UMAP Journal 2017 ICM Contest：美国大学生数学建模特等奖论文全集.pdf

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TheUMAPJournal Publisher COMAP, Inc. Executive Publisher Solomon A. Garfunkel ILAP Editor Chris Arney Dept. of Math’l Sciences U.S. Military Academy West Point, NY 10996 david.arney@usma.edu On Jargon Editor Yves Nievergelt Dept. of Mathematics Eastern Washington Univ. Cheney, WA 99004 ynievergelt@ewu.edu Reviews Editor James M. Cargal 20 Higdon Ct. Fort Walton Beach, FL 32547 jmcargal@gmail.com Chief Operating Ofﬁcer Laurie W. Arag´on Production Manager George Ward Copy Editor David R. Heesen Distribution John Tomicek Vol. 38, No. 2 Editor Paul J. Campbell Beloit College 700 College St. Beloit, WI 53511–5595 campbell@beloit.edu Associate Editors Chris Arney Ron Barnes Joanna A. Bieri Robert Bosch James M. Cargal Lisette De Pillis Solomon A. Garfunkel William B. Gearhart Richard Haberman Jessica M. Libertini Yves Nievergelt Michael O’Leary Andrew Oster Philip D. Strafﬁn Shaohui Wang Krista Watts U.S. Military Academy U. of Houston—Downtn University of Redlands Oberlin College Fort Walton Beach, FL Harvey Mudd College COMAP, Inc. Calif. State U., Fullerton Southern Methodist U. Virginia Military Institute Eastern Washington U. Towson University Eastern Washington U. Beloit College Adelphi University U.S. Military Academy

2017 Vol. 38, No. 2 Table of Contents Guest Editorial Learning and Teaching Interdisciplinary Modeling ICM Modeling Forum Results of the 2017 Interdisciplinary Contest in Modeling Chris Arney ...............................................................................93 Chris Arney, ICM Director, and Amanda Beecher, ICM Deputy Director ............................................................... 105 Analysis and Optimization of Airport Security Check Yikai Huo, Zhiyu You, and Kan Chang ...................................... 129 Judges’ Commentary: Optimizing Passenger Throughput at Airport Security Jessica Libertini ....................................................................... 149 Applying Smart Growth Principles in Boulder, Colorado and Canberra, Australia Rachel Perley, Anna Goetter, and Nina Brown ........................... 161 Judges’ Commentary: Sustainable Cities Kristin Arney, Amanda Beecher, Carrie Eaton, and Jack Picciuto ............................................................................ 181 Migration to Mars Sreeram Venkat, Nikhil Milind, and Nikhil Reddy ..................... 197 Judges’ Commentary: Migration to Mars Chris Arney ............................................................................. 221 ICM–MCM: Procedures and Tips for a Great Experience John Tomicek ........................................................................... 233

Guest Editorial 93 Guest Editorial Learning and Teaching Interdisciplinary Modeling Chris Arney, ICM Director Dept. of Mathematical Sciences U.S. Military Academy West Point, NY 10996 david.arney@usma.edu Introduction Interdisciplinary modeling combines concepts, methods, techniques, and elements of various disciplines (in the sciences, humanities, and arts) to • obtain solutions to problems; • develop understanding of issues; • provide recommendations to decision makers; and • implement and build tools, algorithms, and systems. To be effective for society, interdisciplinary modeling must provide the capability for analysts to solve realistic and challenging problems. Good education programs teach students both disciplinary and interdisciplinary modeling and problem-solving methods, and provide opportunities for students to practice and hone their modeling skills. The Interdisciplinary Contest in Modeling (ICM) R experience is one way to build experience and reﬁne skills. Here we look at the nature, processes, education, and resources related to interdisciplinary modeling and problem solving, with the hope that stu- dents can use this information to prepare for the ICM and improve their interdisciplinary modeling skills.1 The UMAP Journal 38 (2) (2017) 93–104. cCopyright 2017 by COMAP, Inc. All rights reserved. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for proﬁt or commercial advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights for components of this work owned by others than COMAP must be honored. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP. 1The opinions in this article are the author’s alone and do not necessarily reﬂect the opinion of his colleagues, USMA, the Department of the Army, or any other US government agency.

38.2 (2016) 94 The UMAP Journal Interdisciplinary Problems Real issues and modern problems can have many challenging charac- teristics. Some of these are: • Intransparency (lack of clarity of the situation or changing environments and criteria) • Multiple Goals (many stakeholders with competing criteria) • Complexity (large numbers of items, interrelations, decision elements, dimensions, geometries, and time scales) • Dynamics (time considerations, constraints, and sensitivities) • Spatial and Geometric considerations (integral or fractional dimensions) • Political and Social Elements (human or cyber considerations) One element to avoid or minimize in modeling is conﬁrmation bias, which is favoring a preconceived notion. Conﬁrmation bias can dramatically harm or constrain modeling and problem solving. Modelers must be aware of and adapt their model to avoid or resist irrelevant, biased, or erroneous information. Since data are never perfectly accurate nor completely clean, considerable effort to reduce errors or eliminate bad data is needed. ICM problems often require data to be considered—and sometimes obtained or generated—by the teams. This collection, choosing, and weighing of data is an important step in the modeling process that should not be treated lightly by the teams. Mathematical Modeling Mathematical modeling is a structured process with many loops and choices that can make it as much art as science. In performing this process, the modeler needs to describe the phenomena in mathematical terms. The four basic steps in the process (as described in Arney [2014, 169–170]) are: • Step 1: Identify the Problem The problem is stated in as precise form as possible. Sometimes, this is an easy step, other times this may be the most difﬁcult step of the entire process. • Step 2: Develop a Model This is both a translation from the natural lan- guage statement made in Step 1 to mathematical language but also the development of relationships between the factors involved in the prob- lem. Because real-world situations are often too complex to allow the modeler to account for every facet of the situation, simplifying assump- tions must be made. Data collection is often part of model construction. Variables are deﬁned, notation is established, and some form of mathe- matical relationship and/or structure is established.

Guest Editorial 95 • Step 3: Solve the Model The model is solved so that the answer is understood in the context of the original problem. If the model cannot be solved, it may need to be simpliﬁed by adding more assumptions in Step 2. • Step 4: Verify, Interpret, and Use the Model Before using the model, it should be tested or veriﬁed that it makes sense and works properly. Its output should be interpreted in the context of the problem. It is possible that the model works, but it’s too cumbersome or too expensive to implement. The modeler returns to earlier steps to adjust as needed. The modelingprocess is iterativein the sense that the modelermay need togobacktoearlierstepsandrepeattheprocessorcontinuetocyclethrough the entire process (or part of it) several times. If the model cannot be solved or is too cumbersome to use, the model is simpliﬁed. If the model needs to be more powerful, or more complication or rigor needs to be added, the process of relaxing assumptions is called reﬁning the model. By simplifying and reﬁning, the modeler can adjust the realism, accuracy, precision, and robustness of the model. By using this mathematical modeling process, modeling students can gain conﬁdence to approach complex and difﬁcult problems and even develop their own innovative approaches to solving problems. Interdisciplinary Modeling Interdisciplinary modeling is a creative process that, while sometimes based on structured processes such as mathematical modeling, usually in- volves an innovative and complex combination of modeling and problem- solving methods from various disciplines and schools of thought. The traditional modeling process was based on making viable and ap- propriate assumptions and connections to produce a framework. This structured, Newtonian style of modeling and problem solving was often based in mathematics, mechanics, engineering, and physical science (see Teller [1980]). With the advent of the computer and the availability of tremendous amountsofdata,moderninterdisciplinarymodelingoftenreducesassump- tions to a minimum and attempts to embrace the complexity of the real situation. Interdisciplinary modeling combines established methodologies with novel procedures in its processes and structures, thus allowing for complexity and speciﬁcity in its framework. The model is then solved, used, implemented, tested, and/or validated, to • produce a measure, • design an algorithm, • solve a problem,

96 The UMAP Journal 38.2 (2016) • accomplish a task, • understand a phenomenon, • build a system, and/or • make a decision. Modeling can and usually does rely on research that incorporates accu- rate scientiﬁc information and data, relevant knowledge, and innovative perspectives in the model. Interdisciplinary modeling can be quantitative or qualitative, but most viable modern models are hybrid and incorporate many different kinds of steps and processes. The modern form of interdisciplinary modeling is called by various names, such as network modeling, data science, operations research, analytics, informatics, and information science. The most emblematic inventor of these kinds of processes was math- ematician Norbert Wiener, whose theory of cybernetics included models with iterative control/feedback loops. After the initial stages of cybernet- ics in the 1950s, interdisciplinary modeling was used in design and analysis of communication systems, electronics, biological systems, and economics (see Wiener [1961]). This method of interdisciplinary modeling was the key to unlocking issues in computing, artiﬁcial intelligence, neurobiology, psychology, and sociologicalsystems. Thisnewmodelingparadigmnotonlyallowedforthe entry of the ﬁelds of life, behavioral, and social sciences into the modeling world, but also began to challenge the Newtonian simplicity assumption at a conceptuallevel. Otherinterdisciplinarymodelerssoonfollowedto make interdisciplinarymodelingahighlyvaluablemethodologyandtool. Lorenz provided rigorous backing through chaos theory and strange attractors to show that even a perfectly deterministic system can behave in erratic ways. Benˆoit Mandelbrot [1977] demonstrated that a high level of complexity exists in rudimentarygeometricobjects that make up the world as we know it. These ideas are now conceptual elements of interdisciplinary modeling. Measures/Metrics Buildinggoodmeasuresforsystemproperties,data,andthesensitivities of their effects on the achievement of goals for the problem are important, especially if the data set is wider than it is deep and thereby affecting most of the elements of the model. Good measures are needed in many models, especially when the problem is quantitative. In qualitative modeling, the measuring is often performed by comparison. Marcus Weeks [2010] dis- cusses determination of size by a comparison methodology and makes the size comparison relevant to humans.

Guest Editorial 97 A Course in Modeling Interdisciplinary modeling courses seek to address the complex process of translating real-world events into mathematical and scientiﬁc language, solving or running the resulting model (iterating as necessary), and inter- preting the results in terms of real-worldissues. Topics often include model developmentfromdata, regression, generalcurve-ﬁtting,anddeterministic and stochastic model development. Easley and Kleinberg [2010] and New- man [2010] are textbooks that are helpful in such a course. The Guidelines for Assessment and Instruction in Mathematical Modeling Education (GAIME) edited by Garfunkel and Montgomery [2016] is an excellent reference for teaching foundational courses. There are many good modeling textbooks and some are listed below. Interdisciplinary projects based on actual problems and issues are used to integrate the various topics of modeling for the student. Through such a course, students should be able to: • Frame a question using mathematics and science to begin developing a model. • Understand different modeling approaches and the trade-offs with se- lecting an approach. • Interpret the results of a model. During a section on optimization, students learn to: • Take a scenario and transform it into a model focused on optimization. • Understand how to set up an optimization formulation with decisions, an objective, and constraints. • Understand the unique aspects of certain optimization cases, such as linear, integer, and dynamic programming. • Take the solution to an optimization formulation, and interpret the an- swer. • Understand the robustness and sensitivity of a model. Through the study of dynamical systems modeling, students learn to: • Take a scenario and transform it into a model focused on a dynamical system. • Understand how to set up a dynamical system with an independent variable, dependent variables, and a governing relationship. • Interpret the model without solving the differential equations. • Understand the robustness of the model (sensitivity). • Understand the possibility of chaotic solutions.

98 The UMAP Journal 38.2 (2016) From a stochastic point of view, students learn to: • Take a scenario and transform it into a model while incorporating uncer- tainty. • Understand how to set up a probabilistic model with a random variable, sample space, and distribution. • Understand how to set up a Markov model with a state space, a random variable with distribution, and state transitions. Future Trends in Modeling Society and organizations need experts in interdisciplinary modeling in order to make better and faster decisions. Future modelers will need to build viable models to confront complex multidisciplinary and interdis- ciplinary issues in our information-centric world. High-impact areas in- clude analyzing many issues for a larger and smarter Internet, automation of knowledge through artiﬁcial intelligence and machine learning, high- powered cloud computing, autonomous vehicles, and smart robots. Mod- eling in these areas is by nature interdisciplinary. Astrikingexampleofaprojectthatrevealsthefutureofinterdisciplinary modeling is IBM’s development of the Watson system to compete in the information-centric game Jeopardy. Watson’s notable success in that ﬁrst endeavor, and in many applications since, illustrates the potential of inter- disciplinary modeling. Modern science is embracing the future contribu- tions of interdisciplinary modeling as science shifts from little science (sin- gle investigators)and big science (large labs workingon speciﬁc projects) to a future of team science (multidisciplinaryteams of scientists, much like the IBM Watson team and the ICM team framework)(see West [2016]). Modern science, through its use of interdisciplinary modeling, is building a collec- tive power that is more creative, more original, and more effective than any single disciplinary perspective and the simplicity-focused Newtonian modeling of the past. Another example of interdisciplinary modeling is found in cyberspace, where computing and networking are important elements in the model, but so are ethical, political, and social elements. Data science, human psy- chology, and many other disciplines are all parts of the virtual and digital cyber world. The complex issues in cyber modeling are two-fold: • What is the balance between security and performance vs. privacy and information availability? • How do models treat the underlying competitive nature of the attacker vs. defender dynamic? Hackers and malicious systems are pitted against defenders of freedom,

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