A Bottom-Up Approach to PV System Design for Rural Locality Electrification: A Case Study in Burkina Faso

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Introduction
For the past three decades, the search for renewable energy resources has become a hot research topic for safe and clean energy production around the world [1].However, the high investment costs remain a potential barrier, while conventional fossil fuels are sold at lower prices.As in most developing countries, accessibility to energy remains a major concern.Terefore, several papers reported on a low electricity access in sub-Sahara Africa [2][3][4][5].In their investigation, Deborah et al. [5] indicated that only 48% have electricity access.Like the majority of sub-Saharan African countries, Burkina Faso is experiencing a high energy demand due to the rapid population growth, where the rate has doubled in less than two decades.Terefore, the energy coverage has become one of the national priorities.In addition to existing conventional energy sources (hydroelectric and diesel power plants), several solar power plants are being implemented across the country.Although these eforts, the energy access issue is more critical in rural areas [6].To overcome this issue, strategies and programs such as rural electrifcation are initiated for an electricity coverage up to 100% by 2025, as indicated in the "Plan National de Développement Economique et Social (PNDES II)" [7].For the socioeconomic development of remote villages, the promotion of hybrid renewable energy systems is proposed.Te reliabilities of these systems have been reported in the literature.Tus, Enock Mulenga et al. [8], Kumar et al. [9], and Khan et al. [10] evaluated the technoeconomic analysis of hybrid power systems such as PV-Diesel, PV-Biomass, and PV-Hydrogen for the rural electrifcation plan.Other studies [11][12][13][14] focused on optimization techniques for the hybrid power system components sizing.Mishra et al. [15] described the design optimization approach for the grid-connected hybrid renewable system using discrete harmony search (DHS) algorithm.Mustafa Kamal et al. [16] discussed the optimal size for the standalone microgrid using the diferential evolution (DE) algorithm to minimize the total cost of energy and the size of the system.Ali Saleh et al. [17] have developed an appropriate dispatching approach to analyze the stability, reliability, economic, and environmental performance of integrating PV with diesel-batteries power systems.Malla and Bhende [18] described an enhanced process of PV-diesel-battery system using Takagi-Sugeno (TS) fuzzy model for a maximum power extraction under changeable solar irradiation condition.In this process, the active power balance is kept through the PV system to avoid the diesel generator (DG) in running on/of frequently.Although the main objective in the operation of this system is achieved, the study does not mention the optimum assessment of various components.
Among diverse metaheuristic algorithms for optimization, ant colony optimization (ACO) algorithm is the most outstanding methods employed [19][20][21][22][23]. Tis algorithm refers to the behavior of ant colonies looking for food and connecting within one another through pheromone traces that are left behind [24].In this study, the ACO and LPSP algorithms are used to optimally size a hybrid power system for a typical rural village of 4000 inhabitants.Te ACO approach is developed to perform the LPSP algorithm by minimizing the total cost of investment in the system.We propose a PV system which eliminates the need for a DG system.Due to weather and partially or fully shading conditions, batteries are employed to form a hybrid PVbattery system.As in several references [25,26], the yield of the storage system is greatly impacted by various factors such as state of charge (SOC), depth of discharge (DOD), and partial cycling temperature.Terefore, these parameters should be taken into account in the sizing of the storage system.Te main contributions in this work refer to the following: (1) Proposing a reliable hybrid power system (PV-battery) for energy supply in a remote village with an abundant solar radiation (2) A developed bottom-up approach for energy load estimation in a village of 4000 people, based on socioeconomic data and household sample survey, while the assessment model is based on local climate and geographic data (3) A detailed mathematical approach for diferent components of the proposed system (4) Introducing ACO algorithm for optimizing the number of PV modules and batteries of the study system.
In addition to an introduction and conclusion, the paper is organized as follows: Section 2 describes the system as the main element of the design methodology.Te optimization algorithms such as LPSP and ACO methods are described and introduced in Section 3 while the results of simulations and economic and environmental analysis are discussed in Section 4.

System Description
2.1.Remote Locality Description.Te implementation of the hybrid system is carried out in the village of "Zerkoum" (12 °23′ N; 2 °04′ 39″ W) in Burkina Faso, with an estimated population of 600 households.Te village is equipped with basic infrastructure, including schools, administration, health centre, and market.Due to its geographical position, "Zerkoum" is well irradiated and could take advantage of solar energy systems' installation.

Load Profle Assessment.
In this study, the load profle mainly deals with domestic power customers with basic facilities and devices, as presented in Table 1.Te survey aimed to identify the power need while involving a total of 600 households subdivided into 3 groups as follows: (1) Group I: 50% of the population with very low incomes for their basic needs (2) Group II: 30% of the population with middle income and wish to use a TV, DVD player, and 1 or 2 appliances (fan, fridge, and fat iron) (3) Group III: 20% of the population with consistent income.
To obtain an accurate assessment of the methodology that describes the load pattern for all appliances, which are likely to be found in the village, a synthetic electric load shape was produced by employing an electrical local end approach.Te technique is based on a bottom-up model, which uses some fundamental parameter data for the load profle.Based on some earlier works [27,28,29], an approximate appliance load profle for the village is established by using the statistical energy data on the number of households, abovementioned basic facilities, and commercial activities.Te load is stochastically based on the hourly behavior of the customer.Te daily load shape is simulated while considering the use of each appliance.Te daily energy need for two people in diferent households is described in Figure 1.
From the fgure, it can be clearly seen that the diference in the behavior of the two people results in a variation of the fnal electricity consumption which could be taken into account in the assessment model.Te qualitative description of the hourly loadshape profle may be attributed to the presence of each person at home.From the hourly loadshape of diferent activities, the following equation can be formulated for each occupant [27]: where d ci is the daily presence of the i th occupant at home during the simulated day, A j is the j th occupancy activity, α i is the means of the i th occupant, and β ij is the propensity of the i th occupant for j th occupancy activity.Based on 2 Journal of Renewable Energy equation (1), diferent loadshapes are estimated for each activity and income source.Tus, the total energy required for the day is calculated through the expression in [27]: where T n and P n are the duration of use and the nominal power, respectively, of the n th appliance.Te contractual energy threshold of an individual household can be determined as follows [27]: where P Thres is the contractual power threshold.
In the case of energy use in a household, it can occur that when E n ≺ E Thres , then the remaining energy (E rem ) to power other appliances can be calculated as follows: Similarly, the possible location time intervals of successive appliances are restricted to those for which E n ≺E rem .Preferential time slots are defned for the use of appliance n, and this is based on daily usage patterns.Tus, the total power consumption of the household is defned as follows [27]: where P a is the total power of the active appliances during the considered day and is given by the following: P b defnes the power consumption in which C α and βC α are automatic thermostat-controlled cyclic activation along the day and the electrical consumption resulting from the use of the appliance by an occupant of the household, respectively.Te global daily energy demand is therefore equal to the sum of individual households that include all activities with electricity consumption that must meet the electrical power system.Figure 2 illustrates the development of the bottom-up approach used in the studied locality loadshape assessment.
Figure 3(a) shows the hourly average load demand for various services in the locality for one day of operation.Te evaluation of electrical energy consumption is carried out carefully by taking into account the peak consumption for all activities.It can be observed that the consumption peak is reached in the morning and evening.Indeed, these  Journal of Renewable Energy periods correspond to the moment where all residents are in their house and most domestic activities are carried out.On the other hand, the energy consumption is minimal at night when most people are less active at home as well as in the services.Te total energy need for the village is estimated to be 2150 kWh per day with an average peak fow of 150 kW (load factor of 0 and 21) along the year, as shown in Figure 3(b).Te maximum load value was recorded around 21:00 h.In this context, a PV module and a storage system could be an alternative in supplying the load to several houses in the absence of sun irradiation.

Solar Resource Assessment.
Climatic data are measured over hourly intervals by the Research Laboratory of Energy under the direction of meteorology in Burkina Faso.Te average annual solar irradiation obtained from the Ouagadougou meteorological station is evaluated at 5, 5 kWh/m 2 per day and direct sunshine is over 3000 hours per year [28].Tese data obtained are used to characterize the climatic data of the village that contain difuse, horizontal, and refected radiation, relative humidity, and temperature.Figure 4 presents the daily solar radiation of the study locality for a year.From Figure 4, it is obvious that the village is well irradiated throughout the year.Since the hourly output of PV modules depends on the tilt angle and orientation of solar modules, some abovementioned climatic parameters were estimated accordingly from [29,30].Tus, the average energy output (E PV ) of the PV modules is estimated by using the following equation in [31]: where S is the total solar modules area (m 2 ), α is the solar modules efciency (%), H is the annual average solar radiation on titled PV modules (kWh/m 2 ), and P r the coefcient for losses (range from 0, 5−0, 9 and default value is 0, 75).

Components of the Hybrid PV/Battery
System.Te block diagram of the proposed PV/battery system is illustrated in Figure 5.It consists of a PV module system, storage system, converter, and diferent types of consumer's electrical loads.
In this diagram, the PV modules and storage systems are connected to a DC bus, while the electrical loads are linked to an AC bus via a DC/AC inverter.Te maximum power point tracking (MPPT) procedure is used for the PV module generator to extract the maximum output power due to fuctuation of solar radiation under operating conditions.Te storage system is loaded by the current generated by the PV module system where the control of their load is insured by a DC/DC controller.Since the PV system is autonomous, the presence of a storage device is essential to supply the load demands at any time.In this study, the basic relationship for computing PV modules' output power is given by the following equation [32]: where α PV is the rated capacity of the PV modules (kW), β PV is the rating coefcient (%), S net represents the incident solar radiation (kW/m 2 ), on the PV modules, S net,STC is the incident solar irradiance at the standard test condition (STC: 1000 W/m 2 ), c is the temperature factor (% °C), and T defnes the variation between the PV cell temperatures at normal (T Cell ) and STC (T Cell,STC ) given as T � T Cell − T cell,STC .
Taking into account that operating under a temperature parameter around 45 °C in April, a monocrystalline solar module is considered.Te main technical information about the PV module system is described in Table 2   2.5.Storage System Description.Te storage system sizing for a hybrid renewable energy system is a key factor for the project over the lifetime.Tus, the battery bank should be optimum in size, while a proper selection of the storage system characteristics, such as the amp-hour (Ah) or Watthour (Wh) capacity, could play an important role in supplying the load requirements.In consideration of two cases, the state of charge (SOC) is computed by using ( 9) and ( 10) [34]: (1) Energy balance for storage system charging: (2) Energy balance for discharging the storage system: where P sto (t − 1) and P sto (t) denote the storage system energy at the beginning and at the end of the interval t, respectively, P Load (t) represents the load demand at the time t, P PV (t) is the energy generated by the PV modules at the time t, σ is the self-discharge factor, and η sto and η con denote the storage system charging and the efciency of the
2.6.Power Converter Model.Te power converter is chosen based on the maximum load demand, whereas the performances of the inverters are chosen according to the power needs supply during peak hours.Te capacity of the converter can be calculated using the following equation [35,36]: where C con , L ind , and L 0 denote the converter capacity, the total inductive loads, and other loads, respectively.Te total inductive load consists of fridge, refrigerators, and fans, while TV, radio, DVD players, and so on belong to other load classes.

Optimization Approach
From the studied system, any other auxiliary energy source is excluded.Only the battery stores energy in the system.For this optimization approach, the loss of power supply probability (LPSP) presented in [39] is adopted to describe the reliability of power supply to load.Te LPSP is defned as the proportion of the loss of power supply (LPS) to that required by the load during a given period and can be calculated through the following equation [34,37]: Te optimization approach is divided in three steps: (i) estimation of the PV modules' output based on one-year solar data; (ii) estimation of the yearly status of the battery storage which is done with the previous amount of stored energy, PV array output energy, battery efciency, inverter efciency, and load energy demand; and (iii) the LPSP is defned and then the optimization problem is formulated as follows: where L sys is the total cost of the system, L pv is the size of a PV module, L b is the capacity of a battery, L other is the other total costs which are considered to be constant, and α and β are the unit costs of a PV module and a battery, respectively.Te solution to this problem could be achieved by partially diferentiating as follows: Solving this equation could lead to the determination of the capacities of the PV module and the battery for a given LPSP.

Capacity of PV Module and Battery Optimization.
In order to evaluate the performance of the system under various conditions, simulation studies have been carried out using load demand and real weather data of selected villages.Ant colony optimization (ACO) , as a probabilistic algorithm, is used to perform LPSP and system investment cost.ACO is swarm intelligence-based metaheuristic optimization algorithm that was inspired by the foraging behavior of ants [43].ACO imitates the cooperative behavior of an ant colony to fnd the shortest path to a food source.In this approach, a combination of optimization issues with n sizing parameters is made as a multilayered diagram, as illustrated in Figure 6 [44].Te number of layers corresponds to the number of design parameters.Also, the number of nodes in each layer corresponds to the discrete values' number allowed for the corresponding parameters.Terefore, each node in a particular location of the diagram is joined with an allowed discrete value of a design parameter.Artifcial ants travel through this diagram, searching for good paths.An ant colony consists of N ants.Te ants start at the nest node, walk through the diferent layers from the frst layer to the last layer, and end at the destination node in each cycle or iteration.Each ant can choose only one node in each layer in accordance with the state transition rule given by metaheuristic information.Te nodes selected along the path visited by an ant represent a candidate solution [44].On the travelled path, the ant lays down some pheromone based on a local updating rule.In the start of the optimization process, all the edges or rays are initially carried out with the same amount of pheromone.Tus, in this frst iteration, all the ants start from the home node and end at the food node by randomly choosing a node in each layer.Small quantities of pheromone are deposited during the construction phase, while larger amounts are deposited at the end of each iteration in proportion to solution quality.Te optimization process is fnished if any of the given termination conditions are satisfed.Te values of the design parameters indicated by the nodes on the path with the largest amount of pheromone are considered as the components of the optimum solution vector.Overall, at the optimum solution, all ants walk along the same converged path.Te most important characteristic of this algorithm is that it permits the best ant to update its pheromones.
From its interest in complex system optimization, the ACO algorithm has been applied to several optimization problems including those related to renewable energy optimization.
Tus, Kumar et al. [45] employed ACO to optimize the sizing of wind turbines and PV arrays in a hybrid renewable energy system.Te aim was to maximize the energy output of the system while considering the availability of wind and solar resource.ACO was used to determine the optimal dispatch of renewable sources to meet the demand for energy while minimizing the cost and emissions [46][47][48].Moreover, ACO could easily be combined with other methods [45].In our case, this optimization approach is employed to determinate the optimum capacities of PV Journal of Renewable Energy modules and batteries for a minimized cost of the system.Two diferent loads are considered for this optimization: frstly, we consider a constant load, that is, the load energy demand remains almost the same along the year.Secondly, a variable load is considered; in this case, we incremented to 20% or 45% of the initial load demand over the year.Te main aim is to maximize the energy output of the system while minimizing the cost.Te fowchart of the ACO algorithm applied to optimize this hybrid power system can be described as follows: (i) Initialization: Te initial solution is generated using the LPSP approach.Tis solution includes the initial sizes of the PV arrays and battery storage system.(ii) Pheromone update: In this step, the pheromone trails are updated based on the solutions generated in the previous iteration.If a solution generated in the previous iteration produced a higher energy output and lower cost, the pheromone is updated to refect that.(iii) Solution generation: New solutions are generated on the basis of the updated pheromone trails and heuristics.Te heuristics are rules that ensure the PV arrays and battery storage system are sized within the given constraints.Tese solutions represent diferent combinations of PV arrays and battery storage system sizes.(iv) Solution evaluation: solutions are evaluated on the basis of a predefned objective function.Te objective function takes into account the energy output, cost, and other constraints such as the maximum allowed capacity of the battery storage system.(v) Termination: Te algorithm terminates when a satisfactory solution is found.
As a result, the ACO algorithm will generate an optimal solution that represents the optimal sizing of the PV arrays and battery storage system to meet the energy demand of the studied location while minimizing the cost.
Tus, the optimization technique was carried out by taking into account the ACO parameters' approach, as presented in Table 3. Tese parameters were estimated based on the work of Jiang et al. [41].
In the simulation process, the parameters (constant or variable) defned in Table 4 are considered.Te lower and upper boundary stones of decided variables are assessed by the ACO program to concur with the optimal solution.Te number of decided parameters that provide the best results is sorted by setting all possible values by trial and error.
Using the ACO algorithm developed in MATLAB, the LPSP for various pairs of PV modules and batteries is determined, as shown in Figure 7(a).Te optimum capacity arrangement of PV modules and batteries obtained for an LPSP is equal to 0, 011 (15, 70 min per day or 3, 98 days per year of blackout) and are roughly worth 150 000 W and 195 000 Ah, respectively, as observed in Figure 7(b).

Cost Value of System Optimization.
In this section, we discuss the optimal cost value of the PV/battery system for an optimal LPSP value.Tree various load profles such as initial load (I load ) and variables of load profle 1 (1, 2 × I load ) and profle 2 (1, 45 × I load ) are considered.Te obtained Pareto limit profles can be observed in Figure 8. Te safety threshold was set at 1, 1% LPSP as a tolerable threshold for the local electricity supply, viz., up to 15, 70 min per day of failure.All points below the safety threshold are considered optimal points.Tese values are used to determine the cost of the system for a given LPSP value.Te optimal values are those for which the 3 profles are found in the defned safety threshold.From Figure 8, it can be observed that the optimum points correspond to a cost of 418764, 25 USD with a LPSP equals to 0, 0108.Referring to the aforementioned characteristics of commercially available PV module and battery, 650 PV modules of 250 W and 715 batteries of 300 Ah are sufcient to supply the load energy demand.
With the optimal arrangement, the SOC of the storage system is evaluated over one year, and the corresponding results are presented in Figure 9.In both cases (Figures 9(a) and 9(b)), the SOC oscillates between an allowed maximum value SOC max (100%) and minimum value SOC min (60% of SOC).Tese SOCs are greater than assumed minimum SOC of 40%.By adding variable load, the storage system is cycled in a fairly SOC large portion during the period November to March due to the higher energy consumption (Figure 9(b)).Tis allows a correlation between the demand and the storage system use.Te higher the demand is, the higher the storage system use is.Terefore, the storage system is less used for the rest of the year as the demand is relatively low.Te mean SOC vanishes between 80% and 92%.An increase in initial load could impact the SOC range and battery ageing as well.Figure 9 c shows the fuctuation of the energy level in a battery throughout one year with respect to the variable load profle.Tese are due to the overused energy per day of x n,m-1 x n,mn Food Nest Figure 6: Ant colony optimization method in the form of a multilayered diagram [44].
the storage system, which leads to an improper charge of batteries even during sunshine.However, all of these fuctuations could be controlled or reduced with proper strategic management.

Comparison with Other
Confgurations and Environmental Analysis.Tis section presents an analysis of the economic feasibility and environmental impact of three diferent energy systems, namely DG only, PV/DG, and PV/ battery systems for supplying the same load profle.As seen in Figure 3(b), the total daily need for energy needs presents a maximum power peak load of 150 kW and a minimum power peak of 60 kW.
(1) Sizing of the DG system In [49], a technoeconomic analysis of PV/DG hybrid system without storage was performed for a remote village in Burkina Faso.Te authors found that the optimal functioning point of the DG is set at around 90% of its nominal power.Based on this work, it is suggested that the power that could be delivered by DG is 169, 5 kW for this investigation.(2) Sizing of the PV/DG system In the present study, 30% of the PV maximum penetration is considered, as indicated in [50].A PV array of 47 kW and 169.5 kW are required for a PV/ DG system under the assumption that it will meet the load at low irradiation and night.

Economic Analysis Comparison.
Te economic evaluation is based on the life cycle cost (LCC).Te calculations of cost efciency of a typical system over the project duration include various costs, viz., initial capital cost (C in , the recurring costs (M op ), and the nonrecurring costs (R repl ) in USD currency.Te recurring costs represent the sum of all operating and maintenance (O&M) costs, while the nonrecurring costs denote the sum of equipment replacement cost.Te expenses expected that could occur during the life cycle of the system are evaluated using the expression in [50,51]: Te included technical data and assumptions on PV, DG, and battery units in this study are from [41,52,53].According to the type of the system, an economic evaluation is presented.For the PV/DG system LCC analysis, we assumed that 8% of the energy consumed between 6:00 am and 5:00 pm is supplied by the PV generator.In this case, the DG should meet the peak load (150 kW) and runs 24 h per day.Tus, the total electrical load to be generated by these systems is about 19 618, 750 kWh over 25 years.Based on the same load demand over 25 years, the PV/DG system LCC (1 082, 701.9 USD) is found to be lower than the PV/battery system LCC (1 293 025.7 USD), which is also lower than that of the DG system LCC (1 682 850.6 USD).Te life cycle cost breakdown for each selected energy system is shown in Figure 10.
As expected, the investment cost of PV/battery systems is ten times higher than that of DG systems, while O&M costs remain lower, as replacement and salvage costs are minimal.
Indeed, the main issue in the DG system is related to the O&M and the increase in fuel prices.From these results, the PV/DG system is more economical and viable compared to the PV/battery and DG systems.Nevertheless, each system has to be considered on its merits, while taking into account the local conditions, the cost of alternatives, and other parameters such as environment.Although the PV/battery system has a high investment cost, it does not require fuel, high maintenance, and equipment replacement.Compared to hybrid PV/DG systems, the introduction of a DG in the PV/battery system could be a reliable option.

Environmental Analysis.
Electrical energy in several remote localities in Burkina Faso is usually produced by the mean of DG.However, the production of energy through fossil fuels is a source of air pollution [54].Te environmental impacts of autonomous PV systems can only be evaluated properly if comparative study involves other energy supply systems.Te life cycle impact assessment (LCIA) is used to perform the environmental analysis.Indeed, the LCIA is a crucial step in the life cycle assessment (LCA) methodology.It involves the evaluation and quantifcation of the environmental impacts of a product, process, or system throughout its entire life cycle, from raw material extraction to disposal or recycling.Te LCIA provides a systematic approach to understand the signifcance of various environmental stressors and their efects on diferent impact categories.
Without a deep investigation, it can be admitted that PV systems in general are CO 2 emissions free.While a hybrid system involving diesel is a source of CO 2 where LC is the total equivalent amount of CO 2 emitted over the life cycle of the PV system (kgCO 2 ), E is the overall annual energy supplied (kWh/year), and Ө is the lifetime of the PV system (year).For a growing population and economical business activities in a remote village, an increase in CO 2 emission is expected while combining PV and DG for energy production.Some reports [55,56] indicated that the emission factor considered for DG is 1.27 kg of CO 2 /kWh.Te value takes into account emissions during fuel combustion, fuel extraction and refning, the manufacturing of the DG itself, and transport (over 100 km).According to Fleck and Huot [57], the total emissions considered for the diesel fuel consumption is 3.15 kg of CO 2 per liter.During the life cycle of the DG system, about 1854 tons of CO 2 will be released in nature.Compared to the PV/DG system, about 3456 tons of CO 2 are saved over its life cycle while the PV/battery system has a CO 2 emission free.Tis later system allows the saving  Journal of Renewable Energy of 17943 tons of CO 2 compared to the DG system and 14487 tons of CO 2 compared to the PV/DG system.Te mayor drawback in this system is the recycling of the batteries at the end of their lifetime because of lack of policies or regulations in most sub-Saharan African region [28].From the abovementioned, it is clear that the PV/DG system presents advantages compared to PV/battery and DG in terms of cost and environmental pollution, respectively.However, attempts could be made in PV/DG systems to explore the benefts of the incorporation of short-term storage in terms of fuel savings, diesel running time, and storage systems of excess energy.

Conclusions
In this work, a bottom-up approach of energy load estimation for a typical village of 4000 people is proposed based on socioeconomic data and household sample survey.Te behavior of the hybrid PV/battery system is studied, while considering a design of PV systems in respect of hourly global solar irradiance and real load demand profles.An economic analysis is also carried out for an optimal size of diferent components such as PV modules, battery, controller, and inverter by using the ACO technique.Te obtained results show that the PV/battery system is qualifed to satisfy the load demand in the village location.Furthermore, the SOC analysis of the battery reveals the sustainability of the storage system for more than 20% of the initial load.Te economic and environmental aspects of the PV/DG, PV/ battery, and DG systems evaluation reveal that the proposed PV/battery system, consisting of 650 PV modules (250 W), 715 batteries (300 Ah), and a 139 kW inverter, is economically disadvantaged compared to the PV/DG system, but less expensive than the DG system.However, it remains environmentally advantageous at long-term exploitation because it releases free carbon emission.

Figure 1 :
Figure 1: Typical day availability model for two (2) individual persons in 2 diferent households.

Figure 3 :
Figure 3: Energy consumption profles: (a) hourly average load demand profle during the day for all services in the locality and (b) monthly load demand profle for the study village.

Table 3 :
Parameter values for ant colony algorithm.

Table 4 :
Constant and variable parameters used.