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The current module deals with two aspects of optimization. On the one hand, students are equipped with skills in combinatorial optimization problems including mathematical programming with discrete (Integer or Boolean) variables. Cutting-plane and branch and bound algorithms are described along with their convergence properties. The use of meta-heuristics like genetic algorithm, simulated annealing and Tabu search for solving combinatorial optimization problems is also pondered. Finally exact and heuristic methods presented are applied to the traveling salesman and the vehicle routing problems. On the other hand, students are equipped with practical skills in Numerical Optimization problems including lectures in line search methods, Trust region methods, Conjugate gradient methods, Newton and Quasi-Newton methods, theory on constrained optimization and unconstrained optimization methods, interior point methods, and quadratic programming. It is important to note the following milestones for students taking this module.
1) Having successfully completed this module, students should be able to demonstrate knowledge and understanding of: Methods that are used in Numerical optimization, the combinatorial optimization problems, the use of meta-heuristics like genetic algorithm, the convergence of described algorithms, some real-life applications of combinational optimization, the classification of combinatorial optimization problems into easy (polynomially solvable) problems and hard (NP-complete) problems
2. Having successfully completed this module, students should be able to Solve combinatorial optimization problems, Apply the heuristic methods to Dynamic programming, Apply the heuristic methods to traveling salesman and the vehicle routing problems, Recognize applications of combinatorial optimization, Solve certain combinatorial optimization problems by exact methods, Develop and apply heuristic methods to various optimization problems, such as the traveling salesman and vehicle routing problems,
3) Having successfully completed this module, students should be able to: Use mathematical programming language (R, Python, etc) in solving, Numerical optimization problems, Combinatorial optimization problems, Optimization problems (heuristic methods).