Discrete Applied Mathematics/Networks and Optimization Working Group
Organizational web page (not intended for wide public dissemination)
From Rob Ellis, Hemanshu Kaul, and Michael Pelsmajer (Applied Mathematics):
We are interested in starting a joint Ph.D. with a focus on networks and optimization. We hope to involve faculty and students from Applied Math, CS, ECE, Stuart School, and Civil Engg., with broad interests in these areas.
These are two of the very few areas intersecting mathematics that are projected growth areas in industry. There exist somewhat similar, highly successful programs at other schools. We believe that IIT already has the nearly all faculty and courses needed.
The new program will help us recruit students, and give them a useful breadth of knowledge for a career in industry or academia. Having this program at IIT will allow participants to better pursue joint papers and interdisciplinary grants.
We wish to organize a seminar with interested IIT faculty, to get acquainted with each other's research interests, and as a first step toward possibly collaborating on this project.
Would you be interested in participating in this seminar in Spring 2009?
(Adapted from initial email, Dec 2008)
February 2: Zongzhi Li (CAE)
A brief intro to the knapsack problem applied to transportation asset management
February 9: Yong Fu (ECE)
Computational Aspects in Managing Electricity Infrastructure
February 16: Sanjiv Kapoor (CS)
Equilibrium in Resource Allocation Markets
Abstract: In this talk we discuss market equilibrium problems. We will describe various methodologies used for solving the market equilibrium problem. In particular we describe equilibrium pricing of resource allocation markets. Resouce allocation markets include multi-commodity flow problems in networks. We discuss techniques to solve this problem, which are also applicable to solving a larger class of market equilibrium problems.
February 23: Elizabeth J. Durango-Cohen (Stuart)
Supplier Commitment and Production Decisions Under a Forecast-Commitment Contract
Abstract: In this talk we discuss a forecast-commitment contract. In such contracts, the customer provides a forecast, the supplier makes a production commitment to the customer based on the forecast, and the customers minimum order quantity is a function of the forecast and committed quantities. We provide a complete analysis of the suppliers decisions when there is a single customer facing uncertain demand. We first show that the supplier has two dominant commitment strategies: committing to the forecast or committing to the production quantity. We then characterize the jointly optimal commitment and production strategy for the supplier and extend the results to consider a capacity constraint. We discuss managerial insights, and future research directions.
(Skip a few weeks)
March 23: Chuck Jones (Stuart)
Modeling and Solving NP-Hard Problems
The Outline is: 1. Models and Modeling 2. Solving NP-Hard Models 3. Example 4. Recommended Solution Strategy
March 30: (no talk)
April 6: Xiangyang Li (CS)
Online Spectrum Scheduling in Wireless Networks
April 13: Discuss possible joint Ph.D.
April 20: (no meeting)
April 27: (talk cancelled)
May 4: Jiong Sun (Stuart)
Selling to strategic customers with consumption network externalities
With (hastily assembled) brief research descriptions, and links to personal web pages
From Applied Mathematics:
Research Interests include: [spectral] graph theory, combinatorics, coding theory. Random geometric graphs, probabilistic methods, algorithm design & analysis.
Research Interests include: Combinatorics & Graph theory, Discrete Optimization, Discrete Geometry, and their interface with Probability; in particular, both theoretical and applied aspects of (in no particular order) extremal graph theory, probabilistic combinatorics, stochastic combinatorial optimization, optimization on graphs and networks, random discrete structures such as random geometric graphs, models for discrete complex systems such as small-world network models, metaheuristics and local search landscapes in discrete optimization, stochastic models in operations research, multiobjective discrete optimization, and stochastic discrete geometry.
Research Interests include: Discrete applied mathematics, computational and mathematical biology, classification theory, location theory.
Research Interests include: Graph Theory, Combinatorics, Algorithms and Complexity, and Applications.
From Civil, Architectural and Environmental Engineering:
Research Interests include: Transportation systems analysis, evaluation, and asset management; statistical and econometric methods for transportation demand modeling, pavement performance modeling, and safety and security analyses; simulation modeling for intelligent transportation systems applications; risk and uncertainty modeling, and optimization of dynamic traffic networks, infrastructure systems, and logistics problems.
From Computer Science:
Research Interests include: Algorithmic Game Theory, Combinatorial Optimization, Computational Geometry, Graph Algorithms.
Xiangyang Li (and his students)
Research Interests include: algorithm design and analysis for practical questions, including wireless ad hoc and sensor networks; protocol design in networks with selfish participants; protocol design in networks with some malicious participants, related to trusted computing; computational geometry; the properties and applications of social networks formed by social relations.
From Electrical and Computer Engineering:
Research Interests include: broadband networks, adaptive network management, network measurement and wireless mesh networks.
Research Interests include: Multi-hop, multi-channel wireless networks; Next-generation Internet architecture and management; Internet measurement, performance analysis, and resource allocation; Network security and wireless/wireline interworking. Current research activities focus on capacity analysis of single-hop and multi-hop wireless networks, next-generation network management architecture, Internet tomography based on packet-pair probing, multicast over application-oriented networks, cross-layer design for multimedia communications, and cellular/WLAN/WiMax integration.
Research Interests include: His research interests focus on power system stability and control. He is currently developing robust and efficient computational tools that will assist power engineers in planning and operating large-scale electric power systems, while emphasizing security and competitiveness. The goal of Dr. Flueck's research is to numerically compute the safe operating region of electric power systems under varying load/generation levels and facility outage contingencies. Determining the safe operating region of a large-scale power system is computationally demanding, thereby requiring extensive research in numerical methods.
Research Interests include: His research interests include economics and control of electrical power systems, modeling and optimization of large-scale power systems, power system security and reliability, electricity equipment maintenance scheduling, generation and transmission planning, power market design.
Research Interests include: His research focuses on market operation and wide area protection of electric power system, including load forecasting, price forecasting, price-based unit commitment (PBUC), security-constrained unit commitment (SCUC), arbitrage in electricity market, market power analysis and risk management, ancillary services auction, transmission pricing.
Research Interests include: Network Security & Privacy and Applied Cryptography with current focus on Security & Privacy in Cloud Computing, Lower-layer Attack & Defense Mechanisms for Wireless Networks, and Sensor Network Security.
Research Interests include: electric power systems planning, operation, and control.
Research Interests include: design automation for VLSI circuits, especially algorithm engineering of large scale optimization problems.
Research Interests include: wireless communications and mobile networks in general, especially in power control/resource allocation for various wireless networks, integration of heterogeneous networks, and reliable communications over OFDM or MIMO systems.
From Stuart School of Business:
Research Interests include: Supply Chain Management; Incentives, Contracts and Information in Supply Chains; Inventory and Production Planning; Capacity/Pricing Issues. Research utilizes stochastic optimization tools, such as dynamic programming, Markov decision processes, etc to model problems in supply contract analysis, as well as problems with a marketing/operations link.
Research Interests include: My interest is in Modeling and Solving Large non-Linear Decision Problems with evolutionary programming. Some of the methods I have been working with include: Genetic Algorithms, Simulated Annealing, Tabu Search and Ant Colony Optimization. I have used these methods in Scheduling and in Resource Allocation in the private and public sectors.
Research Interests include: My background is in Operations Management (PhD from Carnegie Mellon). I have been working on social networks theory and applications in operations management, product design and innovation strategies. That is, my focus is on social interaction and consumer behavior.
Networks and optimization are two of the very few areas intersecting mathematics that are projected growth areas in industry. There exist somewhat similar, highly successful programs at other schools. We believe that IIT already has the nearly all faculty and courses needed. The new program will help us recruit students, and give them a useful breadth of knowledge for a career in industry or academia. Having this program at IIT will allow participants to better pursue joint papers and interdisciplinary grants.
For applied math students, this will provide an opportunity to apply their mathematical knowledge in an application area in another department. For applied math faculty, this will provide an opportunity to pursue interdisciplinary research directly as well as through their students, and through co-mentoring students from other departments.
What about you? What do you hope to gain out of this program for yourself and your students?
We need to discuss how to organize the program, starting from admission and ending at graduation and employment. Given below are the primary milestones in the academic lifetime of a graduate student at IIT followed by some suggestions and questions related to those milestones. Please consider these to be starting points for discussion and feel free to add your own suggestions/ comments/ criticisms under each topic.
Admission: Each student will apply to and be admitted by his/her home department. The student will either indicate in his/her application the desire to pursue the joint PhD or can apply for the joint PhD after joining the home department. The admissions committee in each dept. will involve their local faculty from joint PhD program in the decision making process. We could appoint an admissions committee for the PhD program that would coordinate the admission process with individual departments.
Funding: The funding will initially be determined by the home department of the student. If the faculty in the program have the funding and desire to hire a student as an RA, then that would be arranged on a case by case basis.
Committee for each student: After admission to the PhD program, each student will choose a primary advisor in his/her home department (which could be changed if research interests change/ evolve), and, in consultation with this advisor, choose a co-advisor from another department within the PhD program. Together they would put together a 5 member committee, with at least 2 members from outside the student's home department.
This committee (whose composition could be changed as the student's interests change) would primarily advise the student and watch over his/ her progress through (at least) one annual review. This would eventually become the thesis committee for the student.
Courses and Qualifying Exams: Some of the options are as follows
In addition, every student has to attend the joint seminar and make at least one presentation each semester/ year on either their research or a paper/ research problem they studied (this would be a zero credit requirement with S or U grade).
Research: The student has to explicitly demonstrate that a component of their thesis was the result of direct work with a faculty (ideally their co-advisor) outside their home department. After the course requirements have been satisfied by the student, the committee's focus will transform into suggesting different possibilities for interdisciplinary research for the student.
Internships and Job: As the program matures and we build contacts in research labs and industry, we could introduce a requirement for at least one summer internship for each student. For now, we can say the internships are "highly encouraged".