## Applied Systems TheoryBack JP / EN

Numbering Code Year/Term G-ENG10 5C604 LJ72 2021 ・ Second semester 2 Lecture Japanese Tue.1 TANAKA SHIYUNJI (Institute for Liberal Arts and Sciences Associate Professor)SAKAMOTO TAKUYA (Graduate School of Engineering Associate Professor) The course deals with mathematical methods of system optimization mainly for combinatorial optimization problems. It covers such topics as the integer optimization and its typical problems, exact solution methods including the dynamic programming and the branch and bound method, approximate solution methods including the greedy method, meta-heuristics including the genetic algorithms, the simulated annealing method, and the tabu search. To acquire the knowledge on formulation of combinatorial optimization problems into integer programming problems, basic concepts, algorithms, characteristics, and application procedures of exact solution methods, approximate solution methods, and meta-heuristics. 1. Combinatorial optimization problems and complexity (1-2 weeks) - necessity and importance of combinatorial optimization, typical problems, complexity, classes P and NP, complexity of combinatorial optimization problems, limitation of exact solution methods, necessity of approximate solution methods and metaheuristics 2. Exact solution methods (3 weeks) - Principle of Optimality, dynamic programming, branch-and-bound method, and their applications 3. Integer programming (2-3 weeks) - formulation as integer programming problem, relaxation problem, and cutting plane algorithm 4. Approximate solution methods (2-3 weeks) - greedy method, integer rounding method, beam search, etc. 5. Metaheuristics (3-4 weeks) - local search, basic ideas behind metaheuristics, iterated local search, variable neighborhood search, genetic algorithms, simulated annealing method, tabu search, etc. 6. Multiobjective optimization (1-2 weeks) - importance of multiobjective optimization, theoretical backgrounds, and solution methods. The number of weeks for each topic is subject to change according to the students' level of understanding. We will provide the schedule of 15 weeks in the class so that the students will be able to prepare for the class. In principle, the grading will be based on the absolute and comprehensive evaluation of the reports on the subjects given in the class. linear programming, nonlinear programming Students are expected to review the class and try various methods by themselves. No textbook is used. Handouts will be provided during class. M. Fukushima: Introduction to Mathematical Programming (in Japanese), Asakura, 2011. Y. Nishikawa, N. Sannomiya, and T. Ibaraki: Optimization (in Japanese), Iwanami, 1982. M. Yagiura, and T. Ibaraki: Combinatorial Optimization ---With a Central Focus on Meta-heuristics--- (in Japanese), Asakura, 2001. B. Korte, and J. Vygen: Combinatorial Optimization ---Theory and Algorithms, Sixth Edition, Springer, 2018. M. Gendreu and J.-Y. Potvin (eds.): Handbook of Metaheuristics, Second Edition, Kluwer Academic Publishers, 2010. K. Miettinen: Nonlinear Multiobjective Optimization, Kluwer Academic Publishers, 1999).