Curricular Optimization- Solving for the Optimal Student Success

University of Kentucky UKnowledge Theses and Dissertations Electrical and Computer Engineering Electrical and Computer Engineering 2019 Curricular Optimization: Solving for the Optimal Student Success Pathway William G Thompson-Arjona University of Kentucky, wgthompson@uky.edu Digital Object Identifier: https://doi.org/10.13023/etd.2019.147 Right click to open a feedback form in a new tab to let us know how this document benefits you Recommended Citation Thompson-Arjona, William G., "Curricular Optimization: Solving for the Optimal Student Success Pathway" (2019) Theses and Dissertations Electrical and Computer Engineering 139 https://uknowledge.uky.edu/ece_etds/139 This Master's Thesis is brought to you for free and open access by the Electrical and Computer Engineering at UKnowledge It has been accepted for inclusion in Theses and Dissertations Electrical and Computer Engineering by an authorized administrator of UKnowledge For more information, please contact UKnowledge@lsv.uky.edu STUDENT AGREEMENT: I represent that my thesis or dissertation and abstract are my original work Proper attribution has been given to all outside sources I understand that I am solely responsible for obtaining any needed copyright permissions I have obtained needed written permission statement(s) from the owner(s) of each third-party copyrighted matter to be included in my work, allowing electronic distribution (if such use is not permitted by the fair use doctrine) which will be submitted to UKnowledge as Additional File I hereby grant to The University of Kentucky and its agents the irrevocable, non-exclusive, and royalty-free license to archive and make accessible my work in whole or in part in all forms of media, now or hereafter known I agree that the document mentioned above may be made available immediately for worldwide access unless an embargo applies I retain all other ownership rights to the copyright of my work I also retain the right to use in future works (such as articles or books) all or part of my work I understand that I am free to register the copyright to my work REVIEW, APPROVAL AND ACCEPTANCE The document mentioned above has been reviewed and accepted by the student’s advisor, on behalf of the advisory committee, and by the Director of Graduate Studies (DGS), on behalf of the program; we verify that this is the final, approved version of the student’s thesis including all changes required by the advisory committee The undersigned agree to abide by the statements above William G Thompson-Arjona, Student Dr Gregory Heileman, Major Professor Dr Aaron Cramer, Director of Graduate Studies Curricular Optimization: Solving for the Optimal Student Success Pathway THESIS A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering in the College of Engineering at the University of Kentucky By William Guillermo Thompson-Arjona Lexington, Kentucky Director: Gregory Heileman, Ph.D, Professor of Electrical Engineering Lexington, Kentucky 2019 Copyright c William Guillermo Thompson-Arjona 2019 ABSTRACT OF THESIS Curricular Optimization: Solving for the Optimal Student Success Pathway Considering the significant investment of higher education made by students and their families, graduating in a timely manner is of the utmost importance Delay attributed to drop out or the retaking of a course adds cost and negatively affects a student’s academic progression Considering this, it becomes paramount for institutions to focus on student success in relation to term scheduling Often overlooked, complexity of a course schedule may be one of the most important factors in whether or not a student successfully completes his or her degree More often than not students entering an institution as a first time full time (FSFT) freshman follow the advised and published schedule given by administrators Providing the optimal schedule that gives the student the highest probability of success is critical In efforts to create this optimal schedule, this thesis introduces a novel optimization algorithm with the objective to separate courses which when taken together hurt students’ pass rates Inversely, we combine synergistic relationships that improve a students probability for success when the courses are taken in the same semester Using actual student data at the University of Kentucky, we categorically find these positive and negative combinations by analyzing recorded pass rates Using Julia language on top of the Gurobi R solver, we solve for the optimal degree plan of a student in the electrical engineering program using a linear and non-linear multi-objective optimization A user interface is created for administrators to optimize their curricula at main.optimizeplans.com KEYWORDS: Optimization, Curricular Analytics, Multi-Objective, Cloud LAMP Stack William Guillermo Author’s signature: Thompson-Arjona Date: May 2, 2019 Curricular Optimization: Solving for the Optimal Student Success Pathway By William Guillermo Thompson-Arjona Director of Thesis: Gregory Heileman, Ph.D Director of Graduate Studies: Aaron Cramer, Ph.D Date: May 2, 2019 Esta tesis est´a dedicada a mis padres ACKNOWLEDGMENTS Without the support and vision of my advisor and chair, Dr Gregory Heileman, this thesis would not have been possible Under his guidance and leadership I have grown as an engineer and a professional Many thanks to Orhan Akbar and Gokhan Bakal, colleagues and friends with help programming this optimization Also many thanks to Adam Roth for his invaluable help and guidance with the LAMP stack iii CONTENTS Acknowledgments iii Contents iv List of Figures v List of Tables vi Chapter Introduction 1.1 Background 1.2 Previous Work 1 Chapter Tools, Structure, and User Interface 2.1 Julia 2.2 JuMP 2.3 Gurobi R Solver 2.4 Jupyter 2.5 User Interface → main.optimizeplans.com 10 10 11 11 12 12 Chapter Optimization 3.1 Overall Constraints and Considerations 3.2 Bin Filling and Optimal Time to Completion 3.3 Multi-objective Optimization with Toxicity Avoidance 17 17 19 23 Chapter Applications in Electrical Engineering 39 4.1 Power Transmission, Optimization of Damping Control 39 4.2 Smart Grid 41 Chapter Conclusions and Moving Forward 44 Bibliography 45 Vita 47 iv LIST OF FIGURES 1.1 Tuition costs at public universities and colleges [3] 1.2 B.S Electrical Engineering Program at the University of Kentucky, 2018 1.3 Example four course curricula subset demonstrating typical progression to circuits in the electrical engineering curriculum 1.4 Curricular complexity metrics in relation to small adjustment in course placement 2.1 User interface created at main.optimizeplans.com 14 2.2 CSV data input front end linking to AWS-PHP LAMP stack to AWS S3 bucket 3.1 B.S Electrical Engineering program at the University of Kentucky, 2018 Op- 15 timized using “bin filling” approach, function decomposition 22 3.2 B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized using “bin filling” approach, function combination 23 3.3 Example Curricula, Unoptimized 33 3.4 optimized example curricula, objective of toxicity minimization 34 3.5 B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized using toxicity avoidance objective 35 3.6 B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized using term imbalance minimization objective 36 3.7 B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized prerequisite string minimization objective 37 3.8 B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized using toxicity avoidance, term balancing, and prerequisite string minimization objectives 38 4.1 192Bus WECC Windfarm 40 4.2 Variability in power output of wind farm by day, for one month [18] 42 v LIST OF TABLES 2.1 EC2 instance t2.medium specifications 13 2.2 LAMP stack description 15 3.1 Course toxicity example relationship 25 3.2 Course toxicity relationship between two courses in the electrical engineering curricula 27 3.3 User defined limits for optimization 29 3.4 Toxicity score (Ts) matrix 30 3.5 Binary course placement matrix X 31 3.6 Possible course combinations in the first term of the example curriculum with representative toxicity scores 33 3.7 First iteration of binary matrix x of example curriculum 34 4.1 Objective and constraints associated with inter oscillatory minimization 40 4.2 Objective and constraints associated with smart grid topology 42 vi Table 3.7: First iteration of binary matrix x of example curriculum C1 C2 C3 C4 C5 C6 t1 1 0 t2 1 Although defined by our algorithm with respect to the JuMP/Gurobi framework, the binary course positioning matrix x and the optimality matrix will not be output These are iterative steps that transpire without user manipulation or need for data ingestion Gurobi will proceed to run through however many iterations necessary to find the optimal result (There are cases in which no optimal result may be found) Once the result has been found by Gurobi, the optimal course progression on a term by term basis may be output and visualized using the curricular analytics toolbox [11] The resultant degree plan found from our example curricula is as follows: Figure 3.4: optimized example curricula, objective of toxicity minimization We will now consider the undergraduate electrical engineering curricula at the University of Kentucky, resolving separate degree plans relative to the objective sought 34 Results Figure 3.5: B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized using toxicity avoidance objective Figure 3.5 displays the resultant degree plan after optimizing for toxic course combination avoidance During the iterative solving for the plan, toxic course combinations were separating from residing in the same semester while synergistic courses were combined All this was done subject to the constraints detailed (including honoring requisite relationships) However, it must be observed that the semesters are not balanced with respect to credit hours For this we introduce the load balancing objective 35 Figure 3.6: B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized using term imbalance minimization objective Figure 3.6 displays the resultant degree plan after optimizing for term inbalance minimization All semesters are now balanced term over term However it must be pointed out that prerequisite strings can be sometimes extremely long Such is the case between WRD110 and WRD111 which are separated by semesters In efforts to place requisite learning outcomes as close to the course which employs its use, we introduce the requisite string minimization objective 36 Figure 3.7: B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized prerequisite string minimization objective Figure 3.7 displays the resultant degree plan after optimizing for prerequisite string minimization All requisites are placed at most with one semester of separation Now all objectives are combined to give the ultimate plan: 37 Figure 3.8: B.S Electrical Engineering program at the University of Kentucky, 2018 Optimized using toxicity avoidance, term balancing, and prerequisite string minimization objectives Figure 3.8 displays the resultant degree plan after optimizing for all three objectives, including term credit hour balancing, prerequisite string minimization, and toxicity avoidance While the toxicity avoidance is vital in optimizing for student success, the degree plan introduces validity in the objectives of balancing course load and keeping requisite courses close to one another The fixed course array constraint makes sure term specific courses are not moved during the optimization (e.g Capstone Design in terms and 8) while the other constraints, automatically checked for during the algorithm, insure all requisites are honored, all while falling in the user defined limitations This ultimate plan combines real world, institution specific pass rates to create the optimal schedule, thus providing a truly powerful tool for administrators across the world 38 Chapter Applications in Electrical Engineering Electrical engineering is truly a beautiful field of study considering the expansiveness of its applications Even though there are quite a bit of differences between nanoscale semiconductor devices and large megawatt power systems, fundamental electrical engineering principles hold true In the same sense, applications of linear and non-linear optimization extend far beyond that of degree plan optimization The same treatment, principles, and methodologies described can easily be translated to problems posed in the field of electrical engineering 4.1 Power Transmission, Optimization of Damping Control In power transmission engineering many design factors need to be accounted for including signal fidelity across long distances and power outage mitigation Once such mechanism implemented to maintain signal fidelity are Wide Area Damping Controllers, or WADCs Optimization techniques could be used with regards to the placement and signal allocation priority of these controllers in large multi-nodal power systems Stability in power systems is of key concern for many system designers The ever-increasing amount of noise introducing or transient nodes in a system introduces many failure modes not previously warranting mitigation techniques These failure/fault modes may be attributed to the large-scale implementation of renewable power generation technology by many power companies In the presence of these large scale renewable systems across long distances arise the nuisance of small signal instability, specifically inter area oscillations When this is the case strategically placed damping actuators throughout a system can be coordinated in such a way to dampen these oscillations This is where optimization techniques could first be introduced, with regards to the placement of the controllers between the two optimal nodes to most quickly resolve the oscillations While novel modal-based control allocation techniques have been introduced and proven across a complex wind farm scenarios with healthy and affected actuators randomly dis- 39 Figure 4.1: 192Bus WECC Windfarm Table 4.1: Objective and constraints associated with inter oscillatory minimization Objectives: Minimize Disturbance Optimal placement of WADC within power system Priority of oscillatory damping signal Example Constraints Geographic limitation Limit on amount of WADCs WADC damping characteristics persed throughout, optimization could be used to further the efficacy of the system [15] Redundancy and protection in the face of these oscillation scenarios is crucial in maintaining a resilient power transmission system considering the increased use of renewable technology seen today Electro-mechanical oscillations between interconnected synchronous generators are phenomena inherent to power systems The stability of these oscillations is of vital concern and is a prerequisite for secure system operation For many years, the oscillations observed to be troublesome in power systems, were associated with a single generator, or a very closely connected group of units at a generating plant Some low frequency unstable oscillations were also observed when large systems were connected by relatively weak tie lines, 40 and special control methods were used to stabilize the interconnected system These low frequency modes were found to involve groups of generators, or generating plants, on one side of the tie oscillating against groups of generators on the other side of the tie [16] In recent times, many instances of unstable oscillations, involving inter-area modes in large power systems have been observed, both in studies and in practice, such as in the western region of the United States Low frequency synchronizing oscillations (particularly around 0.1 hertz) between the Pacific Northwest and Pacific Southwest have long been a characteristic of the western power system These oscillations were primarily caused by the negative damping effect of hydro governors on the swing mode between the two regions, which were connected by a weak system of 230 kV inter-ties [17] Such oscillations are increasingly becoming a cause of concern This has led to a renewed interest in the nature of these modes, methods for systematically studying them, and control optimization methods by which they can be stabilized In the face of ever increasing deployment of renewables into the modern power system, the need for damping of low frequency oscillations will only increase Optimization techniques will prove invaluable as this problem becomes more and more prevalent, mitigating the threat of power system disruption across the world 4.2 Smart Grid Another application where optimization methods could easily be applied is that of the smart grid We are living in the midst of a significant technological transition, away from the passive electric power transmission and distribution system to a connected and resilient platform leveraging many emerging and proven technologies New telemetry and long distance real time data acquisition techniques allow for the implementation of more concise load generation, leading to less waste and a more ecologically conscience utility company Granular load monitoring at the local customer level allows for specific generation benchmarks in relation to a variety of different economic and meteorological conditions Monitoring devices are able to be tied together using common communication protocols creating an ‘internet of things’ environment The adjoining of these ‘connected’ components to a centralized data acquisition hub where data driven decisions can be made has given rise to 41 the term ‘Smart Grid’ Now that a prevalent amount of data exists, optimization techniques can be employed across a variety of use cases Table 4.2: Objective and constraints associated with smart grid topology Objectives: Maximize Power throughput Example Constraints Load matching Capital expenditure Transient disturbance mitigation Transient characteristics Outage minimization Power output and storage Optimization techniques can be deployed using the data collected from the smart grid to minimize over production of power During load transients, the optimal amount of power can be produced for the varying power requirements This in essence would provide “load matching”, so that the power generated can more closely follow the load required by the system Also, regulators can be constructed for line performance characteristics at optimized placements though out the grid, much in the same way that was discussed with respect to WADCs Another area that the optimization techniques can be deployed is with respect to outage mitigation, or “self healing” systems In order to insure the most customers have their power outage resolved (e.g after a catastrophic storm), an optimization can be run with respect to the locations in which crews should address first This will insure that the most customers benefit from the limited resources available by the utility company Figure 4.2: Variability in power output of wind farm by day, for one month [18] When thinking about renewable energy as an integrated power generation member of the smart grid system, power output variability must be taken into consideration in relation to 42 non-predictable energy output (wind meteorological duty cycle variance) This variance gives rise to key smart grid concepts such as load forecasting and load scheduling Wind farms are known for the ability to reliability to produce adequate power for 40% of the hours in a year, yet it is very difficult to predict when those hours will occur [18] With “connected (IoT)” solid-state relay devices to a centralized data center that can monitor real time meteorological conditions, optimization algorithm development can be designed to open or close specific sectors of a wind farm in order to maximize renewable energy production or minimize low wind speed ‘cut-in’ energy waste 43 Chapter Conclusions and Moving Forward The ramifications that curated degree plans have on incoming students are often not fully grasped The plan in essence will dictate the students attempt to follow his or her dream to graduate from their chosen institution The degree plan represents trails and tribulations, long nights in the library, and often unimaginable stress levels The degree plan epitomizes students’ futures, their successes, and their failures All told, the degree plan may be the single most powerful advising tool in higher education In that, administrators must deeply analyze and quantitatively asses their plan before they release to students This thesis attempts to solve for the ultimate student success pathway leveraging the most advanced commercially available solver with optimization algorithms tailored to creating valid, meaningful degree plans An easy to use user interface has been created in order to facilitate the use of these powerful algorithms (main.optimizeplans.com) Moving forward, much work remains to be done Ongoing efforts include the creation of degree plans tailored to the particular student This will include using their ACT score, high school GPA, and demographics to create a degree plan custom to them It will leverage trained machine learning models to find areas of concern, basing problematic ”stop out” areas relative to historical student data of students with similar backgrounds As administrators, the obligation exists to provide the best probability of success to all students, irrespective of their background It is essential for the future and vitality of the American economy and way of life Until this probability of success remains equally high for all students who, through hard work, dedicate their lives to the completion of their degree, work remains to be done Onward Copyright c William Guillermo Thompson-Arjona, 2019 44 Bibliography [1] Elka Torpey Measuring the value of education,” Career Outlook, U.S Bureau of Labor Statistics April 2018 [2] Hemelt, S W., and Marcotte, D E The Impact of Tuition Increases on Enrollment at Public Colleges and Universities Educational Evaluation and Policy Analysis, 33(4), 435–457 https : //doi.org/10.3102/0162373711415261 2011 [3] Bureau of Labor Statistics College tuition and fees in U.S city average, all urban consumers, not seasonally adjusted https : //data.bls.gov/timeseries/CU U R0000SEEB01?outputv iew = data [4] Gregory L Heileman, Chaouki T Abdallah, Ahmad Slim, and Michael Hickman Curricular Analytics: A Framework for Quantifying the Impact of Curricular Reforms and Pedagogical Innovations Albuquerque, NM., 2018 [5] Slim, A Curricular Analytics in Higher Education PhD thesis, University of New Mexico, Albuquerque, NM 2017 [6] Heileman, G L., Thompson-Arjona, W G., Free, H W., and Abar, O Does Curricular Complexity Imply Program Quality? Lexington, Kentucky, 2018 [7] Gill, P E., Murray, W., Wright, M Practical Optimization San Diego, California., 1981 ă [8] Unal, and Uysal A New Mixed Integer Programming Model for Curriculum Balancing: Application to a Turkish University European Journal of Operational Research (2014 [9] J Bezanzon, S Karpinski, V Shah, and A Edelman Julia: A fast dynamic language for technical computing In Lang.NEXT, Apr 2012 [10] Hickman, Michael Masters Thesis Albuquerque, NM., 2017 [11] Heileman, G L., Free, H W., Abar, O and Thompson-Arjona, W G CurricularAnalytics.jl Toolbox https : //github.com/heileman/CurricularAnalytics.jl [12] Dunning, I., Huchette, J., Lubin, M JuMP: A Modeling Language for Mathematical Optimization SIAM Review 2017 [13] Jablonsk´y, J Benchmarks for Current Linear and Mixed Integer Optimization Solvers http : //dx.doi.org/10.11118/actaun201563061923, 07 Number 6, 2015 [14] Gurobi Software Drives Award-winning Inmate Assignment Project MS Today 44.6, 2017 45 [15] M E Raoufat, K Tomsovic and S M Djouadi Dynamic Control Allocation for Damping of Inter-Area Oscillations IEEE Transactions on Power Systems, vol 32, no 6, pp 4894-4903 Nov 2017 [16] Klein, M., Rogers, G.J., and Kundur, P A fundamental study of inter-area oscillations in power systems IEEE Transactions on Power Systems, vol 6, no 3, pp 914-921 Aug 1991 [17] Cresap, R L., and Hauer, J F Emergence of a New Swing Mode in the Western Power System IEEE Transactions on Power Apparatus and Systems, vol PAS-100, no 4, pp 2037-2045 April 1981 [18] Shaffer, Walter The Role of Smart Grids in Integrating Renewable Energy ISGAN Synthesis Report www.nrel.gov/docs/f y15osti/63919.pdf 46 Vita William G Thompson-Arjona Education • B.S Bioelectrical Engineering, Marquette University, Milwaukee, WI, 2015 Appointments • Graduate Research Assistant, Department of Electrical and Computer Engineering, University of Kentucky, Lexington, KY, 2017 – Present • Associate Development Engineer, Power Control Business, Rockwell Automation, Milwaukee, WI, 2015-2018 • Undergraduate Teaching Assistant, Circuits I/II Laboratory, Marquette University, Milwaukee, WI, 2014-2015 • Undergraduate Intern, Enthermics Medical Systems, Milwaukee, WI, 2014 • Undergraduate Intern, Cardiovascular Innovation Institute, Department of Regenerative Medicine, Louisville, KY, 2013 Product Development • KYdegreeplans.com Centralized degree plan creation, visualization, and analytics tool used by the Center for Postsecondary Education across the state of Kentucky • CanBad Autonomous Weighing Systems, Provisional Patent 119769-1 Designed autonomous weighing systems complete with patent pending hardware This included custom PCB with PIC32MZ as MCU interfacing via UART to load cell, SPI to FDTI processor (display), and Bimba/PIAB pneumatics • PowerFlex 755T, Allen Bradley, Rockwell Automation 2015-2018 Key contributor for successful product launch of state-of-the-art variable frequency drive for heavy industry motor control PCB design and implementation of three phase fault and inbalance protection 47 • Virtual Interactive Patient, Medtronic, 2015 Senior design project Programed FPGA to test pacemakers/left ventricular assist devices for robustness against ECG/EKG abnormalities 48 ... 2019 ABSTRACT OF THESIS Curricular Optimization: Solving for the Optimal Student Success Pathway Considering the significant investment of higher education made by students and their families,... Thompson-Arjona, Student Dr Gregory Heileman, Major Professor Dr Aaron Cramer, Director of Graduate Studies Curricular Optimization: Solving for the Optimal Student Success Pathway THESIS A thesis submitted... allowed for integration of the optimization into the Curricular Analytics toolbox, allowing for further advanced analysis [11] The toolbox allows for the resultant 10 degree plan produced from the