Applied Optimization I

Aim

The course is aimed at providing the participants with knowledge in applied optimization, with focus on the application of theory and methods in combinatorial optimization for modeling and solving optimization problems originating from the area of transport and communication. The course also aims at letting the participants gain insights and practical skills in setting up mathematical models and using optimization methods. After completing the course, the participants shall be able to

• connect the subjects of the course to their study program
• describe fundamental theory and methods in combinatorial optimization and integer programming
• describe classical optimization problems in the area of transport and communications
• explain concepts related to problem complexity and the impact of complexity on large scale optimization
• use a modeling system for setting up optimization models and problem solving
• describe and apply modern heuristics for solving large scale optimization

Content

Basics of combinatorial optimization; integer programming models; relations between combinatorial optimization, linear programming, and integer programming; branch and bound, and cutting plane for solving integer models; classical combinatorial optimization problems: shortest path, maximum flow, minimum spanning tree, matching, facility location, traveling salesman, and graph coloring; problem complexity: complexity classes, theoretical and practical impact of complexity on large scale optimization; the impact of the choice of integer model in large scale optimization; basic column generation; problem relaxation and relaxation methods; application of heuristics and relaxation methods. heuristics: greedy heuristic, local search, tabu search, simulated annealing.