After this course, the student is able to:
- Translate the problem description of a transportation problem into a mathematical optimization problem;
- Analyze the characteristics of a mathematical optimization problem (continuous/discrete, convex/nonconvex, linear/nonlinear);
- Apply numerical optimization methods for unconstrained continuous problems (line search-based methods);
- Apply the optimality conditions of continuous constrained optimization problems (KKT);
- Apply metaheuristics (genetic algorithms, tabu search, etc.) to solve large-scale problems;
- Apply exact methods (Branch and Bound) to solve discrete optimization problems with the use of commercial optimization solvers (Gurobi);
- Apply multi-objective optimization methods (epsilon-constraint method, weighted-sum method, lexicographic method).
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Despite the continuous increase in transport demand over the past decades, it is not always possible to build new infrastructure to increase the transport supply. This has triggered the need to use mathematical optimization to utilize the existing infrastructure as efficiently as possible. This course provides insight in some of the fundamental properties of transport policies and traffic management, where individual choice behavior affects network performance.
Basic concepts of graph theory, routing problems, characteristics of graphs, optimization problems with and without boundary conditions, linear programming, Lagrangian and Karush-Kuhn-Tucker conditions, and multi-variate optimization methods, convex optimization, heuristic equilibration techniques and evolutionary algorithms will be applied to common transport problems to improve efficiency.
The main topics covered in the course are:
- Application of graph theory, combinatorial optimization and nonlinear optimization to transport problems;
- Route set generation and choice in transport networks;
- Constrained and Unconstrained optimization;
- Development of mathematical optimization models for common transport problems, e.g. Network Design Problem and Transportation planning, including maintenance and operations.
This course will be assessed by means of assignments (50%) and a written exam (50%). A satisfactory completion of the course requires an overall mark of at least 5.5, and a written exam mark of at least 5.0.
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