Transportation Network Analysis

ABOUT THE COURSE:This course will cover the foundations for analyzing large-scale transportation networks. First, fundamentals related to optimization and analysis of algorithms will be covered. Then, important combinatorial optimization problems such as traveling salesman problem, vehicle routing problem, etc., along with corresponding solution approaches will be discussed. Finally, traffic assignment problems such as user equilibrium and system optimum will be covered.INTENDED AUDIENCE: Students, faculty members and practitioners interested in learning optimization to solve various engineering problems with special emphasis to transportation network problems, resource allocation problems, etc.PREREQUISITES: There is no prerequisite course. Participants should have basic knowledge of calculus, probability, statistics and linear algebra.INDUSTRY SUPPORT: Amazon, Flipkart, Swiggy, Zomato, ORMAE, MOJRO, Optimise Everything, etc., may be interested in this course.

Syllabus

Week 1:Course overview; Introduction to optimization; Linear programming; Optimization formulations of important problems.
Week 2:More examples of optimization formulations; Branch and bound method for solving integer programs.
Week 3:Analysis of algorithms; Order of growth; Algorithms for solving minimum spanning tree problem and traveling salesman problem.
Week 4:Algorithms for solving vehicle routing problems; Genetic algorithms.
Week 5:Introduction to traffic assignment (specifically, user equilibrium); Graphical method for solving user equilibrium; Introduction to continuous optimization (unconstrained optimization).
Week 6:Continuous optimization (constrained optimization); Convex optimization; KKT conditions.
Week 7:Beckmann’s transformation (user equilibrium formulation); System optimization formulation; Braess’s paradox; Algorithms for solving continuous optimization problems (unconstrained optimization).
Week 8:Algorithms for solving continuous optimization problems (constrained optimization) such as convex combinations; Application of convex combinations algorithm to traffic assignment problems.