The knowledge that the course aims to provide students with: students will explore the theory, methods, and algorithms for solving linear continuous optimization problems (i.e., where the variables are continuous) and flows on networks. Outline of linear integer optimization problems (i.e., where the variables are integer) will also be given. Skills that the course aims to provide students with: students will develop skills to construct, given real-life problems, corresponding and adequate mathematical models, and solve them using appropriate algorithms and optimization solvers.

No prerequisites are required. The only prior knowledge is those already acquired in the first-year engineering courses.

1. Continuous linear optimization: problems and models, simplex method, duality (40% of the course). 2. Analysis of the computational complexity of decision problems (5% of the course). 3. Flows on networks: fundamental concepts of graph theory, finding a spanning tree of minimum cost, transportation problem, shortest path problem, minimum cost flow problem, maximum flow problem, and minimum cut problem (50% of the course). 4. Outline of integer linear optimization (e.g., problems of network design, service location, data analysis, routing): exact methods (Branch and Bound) and heuristics (greedy algorithms, Tabu Search, Simulated Annealing, Genetic Algorithms) (5% of the course).

The course integrates properly teaching hours and hours of practice, to the extent of about 60% and 40% of the course, respectively. The exercises are carried out in the classroom and follow the lecture topics. In the LADISPE laboratory, http://www.ladispe.polito.it/ up-to-date, optimization solvers able to solve real-life problems are available to students. Instructions for their use will be provided in the classroom. No specialized programming skills are required.

Books used for teaching: R. Tadei, F. Della Croce, Elementi di Ricerca Operativa, Progetto Leonardo, Editrice Esculapio, Bologna, 2010. M. Ghirardi, A. Grosso, G. Perboli, Esercizi di Ricerca Operativa, Progetto Leonardo, Editrice Esculapio, Bologna, 2009. Other teaching materials, along with examples of previous exams, is available on the course website. Recommended books for further information: H. P. Williams, Model building in Mathematical Programming, 4th ed., Wiley, 1999. H. P. Williams, Logic and Integer Programming, Springer, 2009.

Lecture slides; Lecture notes; Text book; Practice book; Exercise with solutions ; Multimedia materials;

You can take this exam before attending the course

Exam: Written test;

The exam is written and is aimed to check the knowledge of the topics listed in the program of the course and the ability to apply the optimization theories and methods seen in class to the solution of the proposed exercises. The exam has a duration of 2 hours and consists of a written test with 4 questions on the topics contained in the course program. The exam aims to verify the skills referred to in the paragraph "Expected Learning Outcomes": the exam, in fact, includes a first question, of particular importance, which consists in writing, for a given real problem, a corresponding mathematical model of linear optimization that represents it appropriately (see also part 1 of the Program). The remaining questions are related to the computational complexity of decision-making problems and the resolution of optimization problems on networks seen in class (see also Part 2 and Part 3 of the Program). During the written test it will not be possible to consult texts, lecture notes and forms. Furthermore, multimedia devices with access to the web (for example, smartphones, smartwatches and tablets) are not allowed in the classroom. The exam is passed if the written test gets a vote from 18/30 to 30/30 (including praise). A scale of 0 to 32 points will be used for evaluation. The honors will be awarded if the vote is 32/30. The outcome of the test will be communicated to the students through a notice on the teaching portal. Students can view the task and its assessment during a general meeting whose date will be fixed from time to time. The date of the meeting will be communicated to the students through a notice on the teaching portal in conjunction with the publication of the results of the written test.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.