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Author(s)
First Name
Middle Name
Chetan
Surname
Role
Email
Maringanti
ASABE student
Member
cmaringa@purdue.edu
Affiliation
Organization
Address
Country
Purdue University
225 South University Street, West Lafayette, IN. 47907
USA
Author(s) – repeat Author and Affiliation boxes as needed-First Name
Middle Name
Indrajeet
Surname
Role
Email
Chaubey
ASABE Member
ichaubey@purdue.edu
Affiliation
Organization
Address
Country
Purdue University
225 South University Street, West Lafayette, IN. 47907
USA
The authors are solely responsible for the content of this technical presentation. The technical presentation does not necessarily
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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
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Author(s) – repeat Author and Affiliation boxes as needed-First Name
Middle Name
Jennie
Surname
Role
Email
Popp
ASABE Member
jhpopp@uark.edu
Affiliation
Organization
Address
Country
University of Arkansas
Agriculture Building, Room 218,
USA
University of Arkansas, Fayetteville, AR. 72701
Publication Information
Pub ID
Pub Date
072105
2007 ASABE Annual Meeting Paper
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).
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
algorithms (GA) for optimizing the two objectives of : 1) pollution reduction and 2) cost increase. But
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).
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.
2
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
3
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
4
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
5
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
Ranking
1
2
3
4
5
6
7
8
9
10
Table 2. List of sensitive parameters and ranking for the SWAT model
Parameters
Flow
Sediment
Total N
Total P
CN2
CN2
SOL_ORGN
SOL_ORGN
sol_z
SPCON
CN2
CN2
ESCO
SOL_ORGN
sol_z
SOL_ORGN
SOL_AWC
sol_z
surlag
surlag
sol_k
CMTMP
NPERCO
USLE_P
SMFMX
TIMP
USLE_P
sol_z
canmx
SOL_AWC
SOL_AWC
SOL_LABP
TIMP
SMFMX
ESCO
ESCO
rchrg_dp
ALPHA_BF
ALPHA_BF
SOL_AWC
GWQMN
ESCO
SLOPE
PHOSKD
Table 3. Monthly performance indices for calibrated SWAT model
Colt
Palestine
R2
RNS2
R2
RNS2
Flow
0.58
0.42
0.45
0.43
Sediment
0.23
0.17
6

Colt 07047942

Palestine 07047950
Figure 1. Location of L’Anguille River Watershed in Arkansas
The watershed was divided into 32 subbasins and 433 HRUs. The SWAT model was used to
get the estimates of the pollutant loading at the HRU level for the watershed for 15 years of the
calibration period (1990-2004). The various BMPs that were analyzed to be placed in the
watershed were three nutrient management plans (P fertilizer application at optimal rate of 24
and 22 kg/ha for rice and soybean respectively, 50% above optimal rate, 25% below optimal
rate), tillage practices (no till and conservation tillage for soybean, conservation tillage for rice),
and three different widths of buffer filter strips (0, 5, and 10 meters) for soybean. A total of 54
scenarios were considered and SWAT model was run for each of these management scenarios
to estimate the TP loading at the HRU level. The cost information for the various BMPs for year
2007 were obtained from the budgets for farm planning prepared by the University of Arkansas
Cooperative Extension Service (CES, 2007) and USDA-NRCS (2006). The cost information
included the costs of production (fertilizers, fungicides, herbicides, irrigation, labor, fuel, seed,
etc.) for different tillage systems as shown in Table 4. Some of the BMPs considered resulted in
increased crop yields, which was also added into the cost component. All the cost estimates
were made per unit area ($/ha). Allele sets were made with different sets of BMPs that can be
placed in rice and soybean. During the optimization process the algorithm searched among
these BMPs for a particular crop type. A value of ‘0’ was assigned to all other land use and land
cover where no BMPs were applied.
The baseline scenario was taken as the run with no filter strip, optimal rate of P fertilizer
application for rice and soybean, and conservation tillage for both rice and soybean fields. The
pollution effectiveness of the various BMPs is estimated with respect to the baseline. The cost
increase for the placement of BMPs for the watershed is also estimated with respect to the
baseline. All the estimates were based on an annual basis. The two objective functions that
represent TP loading and total cost increase from the watershed were represented as:
7
N
Objective function 1: f1 BMP  =  TPhru × A hru
(2)
hru=1
N
Objective function 2 : f2 BMP  =  CBMP × A hru
(3)
hru=1
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
8
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).
9
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
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
11
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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