S. and M. Mohan in [59] haveproposed short term HT scheduling solution usingGA. As usual problem has been divided into twosub problem; hydro and thermal sub problems.Thermal sub problem has been solved usinglambda iterative technique while GA has beenadapted for hydro sub problem. Line losses andline flow constraints have also taken into accountfor GA based optimal power flow (OPF). Wheneverline flow constraints are violated the GA basedOPF has been applied. Line losses have beencomputed using Fast Decoupled Load Flow(FDLF). The proposed technique has reducedcomplexity that is introduced due do calculation ofline losses in each step, reduces computationalspeed and gives near optimal global solution.

In [57] STHTS has been solved considering theuncertainty involved in this process. Thescheduling of HT system is probabilistic in manyaspects like stochastic operating cast curves ofthermal units, Load demand is also uncertain,inflow in the reservoir is also probabilistic. Theseuncertain parameters have been treated asrandom variables. RGA has used with specialarithmetic-average-bound-blend crossover andwavelet mutation operators. All equality andinequality constraints have been taken intoaccount. Operation limits violations have also been


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taken into account using exterior penalty method.The results obtained are promising.

8. ConclusionsThis paper not only provides a brief survey on

how both well established and newly developedEvolutionary algorithms, both GA and BFA standsfor solution of different aspects of very complicatedand highly non-linear HTS problem but also a briefsurvey on how this HTS problem has been solvedusing different other methodologies in literature ispresented. The merits and de-merits of nearly eachmethodology has been discussed on the behalf ofHTS problem. Most of the time BFA algorithm failsto converge successfully against HTS problem butwith some minor modifications BFA stands equallywith other famous algorithms showing quitepromising results while GA has already shownitself as very robust and versatile optimizationalgorithm where many modifications and differenthybrid flavors of GA have been adapted by variousresearcher to optimize the economical schedulingof HT power system. Despite the young age ofBFA, it shows its strength against complex HTSproblem compelling other researchers to at leasthave a single look on both BFA and GA algorithmsagainst their complicated optimization problems.

References

[1] B.F.W. A.J.Wood, Power GenerationOperation and Control, 2nd ed., I. John Wiley& Sons, New York, USA (1996).

[2] I.A. Farhat and M.E. El-Hawary, ElectricPower Systems Research 79 (2009) 1308.

[3] K.K. Mandal and N. Chakraborty, ElectricPower Systems Research 78 (2008) 1972.

[4] Y. Hong-Tzer, Y. Pai-Chuan and H. Ching-Lien, IEEE Transactions on Power Systems 11 (1996) 112.

[5] N. Sinha, R. Chakrabarti and P.K.Chattopadhyay, IEEE Transactions on PowerSystems 18 (2003) 214.

[6] G.S.C. M.E. El-Hawary, Optimal EconomicOperation of Electric and A.P. PowerSystems, New York (1979).

[7] Z. Jingrui, W. Jian and Y. Chaoyuan, IEEETransactions on Power Systems 27 (2012)142.

[8] C.E. Zoumas et al., IEEE Transactions onPower Systems 19 (2004) 1356.

[9] S. Titus and A.E. Jeyakumar, InternationalJournal of Soft Computing 2 (2007) 13.

[10] C. Yasar and S. Fadil, Solution to LossyShort-Term Hydrothermal CoordinationProblem with Limited Energy Supply ThermalUnits by Using First Order Gradient Method,International Conference on Electrical andElectronics Engineering, ELECO (2009).

[11] M. Kleina, L. C. Matioli, D. C. Marcilio, A. P.Oening, C. A. Vallejos, M. R. Bessa, and M.L. Bloot, http://people.ufpr.br/~matioli/ minha-home/arquivos/submetido_ieee_2011.pdf.

[12] N.J. Redondo and A.J. Conejo, IEEETransactions on Power Systems 14 (1999)89.

[13] C. Liu, M. Shahidehpour and J. Wang,Generation, Transmission & Distribution, IET4 (2010) 1314.

[14] S. Salam, K.M. Nor and A.R. Hamdan,Generation, Transmission and Distribution,IEEE Proceedings 144 , (1997) 482.

[15] T. Norbiato dos Santos and A.L. Diniz, , IEEETransactions on Power Systems 24 (2009)1383.

[16] K. Nolde, M. Uhr, and M. Morari, Automatica44 (2008) 1585.

[17] O. Nilsson and D. Sjelvgren, Mixed-IntegerProgramming Applied to Short-TermPlanning of a Hydro-Thermal System, PowerIndustry Computer Application, ConferenceProceedings, IEEE (1995).

[18] M. Kadowaki , et al., Short-Term HydropowerScheduling Via an Optimization-SimulationDecomposition Approach, PowerTech, IEEE,Bucharest (2009).

[19] J. P. S. Catalao , et al., Mixed-IntegerNonlinear Programming for Head-DependentShort-Term Hydro Scheduling, InternationalConference on Power Engineering, Energyand Electrical Drives, POWERENG '09 (2009).

[20] E.P.S.A.o.O. J.A. Momoh, Marcel and N.Y.Dekker, Electric Power System Applicationsof Optimization (2001).

[21] T. Jianxin and P.B. Luh, IEEE Transactionson Power Systems 10 (1995) 2021.

[22] Y. Sen-Nien, Using Hybrid Ep and Multi-PassDynamic Programming for HydrothermalCoordination Considering ReasonableSpinning Reserve, Transmission andDistribution Conference and Exhibition,2005/2006 IEEE PES (2006).

[23] N. Sinha and L. Loi-lei, Meta Heuristic

Search Algorithms for Short-Term


16/17


114 M. Iqbal et al.

Hydrothermal Scheduling, InternationalConference on Machine Learning andCybernetics (2006).

[24] J.T. Saraiva, et al., Electric Power SystemsResearch 81 (2011) 1283.

[25] A.J. Monticelli, R. Romero and E.N. Asada,Fundamentals of Simulated Annealing, JohnWiley & Sons, Inc. (2007).

[26] K.P. Wong and Y.W. Wong, Generation,Transmission and Distribution, IEEEProceedings 141 (1994) 507.

[27] M. Basu, International Journal of ElectricalPower & Amp, Energy Systems 27 (2005)147.

[28] V. H. Ferreira and G. H. C. Silva, NaturalOptimization Applied to Medium-TermHydrothermal Coordination, 16th Inter-national Conference on Intelligent System

Application to Power Systems (ISAP) (2011).[29] J. Kennedy and R. Eberhart, Particle Swarm

Optimization, Proceedings of IEEEInternational Conference on Neural Networks (1995).

[30] G. Zwe-Lee, IEEE Transactions on PowerSystems 18 (2003) 1187.

[31] M.A. Abido, IEEE Transactions on EnergyConversion 17 (2002) 406.

[32] P. Jong-Bae, et al., IEEE Transactions onPower Systems 20 (2005) 528.

[33] K.K. Mandal, M. Basu, and N. Chakraborty, Applied Soft Computing 8 (2008) 1392.

[34] C. Sun and S. Lu, Expert Systems with Applications 37 (2010) 4232.

[35] K. K. Mandal , et al. , Comparison of DifferentVariants of Differential Evolution Applied toShort-Term Economic Generation Sche-duling of Hydrothermal Systems, IPECConference Proceedings (2010).

[36] E. Dai and B. E. Turkay, Power Dispatch ofHydrothermal Coordination UsingEvolutionary Algorithm International Confe-rence on Electrical and ElectronicsEngineering (ELECO 2009).

[37] Y. Lu et al., Energy Conversion andManagement 51 (2010) 1481.

[38] S. Sivasubramani and K. Shanti Swarup,Energy Conversion and Management 52 (2011) 757.

[39] S. Tiacharoen , et al. , Solving Various Typesof Economic Dispatch Problem Using Bees

Algorithm, International Conference on

Electrical Engineering/Electronics ComputerTelecommunications and InformationTechnology (ECTI-CON) (2010).

[40] V.N. Dieu and W. Ongsakul, InternationalJournal of Electrical Power &Amp, EnergySystems 30 (2008) 93.

[41] M. S. Zambelli and S. Soares, A PredictiveControl Approach for Long TermHydrothermal Scheduling, Power SystemsConference and Exposition (PSCE '09),IEEE/PES (2009).

[42] C. Wenping , et al. , A Fuzzy Adaptive ParticleSwarm Optimization for Long-Term OptimalScheduling of Cascaded HydropowerStation, Power Systems Conference andExposition (PSCE '09) IEEE/PES (2009).

[43] K.M. Passino, Control Systems, IEEE 22 (2002) 52.

[44] S. Mishra, IEEE Transactions onEvolutionary Computation 9 (2005) 61.

[45] W. J. Tang , et al. , Bacterial Foraging Algorithm for Dynamic Environments, IEEECongress on Evolutionary Computation (CEC2006).

[46] T.K. Das, G.K. Venayagamoorthy and U.O. Aliyu, IEEE Transactions on Industry Applications 44 (2008) 1445.

[47] I. A. Farhat and M. E. El-Hawary, Short-TermHydro-Thermal Scheduling Using anImproved Bacterial Foraging Algorithm,Electrical Power & Energy Conference(EPEC), IEEE (2009).

[48] I. Banerjee and P. Das, Evolutionary Multi-Objective Bacterial Swarm Optimization(Mobso) : A Hybrid Approach SimulatedEvolution and Learning, Springer Berlin /Heidelberg (2010).

[49] I.A. Farhat and M.E. El-Hawary, Generation,Transmission & Distribution, IET 4 (2010)989.

[50] I. A. Farhat and M. E. El-Hawary, Schedulingof Variable-Head Hydro-Thermal GenerationUsing an Enhanced Bacterial Foraging

Algorithm, 24th Canadian Conference onElectrical and Computer EngineeringCCECE) (2011).

[51] I. A. Farhat and M. E. El-Hawary, Short-TermCoordination of Hydro-Thermal Systems withCascaded Reservoirs Using BacterialForaging Algorithm, 24th CanadianConference on Electrical and Computer

Engineering (CCECE) (2011).


17/17



[52] I. A. Farhat and M. E. El-Hawary, Short-TermHydro-Thermal Scheduling with Environ-mental Considerations Using Bacterial For a-ging Algorithm, 24th Canadian Conferenceon Electrical and Computer Engineering(CCECE) (2011).

[53] I. A. Farhat and M. E. El-Hawary, Fixed-HeadHydro-Thermal Scheduling Using a ModifiedBacterial Foraging Algorithm, IEEEConference on Electric Power and Energy(EPEC) (2010).

[54] I. A. Farhat and M. E. El-Hawary, Multi-Objective Short-Term Hydro-ThermalScheduling Using Bacterial Foraging

Algorithm, IEEE Electrical Power and Energy

Conference (EPEC) (2011).[55] S.O. Orero and M.R. Irving, IEEE

Transactions on Power Systems 13 (1998)501.

[56] E. Gil, J. Bustos and H. Rudnick, PowerSystems, IEEE Transactions on PowerSystems 18 , (2003) 1256.

[57] J. Dhillon and D. Kothari, Journal of SystemsScience and Systems Engineering 20 (2011)87.

[58] J. Sasikala and M. Ramaswamy, ExpertSystems with Applications 37 (2010) 3352.

[59] V.S. Kumar and M.R. Mohan, InternationalJournal of Electrical Power & Amp, EnergySystems 33 (2011) 827.

[60] A. A. F. M. Carneiro , et al. , A Genetic Algorithm Approach to Optimize the

Operation Planning of Hydrothermal SystemScheduling, Proceedings of Fifth BrazilianSymposium on Neural Networks (1998) 253.

[61] S. Yin and Wa Wong, International Journal ofElectrical Power & Amp., Energy Systems 23 (2001) 565.

[62] M. Xiangping, Z. Huaguang and T. Wanyu,Mathematics and Computers in Simulation51 (2000) 341.

[63] P. T. Leite , et al. , Hybrid Genetic Algorithm Applied to the Determination of the OptimalOperation of Hydrothermal Systems, NinthBrazilian Symposium on Neural Networks(SBRN'06) (2006).

[64] S. Kumar and R. Naresh, InternationalJournal of Electrical Power & Amp; EnergySystems 29 (2007) 738.

[65] M. Mohan, Solution to EnvironmentalEconomic Power Dispatch Problems inHydrothermal Power Systems by UsingGenetic Algorithm, International Conferenceon Electrical and Electronics Engineering(ELECO 2009).

[66] M. Basu, Applied Soft Computing 11 (2011)2845.

[67] S. Jun , et al. , A Hybrid Algorithm for Mid-Long Term Hydrothermal GenerationScheduling, Mechatronic Science,International Conference on ElectricEngineering and Computer (MEC 2011).

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