87214 - Advanced Prescriptive Analytics M

Course Unit Page

Academic Year 2018/2019

Learning outcomes

The aim of this course is to provide the advanced methods for the solution of difficult optimization problem and their applications. Algoritmi per problemi difficili di teoria dei grafi ed ottimizzazione su rete. Graph coloring, paths and circuits, network synthesis (location/allocation)… Heuristics for graph and network optimization problems. Advanced heuristics and exact methods for discrete optimization problems. Branch and cut and Column generation methods. Problem decomposition techniques. Metaheuristics for discrete optimization problems. Optimization with uncertainty. Stochastic optimization and Monte Carlo methods. Heuristics for Stochastic optimization. Robust optimization: reformulations and solution algorithms. Prescriptive analytics and Decision Support. Decision analysis and decision trees. Algorithms configuration, Clustering and Classification. Big Data and large scale problems. Applications in telecommunications, energy distribution and circuits, automation and production (machine scheduling, job/flow shop).

Course contents

Requirements/Prior knowledge
Students are supposed to have a basic knowledge on Operations Research, as well as on the implementation of computer codes and on complexity theory.

Fluent spoken and written English is a necessary pre-requisite as all lectures and material will be in English.

Course Contents

The course presents advanced algorithms for solving optimization problems having practical relevance in several contexts, including telecommunications, control systems, and decision support systems.

The course is divided into two modules.

Module 1: The first module is methodological and presents a number of optimization algorithms, mainly for nonlinear programming.

Non-linear optimization: introduction to Mathematical Programming, models and algorithms. Non-linear models: unconstrained optimization and constrained optimization. Relaxations and penalty function algorithms.

Convex optimization: Lagrangian relaxation in convex optimization. The barrier algorithm. Applications to support vector machine.

Module 2: The second module show possible applications of these algorithms to different real-world problems.
In particular, examples of use of classification and evaluation techniques based on various machine learning mechanism will be presented.
In addition, the module will include the description of prescriptive analytics techniques based on the use of heuristics and metaheuristics algorithms.

Readings/Bibliography

Recommended:

Slides available online.

Additional useful references:

-- C. Bishop, Pattern Recognition and Machine Learning. Springer

 

-- S. Boyd e L. Vandenberghe, Convex Optimization. Cambridge University Press

-- L. Grippo e M. Sciandrone, Metodi di Ottimizzazione Non Vincolata. Springer

-- J. Nocedal e S. J. Wright, Numerical Optimization. Springer


Teaching methods

The course consists of class lectures that concern both the theoretical aspects and the practical application of the algorithms.

Assessment methods

For each module there is a written exam (without books/notes) and an oral test (on the same day).

The final mark will be determined according to both partial marks.

Teaching tools

All teaching material used during the course will be available to the students on AlmaDL

Office hours

See the website of Michele Monaci

See the website of Daniele Vigo