948 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 2, MAY 2006

Minimal Loss Reconfiguration Using GeneticAlgorithms With Restricted Population and

Addressed Operators: Real ApplicationJorge Mendoza, Student Member, IEEE, Rodrigo Lpez, Student Member, IEEE, Dario Morales, Enrique Lpez,

Philippe Dessante, and Roger Moraga

AbstractThis paper proposes and evaluates a method thatimproves the adaptability and efficiency of genetic algorithms(GAs) when applied to the minimal loss reconfiguration problem.This research reduces the searching space (population) when anew codification strategy and novel genetic operators, called ac-centuated crossover and directed mutation, are used. This allowsa drastic reduction of the computational time and minimizesthe memory requirements, ensuring a efficiency search whencompared to current GA reconfiguration techniques. The reducedpopulation is created through the branches that form systemloops. This means that almost all individuals created for the GAare feasible (radial networks) generating topologies that can onlybe limited by the systems operational constraints. The results ofthe proposed reconfiguration method are compared with othertechniques, yielding smaller or equal power loss values with lesscomputational efforts.

Index TermsGenetic algorithms (GAs), losses, minimal loss re-configuration, optimization methods, power distribution.

NOMENCLATURE

b branch resistance.b branch complex current.

, Current vector of branches and maximum current ofbranches.Vector of node currents.Incidence matrix.Node voltage.Node minimum voltage.Node maximum voltage.Radial net branch number.Node number.Source number.

FL Fundamental loop.Total branch number.

Manuscript received May 25, 2005; revised November 3, 2005. This workwas supported by the National Commission for Investigation, Science and Tech-nology of Chile (CONICYT). Paper no. TPWRS-00318-2005.

J. Mendoza and E. Lpez are with the Department of Electrical Engineering,University of Concepcin, Concepcin, Chile (e-mail: jorgemendoza@udec.cl;elopez@udec.cl).

R. Lpez is with the Faculty of Law and Economics, University Paris XI,Paris, France (e-mail: rlopezg@ieee.org).

D. Morales and P. Dessante are with the Dpartement Electrotechnique etSystmes dEnergie, Suplec, Paris, France (e-mail: dario.morales@supelec.fr;philippe.dessante@supelec.fr).

R. Moraga is with the Engineering and Odontology School, Desarrollo Uni-versity, Concepcin, Chile (e-mail: rmoraga@udd.cl).

Digital Object Identifier 10.1109/TPWRS.2006.873124

I. INTRODUCTION

THE reconfiguration of a distribution network is a processthat alters feeder topological structure, changing theopen/close status of sectionalizers and interruptors in thesystem. Under normal operational conditions, the objectives areavoiding excessive transformer load, conductor overheating,and minimizing abnormal voltages and at the same timeminimizing the active power losses of the system. The firstpublication about the reconfiguration problem was presentedby Merlin and Back [1]. In this paper, the global minimum iscalculated starting from a meshed network. This method waslater modified by Shirmohammadi and Hong in [2], where theyreduced computation time by applying an efficient load flow.Civanlar and Grainger in [3] derived a formula to estimateloss reduction using an algorithm called branch interchange.Other heuristic methods have been published that are princi-pally based on switch interchange, sets of rules to determinateopen/close status of sectionalizers, and linearization of theobjective function using approximated formulas for lossesevaluation as those presented in [4] and [5]. In [6], Glamocaninused quadratic programming to formulate the reconfigurationproblem as a transfer problem with quadratic costs. Sarfi in [7]proposed an algorithm based on the division of a distributionnetwork into a groups of feeders. His algorithm used a rapidheuristic technique for system division, taking into account theprincipal ideas proposed by [3] and [8]. McDermott [10] pro-posed a constructive heuristic method for the reconfiguration ofminimal losses. Lopez in [11] proposes a minimal loss recon-figuration method applied to large distribution systems basedon the dynamic programming approach, graph compression,and radial load flow. Finally, the same authors in [12] considerthe variability demand in the reconfiguration process.

In the literature, various methods exist that employ artificialintelligence, among them, genetic algorithms (GAs). This tech-nique bases its search mechanism on the principles of naturalselection for creating a set of feasible solutions (populations).Holland in [13] was the pioneer in the use of this technique andsince its inception has been applied to a wide variety of opti-mization problems. The algorithm structure is based in the gen-eration of a population of individuals that represent the solutions(generation), and then these are evaluated using an objectivefunction; the individuals that have the greatest aptitude are thenselected. Finally, a new population is created using crossover

0885-8950/$20.00 2006 IEEE

MENDOZA et al.: MINIMAL LOSS RECONFIGURATION USING GAs 949

and mutation operators. This allows converging to the best so-lution [14][16].

The first work that applied GA to the reconfiguration problemwas developed in 1992 by Nara [17]. In spite of the excellentresults, the conclusion of this paper and the study developedby Sarfi [18] pointed out the need for computers with greaterprocessing speed. The principal trouble presented in [17] isrelated to the binary codification used; it identified the arc(branch) number that contains the th open switch and identifiesthe switch that is normally open in this arc. That codificationtype can be very long, and it grows in proportion with theswitch number. Also, an approximated fitness function wasused to represent the system power loss.

Nevertheless, the technological advances in computer hard-ware allow today the application of these methodologies withgreater benefits and fewer limitations in terms of the problemdimensions and computational times involved in the populationsize, number of generations, and objective function evaluation.

In [23], the GA method is refined, in the reconfigurationproblem, by modifying the string structure and fitness function.Here, a binary string represents only positions of the openswitches in the distribution network. Consequently, the lengthof the string is reduced, depending on the number of openswitches. The fitness function also considers constraints of thesystems. An adaptive mutation process is used to change themutation probability.

Lopez in [24] made an important contribution to the re-configuration process using GA, with excellent results in thesimulation times, when introducing graph compression, currentflows analysis, stochastic minimum extension trees, and di-akoptic compensatory currents. All of these techniques are usedto simplify the systems model, allowing the evaluation of theobjective function with less computational efforts. Also, a setof filters is introduced in order to eliminate the individuals thattransgress the system operational constraints (like over currentsand voltage ranges). However, the computational efforts arestill significant due to the generated random population, wheremany do not override the radiality and connectivity filters.

In [26], a GA technique is applied to the multiobjective re-configuration problem. This work used the Prufer numbercodification, to avoid a tedious meshed check algorithm. Thecrossover is applied in two points randomly selected. The singlepoint mutation is applied, and the roulette wheel approach isused to select the rest of the individuals.

The work presented in [27] is the only one that develops amethod to create a feasible population. This method is based onthe concept called path-to-node. This scheme is based on thepreliminary identification of alternative paths linking each busto the substation. This path definition creates radial topologiesfor the initial population with excellent results but only usingtraditional genetic operators.

As a whole, the great majority of the GA applications to thereconfiguration problem are done using a binary codificationthat represents the location and codifications of the switches inthe system. In real systems, the above may result in string that istoo long, decreasing the efficiency in the search for the optimum.An attempt to solve this problem has been done by developingnew codification strategies (keeping on with a binary line) and

by new ways of improving the convergence through the proba-bility of adaptive mutation

For this reason, in this paper, a GA addressed population gen-eration criteria that avoids nonfeasible individuals from a net-work structure standpoint is used. This changes drastically theway of using GA in the reconfiguration process. This is basedon the work of Lin in [20], where the switching indexes of thenetwork were analyzed, to determine the opening of the controldevices.

II. SOLUTION METHODA. Minimal System Power Loss Problem

Reconfiguration is encompassed in problems of planning andoperation of primary distribution systems. The principal objec-tive is to find a radial operating structure that minimizes thesystem power loss while satisfying operating constraints. Themathematical formulation for the minimization power loss re-configuration problems is presented in the literature in differentways. In this paper, the problems formulation is presented as in[12]

minimize (1)

subject to (2)(3)(4)(5)

Equation (1) corresponds to the objective function to mini-mize and represent the total power loss of the system. Equa-tion (2) corresponds to the matrix of nodal load current bal-ances. Equation (3) corresponds to feeder thermal limits and tothe maximum capacity of substations. Equation (4) considersvoltage constraints in each node. Equation (5) describes radi-ality constraints of the primary distribution system.

Up until now, the approach to the reconfiguration problemusing GA relied on the use of filter and/or mechanisms to createinitial populations in order to avoid the evaluation of nonfeasibleindividuals. This paper considers the application of system fun-damental loops to make decisions about how to create feasibleindividuals and overall how to obtain feasible individuals laterto apply the genetic operators.

B. Reconfiguration Using Fundamental LoopsThe proposed methodology creates feasible topologies using

topological analysis. It is made to identify the fundamentalclosed loops of the system in order to originate radial topolo-gies.

When analyzing meshed networks, the number of funda-mental loops (FLs) is

FL (6)

This (6) also indicates the total number of elements to bedisconnected in a meshed distribution network in order to obtainthe radial topology.

950 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 2, MAY 2006

Fig. 1. Diagram of a meshed network.

The FLs vectors of a network are defined as an ensemble ofelements that form a closed loop in a circuit that does not containany other closed loop. The last one follows the same rules of themesh current method applied in the circuit analysis theory. ForFig. 1, the close loops selected are

LoopLoopLoop

In order to create a radial topology, one should select fromthe group of fundamental loop vector elements to be discon-nected (one for loop). It is important that the vectors elementsare not repeated (or have the same genetic information) in a se-lected topology. The combination of elements can be generatedwith these vectors, creating all possible radial topologies of thesystem.

For the system shown in Fig. 1, the total number of feasibleradial topologies, using the proposed method, is 30, while 56topologies were observed using a random methodology. This isa great advantage of the proposed method. These considerationsallow the proposed GA to limit the generation of nonfeasible in-dividuals. This also reduces the combinatorial searching space.

C. Genetic AlgorithmsGA is a technique based on the Theory of Evolution. It can

be applied to a wide range of engineering problems.The genetic function principally works at the genotype level,

but they can also function at the phenotype level. The principaloperator is the crossover, and the secondary operator is muta-tion. The way to select individuals is probabilistically based onthe individual fitness.

The GA methodology structure is as follows:1) codification of individuals (topologies);2) generation of a feasible initial population;3) each individual (solution) evaluated through the fitness

function (system power loss);4) application of genetic operators;5) repetition of the third and fourth steps, until reaching the

total number of generations.

Fig. 2. Individual representation.

1) Codification and Feasible Population: In this paper,the individuals are represented by a string of whole num-bers (chromosome) whose dimension is the total number oflines to be disconnected from the network. Consequently, thelength of the string is in accordance with the number of thesystem loopssee (6). Binary codifications used for the radialtopology shown in Fig. 2 are

The binary codifications for [17], [22], [24], and [25] grows inproportion with the switch number of the system (furthermore,when the systems are larger and complex). According to thecodification presented in [23], it clearly reduces the number ofbits used. Nevertheless, if the amount of switch increases, a bignumber of bits for the codification may be needed.

In this paper, each position (gene) of the string represents arandomly selected element of each fundamental loops vector.

proposed method

The main advantage of this codification is based on creatingindividuals guided through the fundamental loops vector, al-lowing to produce radial topologies that, with the nonguided bi-nary codifications, are difficult to achieve

Thus, the individual selection process is done through a prob-abilistic tournament of uniform distribution [22].

2) Application of Genetic Operators: The great majority ofthe GA applications to the reconfiguration problem use the tra-ditional mutation and crossover techniques [17], [21], [22], [24],[26]. Only in some cases, efforts have been done to do the fol-lowing:

choose out of traditional crosses the one more suitable forthe reconfiguration problem [19];

develop a process to change the mutation probability [23],[25].

MENDOZA et al.: MINIMAL LOSS RECONFIGURATION USING GAs 951

Fig. 3. Accentuated crossover process.

In this paper, new genetic operators are developed, based onthe information that is possible to extract from the fundamentalloops, efficiently guiding the individual reproduction.

The crossover is the principal operator of the GAs. This op-erator aims at mixing up genetic information coming from twodifferent individuals (parents), to make a new individual (child).In the proposed method, the fundamental loops vector was con-sider as the cross mask. This means that a point of the string ischosen to interchange genetic information of both parents (as inthe traditional technique) but having in account this cross mask,so that the genetic information does not repeat. This crossovertype is called accentuated crossover.

If we consider two random parents for the systems showed inFig. 1, the methodology to obtain two new children through theaccentuated crossover is show in Fig. 3.

Here, the children number one (Ch1) is nonfeasible becausenumbers 5 and 6 are bits that have the same genetic informa-tion. (They have familiar lines for the vector loops 2 and 3. Thisinformation was obtained from the fundamental loops vector.)

The mutation operator provides a way to introduce newinformation into the knowledge base. This operator randomlychanges one bit in the string, and it is applied with a probabilitythat has been set in the initialization phase. In this paper, thisoperator is applied, taking into account the cross mask to guidethe mutation process, keeping the feasible individuals. Thismutation type was called directed mutation. For example, ifthe mutation process indicates to change the Ch2 in the bits 2,then see Fig. 4 for the result.

At the end of this process, the feasibility of the generated in-dividuals is evaluated using a filter (a remote possibility existsthat a small percentage of individual are not feasible). The in-dividuals, which have passed through the filter, are evaluatedusing the power losses function, taking into account the opera-tional constraints. Then, their aptitudes are compared with thoseof their parents. Subsequently, the individual with the highestaptitude is selected. Finally, elitism is used to assure conserva-tion of the best topology. The proposed block diagram of themethodology is shown in Fig. 5.

In order to determine the total power losses associated to eachtopology and to verify the constraints for each feasible system,a radial load flow algorithm is used for the individual aptitude

Fig. 4. Directed mutation process.

Fig. 5. Proposed method block diagram.

Fig. 6. Civanlar system topology.

evaluation. The model considers a load of constant power ateach node.

III. APPLICATIONS

In this section, the proposed method is applied to three testedsystems. They are called Civanlar [3], Baran [4], and Lopez[11]. These are shown in Figs. 68, respectively, and the resultsare compared with other references. Also, in order to evaluate

952 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 2, MAY 2006

Fig. 7. Baran system topology.

Fig. 8. Lopez system topology.

the computational efforts, the results from a large real systemare shown.

The algorithm was developed in Matlab, and the simulationswere done on a computer with Pentium IV, 1.6 Ghz, 256 MBRAM. The most important system parameters are shown inTable I.

The resultant topologies and power losses, of each system,are shown in Table II for the proposed method. The topologiesfound for this methodology concur with those in [24]. The re-sultant power losses were less than or equal to those found bythe techniques applied in [1][3], [5], [11], [23], [26], and [27](see Table III).

The evolution of the best individual to each assigned gener-ation for the proposed method is shown in Figs. 911, for eachsystem.

TABLE ISYSTEM PARAMETERS

TABLE IIRESULTS OF RECONFIGURATION FOR THE PROPOSED METHOD

TABLE IIIRESULTS OF RECONFIGURATION FOR OTHER REFERENCES

Fig. 9. Evolution GA for Civanlar system.

In the Civanlar system, we can see that the algorithm arrivesto a solution after 12 generations. This corresponds to aroundhalf of the assigned generations.

MENDOZA et al.: MINIMAL LOSS RECONFIGURATION USING GAs 953

Fig. 10. Evolution gas Baran system.

Fig. 11. Evolution gas Lopez system.

When analyzing the system of Baran, the solution quicklyarises to the best individual at the 26th generation. This corre-sponds to 75% of the total. For the Lopez systems, the algorithmfinds the best individual in the 30th generation. This correspondsto the 60% of the total generation. This is an acceptable value,and the solution is considered as a good one.

A comparison of the computational efforts, in accordanceto the population size and generations, between the proposedmethodology and the methodology presented in [24] is shownin Tables IV and V.

Moreover, it is possible to compare the efforts done by theGA of the method proposed with those of [26], for the Cinvalarsystem. In this case, a population of 85 individuals and around120 generations is needed to reach a topology that presentsmajor losses. The same goes for the Baran system [27], whichuses a population of 15 individuals and 47 generations to reachthe same topology solution. However, almost 180 evaluationsare required, which is more than the proposed method.

Consequently, the population size and number generationsare drastically reduced when using the proposed methodology.For this reason, the computational times decrease, even when

TABLE IVRESULTS OF [24]

TABLE VRESULTS OF THE PROPOSED METHODOLOGY

no special techniques (e.g., graph compression, current flowsand stochastic minimum extension trees, and diakoptics com-pensatory currents) are used. This represents an advantage dueto its simplicity. GAs have exhibited an excellent adaptabilitywith a considerable reduction of computational efforts. This en-courages the use of GA in reconfiguration problems.

IV. CONCLUSIONIn this paper, a new methodology for minimal loss recon-

figuration using GA is presented. This technique is based onthe construction of an initial population of feasible individualsusing the system loops and applying specialized genetic oper-ators of accentuated cross and directed mutation. This reducesthe searching space, analyzing only feasible radial topologies.

The proposed method changes drastically the way of usingGA in the reconfiguration process, allowing the optimal recon-figuration of large distribution systems, with less computationalefforts (minimizing the required memory and CPU time), usinga simple code, and overall improvement of the searching ability.

When a small number of switching elements is considered,the proposed methodology uses a smaller searching space (elim-inating from the fundamental loops vector those lines that donot have switching elements), simplifying the problem resolu-tion and reducing (even more) the CPU time involved.

Consequently, this paper proposes a formal and robuststrategy for approaching the large minimal loss reconfigura-tion problems using GA. Better solutions than those attainedthrough other techniques, such as GA or traditional algorithms,are found.

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tree configuration for an urban power distribution system, in Proc. FifthPower System Conf. (PSCC), Cambridge, U.K., 1975, pp. 118.

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[5] S. Goswami and S. Basu, A new for the reconfiguration of distributionfeeders for loss minimization, IEEE Trans. Power Del., vol. 7, no. 3,pp. 14841491, Jul. 1992.

954 IEEE TRANSACTIONS ON POWER SYSTEMS, VOL. 21, NO. 2, MAY 2006

[6] V. Glamocanin, Optimal loss reduction of distribution networks, IEEETrans. Power Syst., vol. 5, no. 3, pp. 774781, Aug. 1990.

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[13] J. H. Holland, Adaptive in Nature and Artificial Systems. Ann Arbor,MI: Univ. Michigan Press, 1975.

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[20] W.-M. Lin and H.-C. Chin, A new approach for distribution feeder re-configuration for loss reduction and service restoration, IEEE Trans.Power Del., vol. 13, no. 3, pp. 870875, Jul. 1998.

[21] A. Augugliaro, L. Dusonchet, and E. Riva Sanseverino, Service restora-tion in compensated distribution networks using a hybrid genetic algo-rithm, Elect. Power Syst. Res., vol. 46, pp. 5966, 1998.

[22] Y. Hsiao, Enhancement of restoration service in distribution systemsusing a combination Fuzzy-GA method, IEEE Trans. Power Syst., vol.15, no. 4, pp. 13941400, Nov. 2000.

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[24] R. Lpez, E. Lpez, R. Moraga, and H. Opazo, Contributions a la re-configuration des rseaux de distribution primaire a travers des arbresstochastiques dextension minimale, des courants diakoptiques et desAlgorithmes gntiques, in Proc. EF2003 SUPELEC, Paris, France,2003.

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[26] Y.-Y. Hong and S.-Y. Ho, Determination of network configurationconsidering multiobjective in distribution systems using genetic algo-rithms, IEEE Trans. Power Syst., vol. 20, no. 2, pp. 10621069, May2005.

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Jorge Mendoza (S03) was born in Concepcin,Chile. He received the D.E.E degree in 2001 and theM.Sc. degree in electrical engineering in 2003 fromthe University of Concepcin, Concepcin, Chile,where he is working toward the Ph.D. degree inelectrical engineering. He holds a scholarship fromCONICYT for his Ph.D. studies.

His main research interests are optimization, nu-merical modeling, reliability, and quality of electricalsystems.

Rodrigo Lpez (S05) was born in Concepcin,Chile. He received the D.E.E degree in 2003 andthe M.Sc. degree in electrical engineering in 2004from the University of Concepcin, Concepcin,Chile. He is working toward the Ph.D. degree fromthe University of Paris XI and lcole Suprieuredlectricit Suplec, Paris, France.

His interest areas are planning, optimization, con-trol, power quality, and numerical modeling of elec-trical systems.

Dario Morales was born in Los Angeles, Chile. Hereceived the Electrical Engineer degree in 2001 fromthe University of Concepcin, Concepcin, Chile. Heis working toward the Ph.D. degree at the Univer-sity of Paris XI and lcole Suprieure dlectricit-Suplec, Paris, France.

His areas of interest are numerical modeling ofpower systems and renewable energy applications.

Enrique Lpez was born in Lota, Chile. He re-ceived the Electrical Engineer degree in 1974 fromUniversidad Tcnica del Estado, Estado, Chile, andthe Ph.D. degree in 1983 from Institut National Po-litechnique de Grenoble (INPG), Grenoble, France.

Currently, he is an Associate Professor in theElectrical Engineering Department, Universidadde Concepcin. His interest areas are planning,optimization, control, reliability, and quality ofelectrical systems.

Philippe Dessante was born in Clichy, France. Hereceived the Ph.D. degree in 2000 from the Universityof Versailles, Saint-Quentin, France.

He is currently a Professor at the Ecole SuprieuredElectricit-Suplec, Paris, France. His main fieldof research is about simulation and optimization inpower systems.

Roger Moraga was born in Santiago, Chile. Hereceived the Electrical Engineering degree in 2004from the University of Concepcin, Concepcin,Chile.

He is currently a Professor at Desarrollo Univer-sity, Concepcin, Chile. His interest areas are plan-ning, optimization, control, power quality, and nu-merical modeling of electrical systems.

tocMinimal Loss Reconfiguration Using Genetic Algorithms With RestrJorge Mendoza, Student Member, IEEE, Rodrigo Lpez, Student MembN OMENCLATUREI. I NTRODUCTIONII. S OLUTION M ETHODA. Minimal System Power Loss ProblemB. Reconfiguration Using Fundamental Loops

Fig.1. Diagram of a meshed network.C. Genetic Algorithms

Fig.2. Individual representation.1) Codification and Feasible Population: In this paper, the indi2) Application of Genetic Operators: The great majority of the G

Fig.3. Accentuated crossover process.Fig.4. Directed mutation process. Fig.5. Proposed method block diagram.Fig.6. Civanlar system topology.III. A PPLICATIONS

Fig.7. Baran system topology.Fig.8. Lopez system topology.TABLEI S YSTEM P ARAMETERSTABLEII R ESULTS OF R ECONFIGURATION FOR THE P ROPOSED M ETHODTABLEIII R ESULTS OF R ECONFIGURATION FOR O THER R EFERENCESFig.9. Evolution GA for Civanlar system.Fig.10. Evolution gas Baran system.Fig.11. Evolution gas Lopez system.TABLEIV R ESULTS OF [ 24 ]TABLEV R ESULTS OF THE P ROPOSED M ETHODOLOGYIV. C ONCLUSIONA. Merlin and G. Back, Search for minimum-loss operational spannD. Shirmohammadi and H. W. Hong, Reconfiguration of electric disS. Civanlar, J. Grainger, H. Yin, and S. Lee, Distribution feedeM. E. Baran and F. Wu, Network reconfiguration in distribution sS. Goswami and S. Basu, A new for the reconfiguration of distribV. Glamocanin, Optimal loss reduction of distribution networks, R. Srfi, M. Salama, and Y. Chikhani, Distribution system reconfJ. Fan, L. Zhang, and J. McDonald, Distribution network reconfigR. Taleski and D. Rajicic, Distribution networks reconfigurationT. McDermott, I. Drezga, and R. Broadwatwer, A heuristic nonlineE. Lpez, H. Opazo, L. Garcia, and M. Poloujadoff, Minimal loss E. Lopez, H. Opazo, L. Garcia, and P. Bastard, Online reconfigurJ. H. Holland, Adaptive in Nature and Artificial Systems . Ann AD. Goldberg, Genetic Algorithms in Search, Optimization and MachZ. Michalewicz, ${\hbox {Genetic}}\ {\hbox {Algorithms}}+{\hbox M. Mitchell, An Introduction to Genetic Algorithms . Cambridge, K. Nara, A. Shiose, M. Kitagawa, and T. Ishihara, ImplementationR. Sarfi, M. Salama, and A. Chikhani, A survey of the state of tG. Levitin, S. Mazal-Tov, and D. Elmakis, Genetic algorithm for W.-M. Lin and H.-C. Chin, A new approach for distribution feederA. Augugliaro, L. Dusonchet, and E. Riva Sanseverino, Service reY. Hsiao, Enhancement of restoration service in distribution sysJ. Z. Zhu, Optimal reconfiguration of electrical distribution neR. Lpez, E. Lpez, R. Moraga, and H. Opazo, Contributions a la D. Shin, J. Kim, T. Kim, J. Choo, and C. Singh, Optimal service Y.-Y. Hong and S.-Y. Ho, Determination of network configuration E. Romero, A. Gomez, J. Riquelme, and F. LLorens, Path-based disC. A. Coello, G. B. Lamont, and D. A. Van Veldhuizen, EvolutionaC. A. Coello, A Comprehensive Survey of Evolutionary-Based Multi