OVERVIEW

The Course introduces to optimization models and methods for the solution of decision problems. It is structured according to the basic topics of problem modelling, its tractability, and its solution by means of algorithms that can be implemented on computers.  Case studies from Engineering, with particular attention to Information Technology, are presented and investigated.

AIMS AND CONTENT

LEARNING OUTCOMES

The Course introduces to optimization models and methods for the solution of decision problems. It is structured in the main topics of problem modelling, computational tractability, and solution by means of algorithms that can be implemented on a computer. Several applications are considered and various case studies are detailed. The target of the Course consists in making the students acquire the expertise to face decision problems by means of models and methods that can operate in the presence of limited resources. The students will be taught to: understanding and modelling a decision process in terms of an optimization problem by defining the decision variables, the cost function to be minimized (or the figure of merit to be maximized), and the constraints; framing the obtained problem within the range of the reference optimization problems (linear/nonlinear, discrete/continuous, deterministic/stochastic, static/dynamic, etc); achieving the matching between the corresponding solving algorithm and a suitable software.

AIMS AND LEARNING OUTCOMES

The students will be taught to:

- interpret and shape a decision-making process in terms of an optimization problem, identifying the decision-making variables, the cost function to minimize (or the figure of merit to maximize), and the constraints;

- framing the problem in the range of problems considered "canonical" (linear / nonlinear, discrete / continuous, deterministic / stochastic, static / dynamic, etc.);

- realizing the "matching" between the solving algorithm (to choose from existing or to be designed) and an appropriate processing software support.

PREREQUISITES

Linear Algebra. Vector and matrix calculus. Basic concepts of Mathematical Analysis and Geometry.

TEACHING METHODS

Lectures and exercises.

SYLLABUS/CONTENT

INTRODUCTION TO OPERATIONS RESEARCH

LINEAR PROGRAMMING

DUALITY

INTEGER PROGRAMMING

GRAPH AND NETWORK OPTIMIZATION

COMPLEXITY THEORY

NONLINEAR PROGRAMMING

DYNAMIC PROGRAMMING

CASE STUDIES FROM INFORMATION TECHNOLOGY

SOFTWARE TOOLS FOR OPTIMIZATION

RECOMMENDED READING/BIBLIOGRAPHY

Lecture notes provided by the teacher and available in electronic format.

TEACHERS AND EXAM BOARD

Exam Board

MARCELLO SANGUINETI (President)

MAURO GAGGERO

DANILO MACCIO'

ANGELA LUCIA PUSILLO

MASSIMO PAOLUCCI (President Substitute)

LESSONS

LESSONS START

https://courses.unige.it/11160/p/students-timetable

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written, if it will be possible to make exams "in presence". Otherwise, the teacher will decide whether the exam via Teams will be written or oral.

ASSESSMENT METHODS

Comprehension of the concepts explained during the Course.

Capability to:

- interpret and shape a decision-making process in terms of an optimization problem, identifying the decision-making variables, the cost function to minimize (or the figure of merit to maximize), and the constraints;

- frame the problem in the range of problems considered "canonical" (linear / nonlinear, discrete / continuous, deterministic / stochastic, static / dynamic, etc.);

- choose and/or develop a solving algorithm and apply it to solve the problem.

Exam schedule

FURTHER INFORMATION

For the Laurea in Mathematics, which "borrows" only 7 cfu, the following topics are excluded:

DYNAMIC PROGRAMMING

CASE STUDIES FROM INFORMATION TECHNOLOGY