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.

The lectures are organized in i) methodology and ii) case-studies from real-world applications. Additional exercises and use of software tools are presented during exercise hours.

AIMS AND CONTENT

LEARNING OUTCOMES

This course provides the basic notions of optimization methods for solving decision-making problems. In particular, it provides the knowledge to mathematically model a decision problem and solve it through linear programming, integer linear programming, nonlinear programming, and graph optimization techniques.

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 COMPUTER SCIENCE AND ENGINEERING AND OTHER ENGINEERING APPLICATIONS

SOFTWARE TOOLS FOR OPTIMIZATION

RECOMMENDED READING/BIBLIOGRAPHY

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

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

https://easyacademy.unige.it/portalestudenti/index.php?view=easycourse&_lang=it&include=corso

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Written.

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.