An ASABE Meeting Presentation Paper Number: 072105

Development of a multi-objective optimization tool for the selection and placement of BMPs for nonpoint

source pollution control

Chetan Maringanti, Graduate Student, Department of Agricultural and Biological Engineering, Purdue University, West Lafayette, IN. 47906, email: cmaringa@purdue.edu

Indrajeet Chaubey, Associate Professor, Department of Agricultural and Biological Engineering and Department of Earth and Atmospheric Sciences, Purdue University, West Lafayette, IN. 47906, email: ichaubey@purdue.edu

Jennie Popp, Associate Professor, Department of Agricultural Economics and Agribusiness, University of Arkansas, Fayetteville, AR. 72701, email: jhpopp@uark.edu

Written for presentation at the 2007 ASABE Annual International Meeting

Sponsored by ASABE Minneapolis Convention Center

Minneapolis, Minnesota 17 - 20 June 2007

Abstract. Nonpoint source (NPS) pollution from agricultural areas can be minimized by the implementation of best management practices (BMPs) at the source (farm), by controlling the movement of pollutants from the agricultural areas into the receiving bodies. However, selection and implementation of BMPs in every farm, to achieve cost effective NPS pollution reduction in a watershed may be a daunting task. This typically requires obtaining an optimal solution, from the many million solutions that are possible, that is ecologically effective and economically feasible for the placement of BMPs. The previous works done to solve this problem have used genetic

The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation. ASABE Paper No. 07xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at rutter@asabe.org or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).

algorithms (GA) for optimizing the two objectives of : 1) pollution reduction and 2) cost increase. But most of the works have considered the two objectives individually during the optimization process by introducing a constraint on the other objective. This approach of finding an optimal solution is not practical as the constrained objective results in a decrease in the degree of freedom in the solution space. In the present work the optimization is performed by considering the two objectives simultaneously. A multi-objective genetic algorithm (NSGA-II) was used to optimize the two objectives which gave a tradeoff between the two objectives for a range of optimal pollution reduction alternatives and their corresponding cost for implementation of BMPs. The model was used for the selection and placement of BMPs in L’Anguille River Watershed, Arkansas, USA for total phosphorus (TP) reduction. The most ecologically effective solution from the model had a TP reduction of 33% from the base scenario for a BMP implementation cost of $14 million. The tradeoff was obtained between the two optimized objective functions which can be used to achieve desired water quality goals with the minimum BMP implementation cost for the watershed.

Keywords. Multi-objective genetic algorithms, BMP, nonpoint source pollution, optimization

The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily reflect the official position of the American Society of Agricultural and Biological Engineers (ASABE), and its printing and distribution does not constitute an endorsement of views which may be expressed. Technical presentations are not subject to the formal peer review process by ASABE editorial committees; therefore, they are not to be presented as refereed publications. Citation of this work should state that it is from an ASABE meeting paper. EXAMPLE: Author's Last Name, Initials. 2007. Title of Presentation. ASABE Paper No. 07xxxx. St. Joseph, Mich.: ASABE. For information about securing permission to reprint or reproduce a technical presentation, please contact ASABE at rutter@asabe.org or 269-429-0300 (2950 Niles Road, St. Joseph, MI 49085-9659 USA).

Introduction Nonpoint source (NPS) pollution from agricultural areas has become one of the biggest challenges in maintaining surface and ground water quality. Agricultural activities, such as, tillage practices and land application of fertilizer and animal manure are important factors contributing to NPS pollution, leading to excess runoff losses of sediment, nutrients and pesticides. A large percentage of water pollution is recognized to be originated from NPS pollution (Novotny, 1999) affecting more than 18% of the impaired river miles measured and 48% of assessed rivers and streams in U.S. (USEPA, 2002). Excess sediment loadings is the most important NPS pollutant of concern, as more than 50% of the sediment loadings in various waterbodies is contributed by the erosion of agricultural areas (Ritter and Shirmohammadi, 2001). The other important NPS pollutants of concern are the nutrients (Nitrogen (N) and Phosphorus (P)) that when present in increased concentrations results in accelerated eutrophication of the waterbodies.

The improvement in the quality of water impacted by excess runoff, sediment, and nutrient losses from agricultural areas can be achieved through the implementation of best management practices (BMPs), at a farm level, by decreasing the NPS pollutant loads leaving the farm (Ritter and Shirmohammadi, 2001). However, effectiveness of BMPs in improving water quality at a watershed scale is also very important. BMP implementation and maintenance is an important factor controlling BMP adoption as it is always desirable to implement a BMP that costs the least and gives the most reduction in pollutant load. Thus a balance has to be made between the ecological and economic implications due to the placement of BMPs. For a given watershed with many farms and multiple BMP options in each farm, there can be many different ways of targeting BMPs and it is desirable to find a solution that gives a cost effective pollution reduction. Finding such a solution through on-site evaluation of various different targeting of BMPs in a watershed is neither practical nor economically feasible. For example, a watershed with 500 farms with 4 different BMPs possible for every farm would require 4500 ~ 10300 evaluations. Therefore an optimization algorithm is needed that searches for the best solution among the various different possibilities to achieve the desired objective of achieving maximum pollutant reduction with minimum increase in cost due to the placement of BMPs.

The BMP optimization problem usually has a large search domain for the objectives (and variables) that needs to be solved to find the optimal solution. Genetic algorithm (GA), a global search technique, performs well in solving the problem of finding a BMP placement scenario from the highly distributed search domain. Genetic algorithm (Holland, 1975; Goldberg, 1989) is a heuristic search algorithm, based on the idea of Darwin’s evolutionary process. It searches the decision space based on the principles of “natural selection” and “survival of the fittest” to reach the optimal solution. Genetic algorithm (GA) has been used as an optimization tool for BMP selection and placement problem (Chatterjee, 1997; Srivastava et al., 2002; Veith et al., 2003; Gitau et al., 2004). Most of the previous work has been concentrated on using a single objective for optimization that combines BMP effectiveness and cost for optimization (Chatterjee, 1997; Srivastava et al., 2002) or sequential optimization of effectiveness and cost as separate objective functions (Gitau et al., 2004; Veith et al., 2003), thus putting constraint on one objective function during optimization of the other. Some solutions might be lost through this process when the objectives are considered separately as both of them are highly dependent on each other. There is a need to develop a multi-objective GA model that considers the two objectives of pollution reduction and cost increase simultaneously.

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This study was aimed at developing a multi-objective optimization model that optimizes the two objectives of maximum pollution reduction and minimum increase in cost due to the implementation of BMPs. Water quality parameter evaluated in this study was TP load. A tradeoff (pareto-optimal front) between these two objectives was obtained with the best cost effective solution for TP reduction. The model is applied in L’Anguille River Watershed (LRW), Arkansas, USA, to achieve cost effective total phosphorus (TP) reduction.

Materials and Methods The main components of the model include an optimization algorithm (NSGA-II; Deb et al., 2002) and a water quality simulation model (SWAT; Arnold et al., 1999).

Genetic Algorithm

Genetic algorithms, which are based on Darwin’s theory of evolution, have been used widely for the BMP selection and placement problem (Chatterjee, 1997, Srivastava, 2002, Gitau et al., 2004). The practical advantage of the genetic algorithms for this problem is its ability to handle the hundreds (or sometimes thousands) of variables that need to be optimized during the process of BMP selection and placement. The genetic algorithms have undergone many conceptual changes since they were first introduced by Holland (1997). The two most popular multi-objective optimization techniques available today are Non-dominated Sorted Genetic Algorithm (NSGA-II; Deb, 1999, 2001; Deb et al., 2002) and Strength Pareto Evolutionary Algorithm (SPEA-2; Zitzler et al., 1999). Deb et al. (2002) tested the performance of these algorithms (NSGA-II and SPEA-2) on nine test functions to conclude that NSGA-II gave a better spread of the solutions and better convergence than SPEA-2 in eight of the nine test functions. NSGA-II was used in the present work as the multi-objective optimization tool for the development of the model.

Soil and Water Assessment Tool (SWAT)

The Soil and Water Assessment Tool (SWAT, Arnold et al., 1998) is a watershed scale simulation model designed for use in gaged as well as ungaged agricultural basins. SWAT model is used to simulate the sediment loss and nutrient losses throughout the simulation region. SWAT model performs well for long-term continuous simulations at both monthly and annual scales (Borah and Bera, 2004). The SWAT model divides the watershed into subwatersheds or subbasins based on the outlets selected within the watershed by the user and further divides subbasins into land areas, called hydrologic response units (HRUs), based on land use and soil properties. In the present study SWAT model is used to estimate the initial NPS pollution loadings (sediment, N, and P) at the farm level with every farm being approximately represented by a HRU. SWAT model was also used to estimate the effectiveness of BMPs for pollution reduction.

The inputs that go into the setup of SWAT model are the digital elevation model (DEM), soil, land use, and climate. These inputs were provided to the SWAT model through the GIS interface. All the GIS maps were obtained from the Center for Advanced Spatial Technologies (CAST) at the University of Arkansas, Fayetteville. A sensitivity analysis of the parameters, that were sensitive for flow, sediment, and nutrients, was done using the sensitivity tool in the SWAT

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model. Calibration of the model having parameters that were found sensitive was done for flow, sediment, and nutrients using the auto-calibration tool in the SWAT model. The calibrated model was used as an input for the optimization process. The BMP effectiveness in reducing TP loads was estimated from the SWAT model simulations. The cost data for various BMPs were obtained from crop production budgets for farm planning specific for the L’Anguille River watershed. The BMP costs that were used in the model were annual costs per unit area of the watershed. These costs included the establishment, maintenance, and opportunity costs.

Allele set preparation

The BMPs are land use and land cover specific, i.e. every land use has a unique set of BMPs that are feasible to be implemented in the particular region. These sets of BMP are called allele sets and serve as an input in the optimization model. For example, consider two farms that grow rice and soybean and the various BMPs that are feasible for these two farms can be shown as:

Allele1 (rice) : [NM1 NM2 NM3]

Allele 2 (soybean) : [NM1 NM2 NM3 Till1 Till2 FS1 FS2]

Where NM represents the various nutrient management practices, Till is the tillage practices and FS is the various widths of filter strips that are placed in the farm. If no change occurs, from the baseline, the allele set for this farm takes a null (‘0’) value representing that no change has occurred from the base scenario.

During the optimization process, the algorithm searches for a particular management practice from the given allele set for a particular land use, and subsequently estimates the pollution loading and the cost estimates for the placement of this particular BMP in the selected farm. The pollutant loading and the costs are summed up for all the farms to get an estimate at the watershed level. The allele set forms the variable space for the BMP selection and the watershed level estimates form the objective functions for the optimization model.

Multi-objective Genetic Algorithm model development

The SWAT output (baseline scenario) for TP loading from various HRUs, BMP effectiveness estimated from various SWAT runs, economic data, and allele sets form the inputs for the optimization model. The two objective functions, which need to be optimized, are a) minimization of TP loading and b) minimization of the cost increase because of the placement of BMPs at the farm (HRU) level. Analysis for the cost increase and pollution reduction is done at the watershed scale. The pareto-optimal front (tradeoff) plot of these objective functions gives a range of optimal solutions that can be used to choose the best possible pollution reduction model which has minimal increase in cost.

The various parameters of a GA are population size, number of generations, crossover rate, and mutation probability. Population size determines the number of individuals considered for the evolutionary process. The members of this population undergo genetic modifications through the process of mutation and crossover to obtain a new set of individuals that might be stronger than the parent. The weaker individuals from the pool are eliminated during this process so that the number of individuals in the population remains the same but the population

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is more fit than before. This process is continued for a given number of iterations known as generations. Usually the performance of GA is improved by increasing the population size and number of generations, but that also increases the computation time to reach a near optimal solution. Crossover and mutation probability are the parameters that create the offspring, and hence are critical in driving the algorithm towards an optimal solution.

Sensitivity Analysis and estimation of GA parameters

A sensitivity analysis was performed on GA parameters to determine the influence of these parameters on the pareto-optimal front. The various GA parameters (population size, generations, mutation, and crossover probability) were changed, one at a time, to evaluate the effects of each parameter on the pareto front. Estimating the goodness of the pareto-optimal front is subjective. The closer the front gets to the origin; the better is the solution to minimize the two objective functions. The parameter value for which the pareto-front was closest to the origin in sensitivity analysis was taken as the parameter estimate for the optimization process.

Case Study

Site description

L’Anguille river watershed (LRW) is located in the Mississippi delta region of east Arkansas (Figure. 1). The watershed covers an area of 2520 km2 and drains the entire stretch (157 km) of the L’Anguille River. LRW is predominantly an agricultural watershed; with more than 60% of the watershed in arable land. Table 1 shows that the main crops grown in the watershed are rice (26%) and soybean (46%). These two crops represent most (~95%) of the agricultural land in the watershed. The present work focused on selection and targeting of BMPs for rice and soybean crop areas. The L’Anguille River was included in the list of impaired water bodies by the Arkansas Department of Environmental Quality (ADEQ) in 1998 (ADEQ, 2003). Excessive sediment and nutrients are the main source of impairment of the river (ADEQ, 2003).

The flow information for the watershed was obtained from two USGS gauging sites. The upstream gauging site is located near Colt, Arkansas (USGS Gauge No. 07047942), and the downstream gauging site is located near Palestine, Arkansas (USGA Gauge No. 07047950) (Figure 1). The SWAT model was calibrated for flow at these two gauging stations. However, continuous sediment and nutrients (N and P) data was only available for Palestine. Therefore calibration for sediment and nutrients were only performed for Palestine. A sensitivity analysis was performed to determine the parameters that were sensitive in the SWAT model for flow, sediment, and nutrients (Table 2). CN2 was the most sensitive parameter for flow and sediment, and the most sensitive parameters for N and P were SOL_ORGN and SOL_ORGP. The SWAT model was calibrated for 15 years (Jan. 1990 - Dec. 2004). Auto-calibration tool in SWAT 2005 was used for calibration of the model. The performance indices of the calibration process are listed in Table 3.

The present work dealt with total phosphorus (TP) reduction. The main objective was to find an optimal solution for placement of BMPs that gives cost effective TP reduction from L’Anguille River watershed. The SWAT output gives phosphorus in three different forms (soluble P, organic P, and sediment P). TP loading (in kilograms) can therefore be calculated as shown in

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equation (1) for a given HRU. An area weighted average of this loading was calculated to get the TP loading from the entire watershed.

TP (kg) = [Soluble P (kg/ha) + Organic P (kg/ha) + Sediment P (kg/ha) ]*Areahru (1)

Table 1. Land use land cover distribution of L’Anguille River Watershed LULC % distribution in

the watershed Rice 25.7

Soybean 45.8 Other 28.5

Table 2. List of sensitive parameters and ranking for the SWAT model Parameters Ranking Flow Sediment Total N Total P

1 CN2 CN2 SOL_ORGN SOL_ORGN 2 sol_z SPCON CN2 CN2 3 ESCO SOL_ORGN sol_z SOL_ORGN 4 SOL_AWC sol_z surlag surlag 5 sol_k CMTMP NPERCO USLE_P 6 SMFMX TIMP USLE_P sol_z 7 canmx SOL_AWC SOL_AWC SOL_LABP 8 TIMP SMFMX ESCO ESCO 9 rchrg_dp ALPHA_BF ALPHA_BF SOL_AWC

10 GWQMN ESCO SLOPE PHOSKD

Table 3. Monthly performance indices for calibrated SWAT model Colt Palestine

R2 RNS2 R2 RNS

2

Flow 0.58 0.42 0.45 0.43 Sediment - - 0.23 0.17

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•

•

Figure 1. Location of L’Anguille River Watershed in A

The watershed was divided into 32 subbasins and 433 HRUs. The Sget the estimates of the pollutant loading at the HRU level for the watecalibration period (1990-2004). The various BMPs that were analywatershed were three nutrient management plans (P fertilizer applicaand 22 kg/ha for rice and soybean respectively, 50% above optimalrate), tillage practices (no till and conservation tillage for soybean, conand three different widths of buffer filter strips (0, 5, and 10 meters) fscenarios were considered and SWAT model was run for each of thesto estimate the TP loading at the HRU level. The cost information for t2007 were obtained from the budgets for farm planning prepared by tCooperative Extension Service (CES, 2007) and USDA-NRCS (200included the costs of production (fertilizers, fungicides, herbicides, irretc.) for different tillage systems as shown in Table 4. Some of the BMincreased crop yields, which was also added into the cost componenwere made per unit area ($/ha). Allele sets were made with different placed in rice and soybean. During the optimization process the althese BMPs for a particular crop type. A value of ‘0’ was assigned to acover where no BMPs were applied.

The baseline scenario was taken as the run with no filter strip, oapplication for rice and soybean, and conservation tillage for both ricepollution effectiveness of the various BMPs is estimated with respect increase for the placement of BMPs for the watershed is also estimbaseline. All the estimates were based on an annual basis. The twrepresent TP loading and total cost increase from the watershed were

Colt 07047942

r

W

zt

oehh6iPtsgl

p to

ore

Palestine 07047950

kansas

AT model was used to rshed for 15 years of the ed to be placed in the ion at optimal rate of 24 rate, 25% below optimal servation tillage for rice), r soybean. A total of 54 management scenarios e various BMPs for year e University of Arkansas ). The cost information

gation, labor, fuel, seed, s considered resulted in . All the cost estimates ets of BMPs that can be orithm searched among l other land use and land

timal rate of P fertilizer and soybean fields. The the baseline. The cost

ated with respect to the objective functions that presented as:

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( )

( )

∑

∑

N

hru hruhru=1

N

BMP hruhru=1

Objective function 1: f1 BMP = TP ×A (2)

Objective function 2 : f2 BMP = C ×A (3)

The objective f1 represents the TP loading (kg) for the entire watershed, which is a function of the BMP that is placed in the HRU. TP (kg/ha) loading from each HRU is multiplied with the corresponding area of HRU (Ahru) and summed up for all the HRUs in the watershed. The objective f2 represents the total cost increase ($) for the entire watershed. CBMP ($/ha) is the cost increase per unit area in a particular HRU because of the placement of BMP. The 433 HRUs formed the decision variables, which were to be placed with a BMP, that minimized the two objective functions.

Results and Discussion The sensitivity analysis of GA model indicated that the pareto-optimal fronts were sensitive to all the GA parameters (Figure 2). Increasing the population size gave more freedom for the individuals to solution space as more individuals were present for the evolution and hence more probability of obtaining a better offspring. The population size was increased from 10 to 400, and during this process all other parameters were kept constant. The solution got better in the beginning when the population was increased from 10 to 200 but when the population was further increased to 400, did not show considerable change in the solution (front). This can be explained by the increased freedom of the solution space that the population of 400 has which requires more generations for the individuals to show a considerable change. Additionally, as all the runs were made for a fixed number of generations some of the individuals in the population did not get enough chance to converge.

The results might be improved if a population of 400 was chosen and the model run was made for more number of generations, but that considerably increases the computation time. Number of generations had a significant influence on the shift of the pareto-optimal front towards the origin, i.e. in finding a better optimal solution. No constant pattern in the shift of pareto-optimal front was noticed for the crossover probabilities; the solution improved when it was increased from 0.1 to 0.4 but when increased to 0.5 the front moved away from the origin. However, when the crossover probability was increased further (>0.5) the front again shifted towards the origin, suggesting faster convergence for high crossover probability. The mutation probability range suggested by NSGA-II was between 0 and 0.0004 but it was noticed that for a bit higher mutation probability (=0.001) the pareto-optimal front moved towards the origin. However, further increase in the mutation probability (=0.1) had a drastic drop in the performance. This can be explained by the decrease in convergence of the population due to excessive mutation rates.

Although, increasing the population size yielded a better solution, but considering the increased computation time and delayed convergence for higher population values, an average value of 100 was chosen for the model. The crossover probability and mutation probability, following the assessment, were 0.9 and 0.001, respectively, which showed a faster convergence during the

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sensitivity analysis. The number of generations was taken to be 20,000, which was high enough to allow convergence of the model. The various parameters that were used for the development of the model are shown in Table 5.

Table 4. Cost estimates for rice and soybean production (2007 prices) TILLAGE SYSTEM ($/ha) RICE SOYBEAN Costs distribution Conservation Conservation No-till Variable Expenses Custom Work 255.61 80.00 78.00 Diesel Fuel 36.02 36.02 36.02 Fertilizer Nitrogen 104.37 n/a n/a Phosphorus 68.54 60.61 60.61 Phosphorus (+50%) 102.82 90.92 90.92 Phosphorus (-25%) 51.41 45.46 45.46 Filter Strips 5 meters width n/a 14.79 14.67 10 meters width n/a 29.57 29.35 Fungicide & Seed Treatment 33.01 Herbicides & Insecticides 128.92 38.77 61.53 Interest on operating in capital 46.87 11.84 11.74 Irrigation expenses 256.05 122.31 122.31 Operator Labor 26.79 14.49 9.91 Repair & Maintenance 32.50 18.13 12.15 Seed 35.76 92.58 92.58 Fixed Expenses Machinery & Equipment 147.75 83.18 53.31

The optimization model run using number of generations as 20,000 and a population of 100 took 45 minutes on an CentrinoDuo@2.16GHz computer. The pareto-optimal front for the optimal solution is shown in Figure 3. It can be noticed that the optimal solution has a very good spread range which shows that there was a good nondominance sorting for the different optimal solutions reached by the individuals in the population. The baseline TP loading for the watershed was 390 metric tons. Figure 3 shows that the best ecologically effective solution ‘A’ has a TP loading of 262 metric tons i.e. 33% reduction in the TP for the whole watershed for a cost increase of 14 million dollars for the placement of BMPs (10 grams of TP reduction / $ spent).

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260 280 300 320 340 360 380 4000

2

4

6

8

10

12

14

Total P (metric tons)

Cos

t inc

reas

e (m

illio

n $)

Population

Population 10Population 50Population 100Population 200Population 400

260 280 300 320 340 360 380 4000

2

4

6

8

10

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Total P (metric tons)

Cos

t inc

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e (m

illio

n $)

Generation

Generation 100Generation 1000Generation 10000Generation 40000

260 280 300 320 340 360 380 4000

2

4

6

8

10

12

14

Total P (metric tons)

Cos

t inc

reas

e (m

illio

n $) Crossover

Crossover 0.1Crossover 0.4Crossover 0.5Crossover 0.7Crossover 0.9

260 280 300 320 340 360 380 4000

2

4

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Total P (metric tons)

Cos

t inc

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n $) Mutation

Mutation 0.0001Mutation 0.001Mutation 0.01Mutation 0.1

Figure 2. Pareto-optimal front for the sensitivity analysis of GA parameters.

Solution ‘B’ gives the best economically effective solution but gives a very low TP reduction (<15%) from the baseline for an implementation cost of $0.4 million. Solution ‘C’ gives equal weight age to the two objectives and can be chosen when none of the objectives can be compromised. This tradeoff can be used in the development of TMDLs in the watershed to meet the goals of the pollution reduction by giving a cost effective solution with which the goals are met.

Table 5. Optimal parameters chosen for GA form sensitivity analysis Parameter Value Population 100 No. of generations 20000 Crossover probability 0.9 Mutation probability 0.001

10

270 280 290 300 310 320

2

4

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8

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12

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Total P (metric tons)

Cos

t inc

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e (m

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n $)

← A

B

↓

← C

A : Solution for maximum TP reductionB : Solution for minimum Cost increaseC : Solution which compromises on TP and Cost increase

Figure 3. Watershed scale pareto-optimal front for L’Anguille River Watershed

Summary and Conclusions

Watershed level placement of BMPs to achieve maximum NPS pollutant reduction with minimal increase in BMP implementation costs is an active area of research. This requires finding an optimal solution from a many millions of feasible alternatives for the selection and placement of BMPs. BMP optimization problem requires searching a large variable space to get an optimal solution. Genetic algorithms (GA) are search techniques which search the solution space globally and hence perform better than the local search techniques (for example back propagation, SIMPLEX, etc) to solve problems with large variable space. Most of the previous works done in developing models for this problem have used GA for optimization by considering the two objectives of cost increase and pollution reduction individually by placing a constraint on one objective while optimizing the other. The drawback with this approach is that some solutions might be lost because the two objectives are considered separately. We have addressed this problem with the development of a multi-objective optimization algorithm framework that considers both these objectives simultaneously.

The multi-objective optimization of the two objective functions was performed using the genetic algorithm NSGA-II. The inputs for the optimization algorithm included initial TP loadings from a calibrated SWAT model, allele set with various options for BMP selection in a particular land use, pollution reduction efficiencies, and cost estimates for each BMP. The SWAT model was

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used to simulate various BMP scenarios for the watershed; these scenarios were then used in the development of pollution reduction effectiveness for the various BMPs. A sensitivity analysis of the parameters of NSGA-II was performed to find the parameters that had significant influence on the solution. This process also estimated the parameters for NSGA-II during the process. The final optimized result gave a tradeoff between the two objective functions.

The proposed multi-objective optimization model is applied for the selection and placement of BMPs in L’Anguille River Watershed to give a cost effective TP reduction. A pareto-optimal front for the two objective functions was developed, which gave a range of optimal solutions that are feasible for BMP implementation. The pareto-optimal front gave the most ecological solution with a TP reduction of 33% for a cost increase of $14 million.

The optimization model developed is a general model and is applicable to any other watershed to develop the pareto-optimal fronts. The model gives a range of options available for pollution reduction and their corresponding costs for the implementation of BMPs. This tradeoff can help the watershed modelers in TMDL development and to estimate the corresponding cost for the placement of BMPs for given TMDL goals.

The current study dealt with the development of the multi-objective optimization model for cost effective TP reduction. This can be extended to other NPS pollutants (sediment, and N) to develop a combined pollution reduction model for the selection and placement of BMPs. The computation time for the optimization process can be decreased if a local search algorithm (back propagation, SIMPLEX) is combined with the genetic algorithm, which is a global search algorithm. This hybrid model would contain the advantages of both these techniques and would accelerate the search process of BMPs that meet a given objective function.

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