Cod Esame INQ0091561 CFU 9 Ore Tot 72 This course is an introduction to Operations Research. Some of the basic topics of Operations Research and Mathematical Optimization are considered: Linear Programming, Integer Linear Programming, and Graph Theory. Particular emphasis is given to Integer Linear Programming, with an exposition of the most recent resolution techniques, and in particular of the branch-and-cut method. Topics: Linear Programming: models and geometry, the simplex algorithm (in matrix and tableau form), revised and dual simplex algorithms. Integer Linear Programming: cutting plane, branch-and-bound and branch-and-cut algorithms. Graph Theory: Definitions. Polynomially solvable problems: shortest spanning tree, shortest path and CPM, network flow. Models for NP-complete problems: knapsack, travelling salesman, set covering and packing, Steiner tree, and plant location problems. Exam: Written examination. Textbook (covering the whole course): M. Fischetti, Introduction to Mathematical Optimization, available through Amazon at https://www.amazon.it/dp/1692792024 Categoria Corsi di Laurea Magistrale / Primo Semestre

Cod Esame INQ0091561 CFU 9 Ore Tot 72 ZOOM link Fischetti's classroom: https://unipd.zoom.us/j/364970024 This course is an introduction to Operations Research. Some of the basic topics of Operations Research and Mathematical Optimization are considered: Linear Programming, Integer Linear Programming, and Graph Theory. Particular emphasis is given to Integer Linear Programming, with an exposition of the most recent resolution techniques, and in particular of the branch-and-cut method. Topics: Linear Programming: models and geometry, the simplex algorithm (in matrix and tableau form), revised and dual simplex algorithms. Integer Linear Programming: cutting plane, branch-and-bound and branch-and-cut algorithms. Graph Theory: Definitions. Polynomially solvable problems: shortest spanning tree, shortest path and CPM, network flow. Models for NP-complete problems: knapsack, travelling salesman, set covering and packing, Steiner tree, and plant location problems. Exam: Written examination. Textbook (covering the whole course): M. Fischetti, Introduction to Mathematical Optimization, available through Amazon at https://www.amazon.it/dp/1692792024 Categoria Corsi di Laurea Magistrale / Primo Semestre

Cod Esame IN11112347 CFU 9 Ore Tot 72Categoria Corsi di Laurea Magistrale / Primo Semestre

Cod Esame IN11112347 CFU 9 Ore Tot 72Categoria Corsi di Laurea Magistrale / Primo Semestre

Cod Esame INQ0091640 CFU 6 Ore Tot 48 Categoria Corsi di Laurea Magistrale / Secondo Semestre

Cod Esame INL1000205 CFU 6 Ore Tot 48Categoria Corsi di Laurea Magistrale / Secondo Semestre

Cod Esame INL1000205 CFU 6 Ore Tot 48Categoria Corsi di Laurea Magistrale / Secondo Semestre

Introduction and models for the Travelling Salesman Problem (TSP). Code setup and input parsing in C (TSPlib format). Basic ILP model and its solution through branch-and-cut (using IBM ILOG Cplex software). Compact models and their implementation in Cplex. Benders-like solution scheme using Subtour Elimination Constraints (SECs). SEC separation using Cplex's callbacks. Computational comparison of alternative exact approaches to TSP through performance profile plots. Heuristics and meta-heuristics for TSP: constructive heuristics, k-opt refining, tabu search, variable neighborhood search, simulated annealing, genetic algorithms etc. Writing a scientific paper (in Latex) on the implemented methods and on the corresponding computational performance. Teaching scheme: Front lessons (plus homeworks) via ZOOM at Fischett's classroom https://unipd.zoom.us/j/364970024 Exam: oral discussion of a thesis developed during the course (2-person groups). Bibliography: Notes provided by the teacher and available at http://www.dei.unipd.it/~fisch/ricop/RO2/ Categoria Corsi di Laurea Magistrale / Secondo Semestre