Using Machine Learning and Genetic Algorithms to Optimize
Scholarship Allocation for Student Yield
Lovenoor Aulck

Dev Nambi

Jevin West

University of Washington
Seattle, WA, USA
laulck@uw.edu

F.H. Cancer Research CenterSeattle, WA, USA
dnambi@fredhutch.org

University of Washington
Seattle, WA, USA
jevinw@uw.edu

ABSTRACT
Effectively estimating student enrollment and recruiting students
is critical to the success of any university. However, despite having an abundance of data and researchers at the forefront of data
science, universities are not fully leveraging machine learning anddata mining approaches to improve their enrollment management
strategies. In this project, we use data at a large, public university toincrease their student enrollment. We do this by first predicting theenrollment of admitted first-year, first-time students using a suiteof machine learning classifiers (AUROC = 0.85). We then use the results from these machine learning experiments in conjunction withgenetic algorithms to optimize scholarship disbursement. We show
the effectiveness of this approach using actual enrollment metrics.
Our optimized model was expected to increase enrollment yield by
15.8% over previous disbursement strategies. After deploying themodel and confirming student enrollment decisions, the university
actually saw a 23.3% increase in enrollment yield. This resulted
in millions of dollars in additional annual tuition revenue and acommitment by the university to employ the method in subsequent
enrollment cycles. We see this as a successful case study of how
educational institutions can more effectively leverage their data.

KEYWORDS
education, funding, tuition, university, college, machine learning,
genetic algorithm
ACM Reference Format:
Lovenoor Aulck, Dev Nambi, and Jevin West. 2019. Using Machine Learning
and Genetic Algorithms to Optimize Scholarship Allocation for Student
Yield. In SIGKDD ’19: ACM SIGKDD Conference on Knowledge Discovery andData Mining, August 4–8, 2019, Anchorage, AK. ACM, New York, NY, USA,
9 pages. https://doi.org/10.1145/1122445.1122456

1

INTRODUCTIONManaging student enrollment is one of the core administrative tasksof any university. However, it is far from simple as universities aim
to attract and retain the best students with limited resources [4, 13].
Enrollment management has wide-ranging implications on institutions’ student body composition as well as their budgeting andPermission to make digital or hard copies of all or part of this work for personal orclassroom use is granted without fee provided that copies are not made or distributedfor profit or commercial advantage and that copies bear this notice and the full citationon the first page. Copyrights for components of this work owned by others than theauthor(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or
republish, to post on servers or to redistribute to lists, requires prior specific permission
and/or a fee. Request permissions from permissions@acm.org.
SIGKDD ’19, August 4–8, 2019, Anchorage, AK© 2019 Copyright held by the owner/author(s). Publication rights licensed to ACM.
ACM ISBN 978-1-4503-9999-9/18/06. . . $15.00
https://doi.org/10.1145/1122445.1122456

finances, where a reliance on tuition income necessitates accurately
forecasting student enrollments [12, 27]. One instrument that hascontinually been leveraged in the pursuit of enrollments and theassociated tuition income is financial aid as receiving a financial aid
award increases the likelihood of a student enrolling [10, 13, 16].
While financial aid remains a powerful mechanism for institutions
to reach their admissions and revenue targets, miscalculating projected student enrollments and mismanaging financial aid funds
can have severe implications (such as rescinding over-committed
offers1 )[2]. Furthermore, as institutions face tightening budgets
and find their pricing policies continually under scrutiny, it remains imperative for them to optimize the resources they have by
maximizing enrollments and the associated tuition revenue fromfinancial aid programs [6, 7, 11, 15]. As such, accurately predicting
enrollment and optimizing how student aid is disbursed is criticalto enrollment management with financial implications that cascade
across the entirety of an institution. In this work, we develop an
approach to address this challenge, implemented it for a recent entering class, and found that it far outperformed previous strategies.
Predicting enrollment and optimizing the allocation of student
aid requires data on student admissions, operational expenses, andbudgets. This data is stored in institutions’ organizational databases
or can be extracted from historical and operational records. However, despite having this abundance of data on previous enrollments
and finances, institutions are often slow to leverage it to gain actionable insights and improve institutional processes [17, 23, 30].
What’s more, using data for insights in education is less prevalent
at traditional campuses (i.e. schools where learning is primarily
on-campus) and more common in online and computerized environments, which are much more amenable to the collection andanalysis of digitized data [20]. To this end, traditional universities
remain “data-rich” but are “information-poor” in that they have theraw data needed to extract intelligible insights but are unable to doso due to infrastructure limitations and untrained personnel, among
other reasons [25]. This results in the outsourcing of data-centric
enrollment work (including enrollment prediction and developing
scholarship disbursement strategies) to full-service consulting firms,
which do not disclose their proprietary approaches or how theirresults are evaluated [14]. The lack of motivation for consulting services to disseminate their work coupled with institutions trying tomaintain competitive advantages in recruitment limits the extent ofpublished research on how institutions can more effectively utilize
data in enrollment management to improve existing processes. As
a result, this dearth of literature provides little to demonstrate howdata mining and machine learning can assist in the critical missionof enrollment management and in allocating financial aid.
1 See https://bit.ly/2Scxqj6 as a recent example.

SIGKDD ’19, August 4–8, 2019, Anchorage, AK

Aulck, L. et al.

In this project, we mine data from a large, public university in the
United States (US) to optimize the disbursement of a merit-based
scholarship for domestic non-resident students. We do this in two
steps. We create a predictive model of student enrollment. We thenuse a genetic algorithm to optimize scholarship disbursement tomaximize student enrollment based on this predictive enrollment
model. We conducted this work during the most recent admissions
cycle of the university and the optimized awards were given to thelatest entering class. After seeing improvement in student enrollment yield and an increase of millions of dollars in annual tuition
revenue, the university incorporated our approach into their enrollment management process. We believe this project is a case study
for other institutions seeking to similarly leverage institutional datafor improving enrollment forecasting and financial aid allocation.

undisclosed university, also finding that neural networks outperformed the other models when judging by classification accuracy[3]. Recently, Shrestha et al. looked to predict whether undergraduate and graduate international students admitted to an undisclosed
Australian university would enroll [24]. Their approach included
looking at Naive Bayes, decision trees, support vector machines,
random forests, K-nearest neighbors, and neural networks. In theirsetup, logistic regression and neural networks fared best. It should
be noted that there is a scarcity of literature among the works
listed above on using ensemble approaches in predicting student
enrollment and comparing their performance to neural approaches.

2

While there are some examples of works examining the use of machine learning in predicting enrollment, there is very little detailing
scholarship disbursement strategies, especially ones leveraging
machine learning and/or numerical optimization techniques. One
example is the work of Alhassan and Lawal, who demonstrated theuse of tree-based models for determining which students would beawarded scholarships in Nigeria [1]. Alhassan and Lawal describe
the results as “effective” and “efficient” compared to approaches
previously used but did not provide more on the success of the
disbursement strategy. Spaulding and Olswang demonstrated theuse of discriminant analysis to model the enrollment decisions ofstudents based on varying need-based financial aid awards at an
undisclosed university in the US [26]. They found that changes intheir award policy would yield only small upticks in enrollment.
One work used machine learning to predict enrollment in conjunction with a numerical optimization technique to disburse scholarships. Sarafraz et al. used neural networks with genetic algorithms
to optimize financial aid allocations and while our research is similar in spirit, there are a few notable differences [22]. Firstly, thescholarship fund optimized in this work is merit-based, meaning
there are upper and lower bounds on scholarship awards that are
specific to each student. This makes for a more difficult optimization
task. We also examine alternative predictive models beyond justneural networks (such as ensemble approaches) and use a larger
dataset in terms of both the number of observations and the numberof features (over 72,000 observations vs 4,082; over 100 featuresvs 6). We also provide a comprehensive description of final model
performance across multiple metrics and a detailed outline of how
genetic algorithms can be used for aid disbursement, including abinning framework to drive the optimization task. Finally, we sharereal-world enrollment metrics after employing the scholarship optimization to demonstrate the effectiveness of our approach.

RELEVANT WORKThe following discussion of relevant work is not exhaustive withrespect to enrollment prediction and financial aid optimization. It
is intended to give examples of relevant approaches with a focus
on more recent work. While there is some work showing how to
predict enrollment, there is very little showing how to allocate
scholarships and hardly anything that ties the two together.

2.1

Predicting Enrollment

A few studies have employed machine learning and data mining
techniques to predict enrollment at a university using non-neuralapproaches. DesJardins developed a logistic regression model using
a dataset of approximately 14,400 students from an undisclosed tierI research university in the US Midwest. DesJardins’ model gave an
area under the receiver operating characteristic curve (AUROC) of
0.72 when predicting whether or not a student will enroll [5]. Similarly, Goenner and Paul used logistic regression to predict which ofover 15,000 students at a medium-sized US university would eventually enroll [9]. With a highly imbalanced dataset, their regression
model gave an AUROC value of 0.87. Nandeshwar and Chaudhari
later used a suite of learners, including Naive Bayes and tree-basedmodels, to predict which of approximately 28,000 students would
enroll at West Virginia University [19]. They were interested invariables contributing to students’ decisions (finding financial aid
to be an important factor) and did not give an assessment of how
well their models fared outside of accuracy (which was about 84%).
In addition to the above studies examining non-neural approaches
for predicting enrollment, some studies have also found that neuralapproaches fare very well for the same task and often perform better than non-neural approaches. For example, Walczak evaluateddifferent neural network designs when examining predictions ofstudent enrollment at a small US private liberal arts college, stressing the problem as one of resource allocation [28]. Using a few
thousand students, Walczak found that backpropagating neuralnetworks fared best among those compared. Walczak and Sicich
later compared neural networks versus logistic regression to predict whether students would enroll at a given institution at botha small US private university and at a large public US university[29], finding that neural networks performed better than logistic
regression. Chang used logistic regression, decision trees, and neural networks to predict the enrollment of admitted applicants at an

2.2

3

Scholarship Optimization

METHODS

We present the methods for this work in the following order: first,
we give an overview of the setting for this research; then, we describe the data as well as feature engineering performed on thedata; we then describe the process for predicting enrollment; finally, we discuss optimization constraints and outline the process
for scholarship optimization.

Optimizing Scholarship Allocation

3.1

Setting

This scholarship optimization work was performed at a large, public US University (the University2 ) in early 2018. The scholarshipfund examined was created to maintain the University’s academic
standards while maximizing the enrollment of first-time, first-year(freshmen) domestic non-resident (DNR) students by giving themfinancial incentive to enroll at the University. DNR students are
students from the US who are not from the state in which the University is located. DNR students account for significantly larger
tuition charges than their resident (i.e. in-state) counterparts and,
therefore, their enrollment is of high importance from a budgeting and finance perspective. Tens of millions of dollars in total areawarded annually to these students as part of the scholarship fundwith millions eventually spent each year on students who enroll.
The scholarship fund that we examined (DNR scholarships) was
designated to be disbursed in a merit-based manner. As such, students with higher academic profiles, as defined later, were given
equal or larger scholarships than those with lower academic profiles, regardless of financial need. Additionally, only freshmen DNR
students who were accepted to the University were eligible to receive a DNR scholarship award. All admitted DNR students wereautomatically considered for a DNR scholarship and students did
not need to apply for the scholarship separately.
In years prior, developing the disbursement strategy for the DNR
scholarship was outsourced to external consulting services. For thelast full application cycle (the 2018 entering class), it was brought
under the technical stewardship of the University. This is the application cycle for which we optimized scholarship disbursement. It
should be noted that the models that were previously developed
for the disbursement of this scholarship fund were proprietary to
the consulting service and could not be leveraged in any way. However, student application, enrollment, and scholarship data fromprior years was available. When describing results, we compare
the results from our approach to that developed by the consulting
service. We cannot compare the approach detailed in this writing
to a completely unoptimized approach or one that is randomized.
Award-receiving students concurrently learned of the amountof their scholarship and of their admittance to the University. However, not all applications were scored by admissions officers when
the first round of awards were to be given. This was primarily
due to the time taken to review tens of thousands of admissions
applications and typical review timelines at the University. We did
not know of every admitted student at the time of optimization yet
the scholarship awards were only to be given to admitted students.
Thus, the last full application cycle’s data could not be used directlyin the optimizations. Instead, our approach used data from previous
years to develop a fund allocation strategy and then apply thisstrategy to the last application cycle. This was with the expectationthat applicants in the last application cycle were similar to years
prior and we checked to ensure that this was the case.

3.2

Data

The data for this work consisted of information on all freshmen
DNR applicants to the University from 2014-2017 with usable data.
This totaled 72,589 students. Data from the study came from two
2 University administrative offices requested that the institution not be identified.

SIGKDD ’19, August 4–8, 2019, Anchorage, AK
major sources, both of which were regularly maintained by the
University: the students’ admissions applications and their Free Application for Federal Student Aid (FAFSA) information. The FAFSA
is an application prepared by incoming and current US college students to determine their eligibility for financial aid. It should be
noted that no additional data was collected for this project. Examples of data pulled from students’ admissions applications included
their high school courses taken, entrance exam scores, college GPA(if they had taken classes for credit), whether they received anathletic scholarship, whether they were a first-generation college
student, and their parents’ educational attainment. These were
all self-reported and verified by the University as needed. Data
directly from and derived from student FAFSA filings included students’ family income, their expected family contribution to college
expenses (as calculated by the University), and institutional loan
amounts awarded to the student. Also included in the data wereindicators of whether each student was accepted to the University
and whether the student eventually enrolled. Of the 72,589 students
in the dataset, 34,874 were admitted (48.04% of all) and 5,081 enrolled (14.57% of admitted, 7.00% of all). Demographic variables
such as gender, race, and ethnicity were available but were notincluded in the data as discussed in Section 4.1.
Within the data were values on tuition amounts students would
pay on an annual basis, their financial aid grants and scholarships
awarded (outside of DNR scholarship awards), and their DNR scholarship award amount. These variables were not included in any
prediction or optimization model on their own. Instead, we created a “reduced_tuition” variable which was the annual tuition
amount for the students less their total grants and scholarships(i.e. the other two variables summed). We used this variable as asingle financial aid and tuition-related feature for the predictions
and optimizations discussed below.
DNR applicants to the University were on average 18.0 years oldat the time of application. About 17% of applicants had taken partin a college in high school program but about 99.5% of applicants
were applying as freshmen entrants, meaning they were below thecredit threshold to be considered sophomores upon entry to the
University. About 66% of applicants had filled a FAFSA.

3.3

Feature Engineering

Prior to prediction and optimization, we engineered features fromexisting variables. First, we either converted categorical variables todummy variables or replaced them with a binary indicator variable.
Then, we grouped students based on their FAFSA award amounts
into 6 discrete bins, each of which was used as a categorical feature.
We created binary indications of whether students attended eachof the 10 most popular high schools for student applications anddid the same for the 10 most popular states from which students
applied. A binary indication was also created for a student athlete
designation as each sport had its own application codes. In addition,
we also created a separate binary indication for whether the student
was transferring any credits from a college in high school program.
Students’ academic interests were also pulled from their applications and were grouped into 12 broader categories. We then createdbinary indications of whether a student was interested in each of
the categories. Only students’ first application to the University

SIGKDD ’19, August 4–8, 2019, Anchorage, AK
and the resulting admissions/enrollment decisions were included in
the data. This resulted in a total of 108 features. Not all applicants
filed a FAFSA form and we imputed missing FAFSA-related values
using gradient boosted regression trees [8].

3.4

Predicting Enrollment

To predict enrollment, we first randomly divided the data using a
80-20 training-test split, with 57,359 students in the training set and
14,340 students in the test set. We did not re-balance the data withrespect to classes. We scaled the training data by subtracting themedian of each feature and dividing by the feature’s interquartile
range. We subsequently scaled the test data using the scaling values
from the training data. The binary outcome variable indicating
whether the student enrolled at the University was not scaled.
After performing the training-test split, we trained 7 machinelearning (ML) classifiers on the training set to predict enrollment.
These classifiers were: a bagging tree ensemble (BC), gradientboosted trees (XGB), K-nearest neighbors (KNN), random forests(RF), regularized logistic regression (LR), support vector machines(SVM), and a neural network with 3 hidden layers (MLP). We tuned
the hyperparameters for each of the classifiers using 5-fold crossvalidation on the training set. We report performance from all classifiers on the test set, which was not used to train the classifiers
and only used to evaluate final performance. We used the classifier
with the best performance to optimize aid disbursement.

3.5

Modeling Constraints

Several constraints were posed on the scholarship disbursementin accordance with the strategic goals University administrators.
These constraints underwent many changes during the modelingprocess, not all of which will be discussed. Due to University policy,
exact values for awards and budgets will also not be discussed.
That said, the constraints on the disbursement strategy were as
follow, where F represents funds in DNR scholarship offers, B represents funds in the DNR scholarship budget, N specifies a countof students, and S specifies a scholarship award amount:(1) The total amount spent on DNR scholarships (F spent ) cannot
exceed a pre-determined amount (B spent ): F spent ≤ B spent(2) The total amount offered to students in DNR scholarships
regardless of whether they enroll (F offered ) cannot exceed apre-determined amount (B offered ):F offered ≤ B offered(3) The percentage of admitted students who are awarded scholarships (N %awarded ) should be approximately equal to a predetermined percentage (N %target ):N %awarded ≈ N %target(4) The award amounts must be divisible by $300 to allow for
round hundred-dollar splits across three academic terms.
(5) There is a minimum value for a single scholarship award(S min ) but no pre-determined maximum value.

3.6

Optimizing Scholarships

After developing a classifier to predict enrollment, we used theprediction outputs of the classifier as an objective function in optimization. The aim of the optimization was to develop a strategy that
disbursed the DNR scholarship budget in a manner that maximized
student enrollment. In this work, we used a genetic algorithm (GA)for optimization as GAs are known to work well when we have

Aulck, L. et al.
a well-defined measure to optimize (i.e. student enrollment) but
not a well-defined, continuous, and/or differentiable objective function. GAs are also known to find near-optimal solutions quickly,
which was essential when we wanted to rapidly outline different
budgeting and allocation scenarios early in our modeling.
GAs are a class of evolutionary algorithms and are inspired bybiological evolution. GAs generally involve iteratively starting withsome population of chromosomes, undergoing selection acrossthis population according to a measure of fitness, using genetic
crossover and mutation to produce offspring from the most fit
individuals, and then using this offspring as the population for the
next iteration [18]. The overall population fitness improves witheach iteration and the GA eventually converges towards an optimal
solution. As this description of GAs relates to this work, we startwith a population of award disbursement strategies whose “genetic
material” (chromosomes) are a set of scholarship award values; themeasure of fitness to assess these individuals is based on predicted
enrollment after accounting for constraints, as detailed below; andthe crossover and mutation functions used to create offspring are
based on changes of scholarship award values, as described below.
We used the data for the previous year’s (2017) admitted class inthe optimization of scholarship funds. In all, this was 9,479 students(N total ). In this sense, we used data from the year prior to optimize
the disbursement for the most recent application year. We pared thedata down to a single year’s application cohort to avoid having toconsider if any of the optimization constraints in Section 3.5 werebeing violated for each of the application years simultaneously.
We generated a set of possible scholarship awards that spanned
S min to a chosen maximum (S max ) in $300 increments and included$0. Award values had a non-zero minimum value of S min based on
historical awards, though stewards of the scholarship fund were
amenable to lowering it. Ultimately, as discussed in Section 4.2,
this floor was lowered in favor of a scholarship award with a valueof S min2 . We did not determine S max beforehand but instead set itsuch that the optimization procedure did not generate an output
that included a S max scholarship award. S min was evenly divisible
by $300 and we generated possible scholarship awards in $300
increments to satisfy constraint (4) from Section 3.5.
Part of the difficulty of this particular optimization task lies in
the fact that awards were to be given in a merit-based manner. As
such, the scholarship award for any student is dependent on theawards of students with similar academic profiles. For example,
if one was to rank all admitted students in the application poolbased on a measure of merit, the minimum possible award given
to a particular student would be determined by the award given to
the student with the merit that is immediately lower. Similarly, themaximum award a student would be eligible for would be equal tothe award given to the student with the merit that is immediately
higher. As such, if optimizing on a per-student basis, altering theaward for any given student to influence their enrollment decision
could result in a cascade during the optimization that subsequently
effects every other student’s award amount. This results in a very
complex fitness landscape when optimizing scholarship awards forthousands of students individually.
As a solution to this issue of an optimization cascade, we firstranked and binned students based on academic merit such that allOptimizing Scholarship Allocation

Individuals with K scholarship bins

Population of p individuals

students in the same bin received the same scholarship award. To
perform this binning, we first sequentially ranked students basedon 3 variables: their application academic score, their high school
GPA, and their scores on college entrance exams, in that order.
This ranking was students’ “academic profile.” Each student’s application academic score was based on an institutional scoring
system of their academics and was the primary variable for determining their academic profile. We were provided this metric by
the University admissions office - it was not calculated by us. Ties
between students having the same application academic score werebroken by looking at their high school GPA; any remaining ties
thereafter were broken using students’ entrance exam scores. Oncestudents were ranked, they were divided into 20 ventiles based on
their academic profiles (i.e. students were grouped across every
5th percentile) with each ventile receiving the same scholarshipaward amount. Using ventiles allowed for us to have sufficient flexibility when exploring the fitness landscape during optimization
while also not being so granular as to continually be caught inlocal extrema. Additionally, ventiles helped mitigate the effect of
optimization cascades by giving identical awards to students withsimilar academic profiles. We refer to each of these ventiles as a“bin” and each bin served as the chromosomal building block for
the GA. A single scholarship allocation strategy consisted of thescholarship awards across all 20 scholarship bins and is referred
to as an “individual” henceforth when used in the context of the
GA. As such, each individual’s genetic material can be thought ofas being in the form of chromosomes which were composed ofscholarship award bins.
We then created a fitness function to evaluate the effect of altering the reduced_tuition variable on student enrollment. Specifically, this function took the genetic material of a scholarship individual (i.e. a set of scholarship awards for each bin) and thenre-evaluated the reduced_tuition variable for each student basedon their updated DNR scholarship award. As noted above, we created the reduced_tuition variable by taking the tuition due for a
student and subtracting their total grants and scholarships; it was
the only financial aid and tuition-related variable used in the predictive model. The function re-calculated each student’s likelihoodfor enrollment based on the updated values for reduced_tuition
using the predictive enrollment model. The final output for the fitness function was a calculation of the number of students predicted
to enroll for a given scholarship individual, which we used as thefitness criterion for evaluating individuals.
The organization of the population, individuals, and bins for
the GA optimization is shown in Figure 1. We generated an initial
population of p individuals by randomly selecting K scholarshipawards (one for each bin) and sorting for each individual. For thiswork, p = 1000 and K = 20. Each bin effectively contained thesame number of students (N bin ), which was approximately equal to
N totalK . Awards were not unique for each bin and could be duplicated.
N bin multiplied by the scholarship award for each bin equalled
the funds awarded for that respective bin; the sum of these acrossall K scholarship bins for a given individual was F offered for that
individual. The predicted number of enrollees for each scholarshipbin multiplied by the scholarship award for that respective bin
equalled the funds spent for that bin; the sum of these across all K

SIGKDD ’19, August 4–8, 2019, Anchorage, AK

Lower academic

Higher academic

profilesprofiles

i=1

S 11

S 12

S 13

S 14

...

S 1K

i=2

S 21

S 22

S 23

S 24

...

S 2K

i=3

S 31

S 32

S 33

S 34

...

S 3K

Sp4

...

SpK

..
.
i=p

Sp1

Sp2

Sp3

Figure 1: Genetic algorithm setup. Individuals (i) are scholarship allocation strategies of K scholarship bins (j). The population consists of p individuals. Each Si j is a scholarshipaward value for the i th individual and the j th scholarshipbin. The bins are sorted based on academic profile such that
Si1 ≤ Si2 ≤ Si3 ... ≤ SiK for any given i (but not necessarily
across individuals). For this work, K = 20 and p = 1000.
scholarship bins for a given individual was F spent for that individual.
The number of bins with non-zero award values divided by K was
equal to N %awarded for an individual.
We penalized each individual’s fitness if the optimization constraints in Section 3.5 were violated. We initialized a single penalty
coefficient (σ ) to 1.0 and then successively enforced each of thefollowing squared penalties for a given scholarship individual:• if too much was spent on scholarship awards:
B spent 2)
F spent > B spent → σ = σ ∗ ( Fspent• if too much was offered in scholarship awards:
offered 2
F offered > B offered → σ = σ ∗ ( BFoffered)• if too many students were awarded a scholarship:
N %target 2
N %awarded > N %target → σ = σ ∗ ( N%awarded)• if too few students were awarded a scholarship:
N %awarded < N %target → σ = σ ∗ ( NN%awarded)2%targetUltimately, we multiplied the output of the fitness function by thepenalty coefficient to penalize constraint-violating individuals. If
there were no constraints violated, the penalty coefficient remained
at 1.0 and the fitness evaluation of the individual remained unchanged. Note that all constraints were given equal weight.
The general process for the GA was as follows. We randomly
generated the initial population of individuals as described above.
We then calculated the fitness of each individual using the fitness
function and took a subset of the most fit individuals from the population (10%) as the basis for the next generation of the population.
We employed genetic crossover to this subset of the population to
generate offspring. We used two-point genetic crossover, wherein
two points were randomly selected along chromosomes and thegenetic material from one individual was swapped with that from

SIGKDD ’19, August 4–8, 2019, Anchorage, AK
another between the two points, much like a two-point crossover
mutation in nature. In other words, for a pair of randomly selectedindividuals, we randomly selected two scholarship bins from ventiles 1 through 20 and all scholarship award values between thetwo bins from one individual were swapped with those from theother individual and vice versa.
After enough offspring were generated by crossover to refill
the population, the offspring underwent mutation. We used three
types of mutations: an increase mutation, a decrease mutation, anda swap mutation. For a mutation, we randomly selected an individual and then randomly selected a bin from this individual. The
corresponding award for this bin was either increased to anotherpossible award amount (increase mutation), decreased to anotherpossible award amount (decrease mutation), or swapped for anotherrandomly selected award amount (swap mutation). The probabilityof performing either an increase, decrease, or swap mutation wereequal unless the scholarship award value equaled S min or S max , inwhich case we eliminated the possibility of a decrease mutation or
an increase mutation, respectively. After mutations, we re-sorted
the scholarship bins across each individual to ensure students withhigher academic profiles received larger awards. We kept the initial subset of the most fit individuals unchanged during crossoverand mutation; instead, we altered replicas of these individuals so
we could compare the most fit individuals from one generation to
those from the next generation. The new generation of individuals
then served as the population for the next algorithmic iteration. We
repeated the above process for 20 generations of the population andused the most fit individual thereafter as the scholarship allocation
strategy. The process for the GA is shown in Process 1.
Process 1: Genetic algorithm process for scholarship allocation(parameters for project are in parentheses)
1: Generate initial population (p = 1000 with K = 20 bins each)
2: Evaluate fitness of each individual (where fitness isenrollment count predicted by XGB classifier)3: For each of G generations: (G = 20)

Keep subset of population with highest fitness (10% kept)
Use two-point crossover across individuals to fill population
6:
Mutate random bins of random individuals
7:
Evaluate fitness of each individual
8: Use individual with highest fitness after G generations

4:
5:

4

Aulck, L. et al.
Table 1: Classifier performance sorted by rank across all metrics. Names of classifiers are provided in Section 3.4.

1.
2.
3.
4.
5.
6.
7.

Model

Accuracy

AUC

F1-score

XGB
RF
MLP
BC
LR
SVM
KNN

93.10%
93.06%
93.01%
93.05%
92.96%
93.00%
92.80%

0.846
0.848
0.845
0.833
0.805
0.780
0.793

0.905
0.901
0.902
0.901
0.900
0.900
0.893

of prediction accuracy, AUROC, and F1-score in Table 1. We used
the same observations as a test set to compare performance acrossclassifiers; for the test set, the majority class represented 92.8% ofobservations (i.e. 7.2% of students in the test set eventually enrolled
at the University). All classifiers performed similarly in terms ofboth accuracy and F1-score. Because of the large class imbalance,
there were only modest gains in terms of accuracy over the majority
class representation. Ensemble classifiers (RF, XGB, and BC) had thehighest accuracies while KNN performed on par with the majority
class representation (note: it was checked that the KNN model
did not predict that all observations were of the majority class).
The highest F1-score, meanwhile, was given by the XGB classifier,though it was not substantially higher than other classifiers.
We show ROC curves for the classifiers in Figure 2. The generalshape of the ROC curves was similar across the classifiers but withmeaningful variation in AUROC. Specifically, RF, XGB, and MLP
tended to perform similarly in terms of AUROC and had the highest
AUROC values. This is in line with previous work where neuralnetworks tended to perform well when predicting enrollment, even
without more complex architectures in this case. That said, theensemble classifiers performed similarly well for the task at hand.
Demographic data was not used in the models. We expect that
including demographic variables in the prediction models would
improve predictive performance to some degree, albeit at the expense of potential explicit discrimination with respect to recipientcharacteristics. As such, we decided to exclude demographic variables when building the classifiers. While doing so limits the degree

RESULTS AND DISCUSSION

Using the methods described in Section 3, we developed a predictiveclassifier of student enrollment and used it in conjunction with agenetic algorithm that optimizes the allocation of a scholarshipfund. Ultimately, the university saw a 23.8% increase in enrollment
yield after using our approach. This resulted in millions of dollarsof additional annual tuition revenue. The following section presents
these results in greater detail in the same order as the methods.

4.1

Predicting Enrollment

Previous studies have shown the effectiveness of ML in predicting
enrollment. We examined seven different predictive classifiers forthis task. We show the performance of these classifiers in terms

Figure 2: ROC curves for enrollment prediction

Optimizing Scholarship Allocation

SIGKDD ’19, August 4–8, 2019, Anchorage, AK
Table 2: Predicted enrollments after adjusting the classification threshold for test data and all data (training + test data).

ActualPredicted

Test Data

All Data

1,032
1,049

5,081
5,166

of similarly adjusting the classification thresholds when using theother ML classifiers and determined that using XGB would still be
the most viable for scholarship optimization.
Figure 3: Confusion matrices for predicting enrollment using XGB and a classification threshold of 0.5 (left) and an
adjusted classification threshold of 0.22 (right)of explicit discrimination, the possibility of implicit discrimination
remains - particularly with respect to associations between demographics, income, geographic location, and academic performance[21]. Checking and controlling potential demographic imbalances
is beyond the scope of this particular work but was handled bystewards of the DNR scholarship fund after optimization.
We examined classifier performance across all metrics and decided to use XGB to optimize scholarship allocation. Prior to optimization, we adjusted the classification threshold for the prediction
probability to the nearest one-hundredth such that the number ofstudents predicted to enroll by the model was nearest to the actual
enrollment count. By adjusting the threshold in this manner, weused a lower probability decision threshold (0.22) than the valueof 0.5 that is typically used in binary classification. We understoodthat doing so came at the expense of an increased rate of false
positives (Type I error) but it also allowed for the prediction counts
to be closer to actual counts, which was necessary when discussing
predictions with administrative stakeholders. We show the effectsof this adjustment in Figure 3, where the confusion matrix using thetypical threshold of 0.5 is shown along with the confusion matrix
using the adjusted threshold of 0.22.
Of note from the confusion matrices is the degree to which
students who were not going to enroll at the University could be
predicted while it was much more challenging to identify those
who would enroll. This speaks to the selectivity of the University
in that many of the candidates who would not enroll were simply
those who were not accepted to the University. Concurrently, thedifficulty with identifying students who will enroll aligns with thefact that these DNR students are applying to a university that isaway from their respective homes and social bases. Also, those thatare accepted to the University tend to be of higher academic standing, giving them more potential college choices. Thus, the general
likelihood of a DNR student enrolling is difficult to determine when
considering potential social factors and college options.
Lowering the classification threshold resulted in predicted enrollment counts in line with what was seen in the data, as shownin Table 2. Lowering the classification threshold also allowed for agreater number of true positives while also balancing the numberof false positives and false negatives. We also examined the effect

4.2

Optimizing Scholarships

After we developed a model for predicting student enrollment, weused a GA to design a scholarship disbursement strategy. We used
the GA in a setup with students grouped in ventiles, with eachventile receiving the same award amount. The genetic material(awards for each ventile) for individuals (allocation strategies) wasaltered for each iteration of the GA and then fitness was determined.
Fitness was based on predicted enrollment after accounting for theviolation of constraints. Due to the application review timeline at
the University, we did not know which students of the most recent
entering class (2018) would be admitted and used the prior year’s
application data (2017) to develop a disbursement strategy. Because
the disbursement strategy relied on students being grouped into
ventiles, we easily applied it to the most recent entering class after
checking that the two classes were similar. Additionally, the binning
strategy and the use of ventiles alleviated concerns about the sizeof the entering class as specific award amounts were disbursed toproportions of the entering class and not to a fixed count thereof.

Figure 4: Fitness measures across generations of genetic algorithm. Fitness was equivalent to predicted enrollment.
We show fitness (predicted student enrollment) measures acrossthe population of individuals for each generation of the GA in
Figure 4. As expected, the maximum, mean, and median valuesof fitness increase across generations, though these increases aremuch smaller for later generations. The minimum fitness values
for the population follow a similar trend with some variation. All
metrics eventually converge to the predicted enrollment, which isshown as a percentage. Monte Carlo simulations will be used in
the future to outline a distribution of likely enrollment counts.

SIGKDD ’19, August 4–8, 2019, Anchorage, AK

Aulck, L. et al.

Figure 5: Historical scholarship allocations for the DNR scholarship. The highlighted year (2018) shows the optimized scholarship allocations from this work. Upper bounds for the bins are inclusive. Percentages are of award-receiving students only.
The exact award amounts for the DNR scholarship cannot be
disclosed due to University policy. Additionally, the percentage ofstudents receiving scholarship awards was not consistent acrossprevious years. For example, in some years, 30% of accepted DNR
students may receive a scholarship while in other years, 70% of
accepted DNR students may receive a scholarship. Furthermore, tuition charges change annually at the University. Thus, in an attempt
to provide a normalized measure for comparison across enteringclasses without disclosing exact award amounts, we compare award
allocation strategies across time based on the discount on tuition.
For example, a student receiving a $5,000 scholarship when tuition
is $20,000 receives a 25% discount on tuition. We show previous allocations of the DNR scholarship to scholarship-receiving students
as a discount on tuition in Figure 5. This discount on tuition factors
in tuition cost for a full-time DNR student but not additional living
or educational expenses (i.e. housing, food, books, etc). To further
illustrate the use of discount on tuition, when looking at Figure 5,
it can be seen that approximately 15% of all scholarship-receiving
students received an award that discounted their tuition by 8-12%
in 2014 while in 2017, approximately 60% of students received asimilar award. It is apparent from examining previous allocations
that the manner in which the awards were historically allocatedshifted greatly from year to year. As noted previously, these previous allocations were determined by an external consulting service
and we could not leverage their underlying approach in this work.
We also show the scholarship allocation strategy for the 2018 entering class (for which the scholarship disbursement was optimizedin this project) in Figure 5. This strategy tended to favor smaller
scholarships, which aligns with the optimized allocation strategy
that Sarafraz et al. reported [22]. In fact, scholarship stewards had
initially placed a lower limit on the scholarship awards (S min ) during modeling, which was equal to the lowest scholarship amountthat had historically been awarded to students. This lower limit
was between a 8-12% discount on tuition. After we discussed preliminary results of the optimization and the effectiveness of smallerawards with the scholarship stewards, it was determined that thelower limit on the awards would be changed to S min
2 . Thus, the 2018
entering class had some scholarship awards that were lower thanthose received by previous entering classes. These lower awards

Table 3: Historical, predicted, and actual yields after scholarship disbursement.
Timeframe

Yield% Increase

Historical

2014-201710-12%

N/A

Predicted
Actual

2018
2018

13.9%
14.8%

15.8%
23.3%

discounted tuition by 4-8%. It is also noteworthy that the optimized
disbursement strategy gave a distribution of awards that was rightskewed, in contrast to previous allocation strategies, which werepredominantly left-skewed or near uniform. This speaks to the ideathat smaller scholarships awarded to students of lower merit may
be more effective than larger scholarships are for those of higher
merit (keeping in mind that students who received smaller awards
were also of lower merit for this merit-based scholarship). Thisaligns with intuition that those with higher academic profiles likely
have more college options and require additional recruitment, be it
additional financial aid or in some other form.
After we developed the scholarship distribution strategy for the2018 entering class, the University distributed scholarship awards
to admitted DNR freshmen. We then waited as these students indicated their enrollment decisions a few months later. In recent years,
the yield for DNR students at the University was about 10-12% withlittle/no increase, as verified by scholarship stewards, where “yield”
refers to the percentage of admitted students who enrolled at the
University. Historical yields were not based on an unoptimized or
randomized scholarship allocation strategy but were the productof the scholarship allocations derived by an external consulting
service. Thus, because we were comparing the results from ourapproach to those from a previously optimized strategy (and not
an unoptimized or random allocation strategy), we expected tosee a modest improvement. Instead, we saw an increase in yieldthat was much higher than our modeling suggested. Table 3 shows
the historical yields, the predicted yield based on our optimized
approach, and the actual yield based on student enrollment for the2018 entering class. When comparing to the upper bound on historical yield (12%), we anticipated that the scholarship optimizations

Optimizing Scholarship Allocation
would increase student yield by 15.8% (12% to 13.9%) based on theenrollment figures we had seen during the optimizations. In reality,
yield increased by 23.3%. This amounted to hundreds of additional
students enrolling with each paying tens of thousands of dollars annually in tuition. Overall, the net effect was an increase in millionsof dollars in annual tuition revenue for the University. The University has since incorporated our approach into their enrollment
modeling process and will be using it for future disbursements ofthis scholarship fund. Of note is that the above yields are based on
proportions of students that enrolled and the size of the enteringclass makes little difference when comparing yields. The University
also admitted roughly the same percentage of DNR students asyears past and nearly all conditions during the application process
were identical to previous entering classes. That said, the exact
degree to which this increased yield can be causally attributed tothe scholarship optimizations warrants further investigation.

5

CONCLUSIONSIn this work, we show how existing data at a university can be used
to improve enrollment management. We combine machine learningwith numerical optimization and use student application data at a
public university to optimize a scholarship fund. We find that the
optimized approach increased student enrollment and generated
millions in additional tuition revenue. It has since been incorporated
into the university’s enrollment forecasting.
We show that ensemble classifiers can give strong performance
when predicting enrollment and we use a binning strategy basedon student merit to make the optimization task more tractable. This
strategy eliminated the need for per-student optimizations, thereby
limiting the complexity of the fitness landscape during optimization. After optimization, we see that smaller scholarship awards
work better for maximizing enrollment. In all, the university had
historically seen little/no increase in enrollment yield and we projected that the optimized scholarship disbursement would increase
yield by 15.8%. In reality, enrollment yield increased by 23.3%.
Universities are at the forefront of training the next generation ofdata scientists and developing data-centric tools/techniques. However, they are far behind in applying data science to their own
administrative data and processes. This project attempted to movethem in this direction. Using a suite of machine learning tools, wewere able to increase a university’s revenue from a scholarship fundby millions of dollars. We think there are many similar opportunities to harness the power of data science in the realm of education
administration, especially in resource allocation.

ACKNOWLEDGMENTS
The authors would like to thank the University data, enrollment,
and financial aid stewards for their assistance on this project.

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