Ingegneria Gestionale | ALGORITMI DI OTTIMIZZAZIONE

cod. 0622600026

ALGORITMI DI OTTIMIZZAZIONE

	0622600026
	DIPARTIMENTO DI INGEGNERIA INDUSTRIALE
	EQF7
	MANAGEMENT ENGINEERING
	2016/2017

PERCORSO COMUNE Cohort 2015/2016

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2014
	PRIMO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/09	6	60	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

	Objectives
	KNOWLEDGE AND UNDERSTANDING: THE COURSE AIMS TO DEEPEN AND BROADEN THE KNOWLEDGE OF INTEGER LINEAR PROGRAMMING PROBLEMS, INTRODUCED IN THE OPERATIONS RESEARCH COURSE. THE COURSE AIMS AT SHOWING HOW TO SOLVE LINEAR PROGRAMMING PROBLEMS WITH A HUGE NUMBER OF VARIABLES OR CONSTRAINTS. MIXED LINEAR INTEGER PROGRAMMING PROBLEMS ARE ALSO OBJECT OF THE COURSE THAT AIMS TO DEEPEN THE KNOWLEDGE OF MATHEMATICAL MODELING OF COMBINATORIAL OPTIMIZATION PROBLEMS AND OF EXACT AND APPROXIMATION ALGORITHMS TO SOLVE THEM. APPLYING KNOWLEDGE AND UNDERSTANDING: ABILITY TO RECOGNIZE AND TO FORMULATE LINEAR OPTIMIZATION PROBLEMS AND MIXED INTEGER LINEAR OPTIMIZATION PROBLEMS. KNOWLEDGE OF THE MATHEMATICAL PROPERTIES OF THE PROBLEMS AND OF THEIR INHERENT COMPUTATIONAL COMPLEXITY. KNOWLEDGE OF THE MOST RECENT AND EFFICIENT ALGORITHMS FOR THE EXACT SOLUTION OF THE PROBLEMS OF PLI. KNOWLEDGE OF THE MAIN ELEMENTS FOR SOLVING LARGE PROBLEMS: CALCULATION OF LOWER BOUND AND DESIGN OF HEURISTIC ALGORITHMS. AUTONOMY OF JUDGMENT: ABILITY TO ASSESS AND COMPARE THE SOLUTIONS OF A MATHEMATICAL PROBLEM OF MEDIUM COMPLEXITY FORMULATED USING A MATHEMATICAL MODEL OF LARGE IN SIZE OR A MATHEMATICAL MODEL WITH INTEGER VARIABLES. COMMUNICATION SKILLS: ABILITY TO ORGANIZE THEMSELVES INTO WORKING GROUPS. ABILITY TO COMMUNICATE EFFECTIVELY IN WRITTEN AND / OR ORAL EXAM IN ENGLISH. LEARNING SKILLS: ABILITY TO CATALOG, OUTLINE AND REVISE THE GAINED KNOWLEDGE.

KNOWLEDGE AND UNDERSTANDING:
THE COURSE AIMS TO DEEPEN AND BROADEN THE KNOWLEDGE OF INTEGER LINEAR PROGRAMMING PROBLEMS, INTRODUCED IN THE OPERATIONS RESEARCH COURSE. THE COURSE AIMS AT SHOWING HOW TO SOLVE LINEAR PROGRAMMING PROBLEMS WITH A HUGE NUMBER OF VARIABLES OR CONSTRAINTS. MIXED LINEAR INTEGER PROGRAMMING PROBLEMS ARE ALSO OBJECT OF THE COURSE THAT AIMS TO DEEPEN THE KNOWLEDGE OF
MATHEMATICAL MODELING OF COMBINATORIAL OPTIMIZATION PROBLEMS AND OF EXACT AND APPROXIMATION ALGORITHMS TO SOLVE THEM.

APPLYING KNOWLEDGE AND UNDERSTANDING:
ABILITY TO RECOGNIZE AND TO FORMULATE LINEAR OPTIMIZATION PROBLEMS AND MIXED INTEGER LINEAR OPTIMIZATION PROBLEMS. KNOWLEDGE OF THE MATHEMATICAL PROPERTIES OF THE PROBLEMS AND OF THEIR INHERENT COMPUTATIONAL COMPLEXITY. KNOWLEDGE OF THE MOST RECENT AND EFFICIENT ALGORITHMS FOR THE EXACT SOLUTION OF THE PROBLEMS OF PLI. KNOWLEDGE OF THE MAIN ELEMENTS FOR SOLVING LARGE PROBLEMS: CALCULATION OF LOWER BOUND AND DESIGN OF HEURISTIC ALGORITHMS.

AUTONOMY OF JUDGMENT:
ABILITY TO ASSESS AND COMPARE THE SOLUTIONS OF A MATHEMATICAL PROBLEM OF MEDIUM COMPLEXITY FORMULATED USING A MATHEMATICAL MODEL OF LARGE IN SIZE OR A MATHEMATICAL MODEL WITH INTEGER VARIABLES.

COMMUNICATION SKILLS:
ABILITY TO ORGANIZE THEMSELVES INTO WORKING GROUPS. ABILITY TO COMMUNICATE EFFECTIVELY IN WRITTEN AND / OR ORAL EXAM IN ENGLISH.

LEARNING SKILLS:
ABILITY TO CATALOG, OUTLINE AND REVISE THE GAINED KNOWLEDGE.

	Prerequisites
	STUDENTS SHOULD KNOW BASIC CONCEPTS OF OPERATIONS RESEARCH.

	Contents
	MATHEMATICAL PROGRAMMING AND OPTIMALITY CONDITIONS. DUALITY THEORY. MAIN ELEMENTS OF THE ELLIPSOID METHOD. DUAL SIMPLEX. SOLUTION ALGORITHMS FOR LARGE SIZE PROBLEMS: COLUMN GENERATION METHOD. PRIMAL-DUAL METHOD. DISCRETE OPTIMIZATION: NETWORK FLOW PROBLEMS. MAIN CLASSES OF COMBINATORIAL PROBLEMS. VALID INEQUALITIES. RELAXATIONS. BENDERS DECOMPOSITION. EXACT SOLUTION METHODS: BRANCH AND BOUND, BRANCH AND CUT, CUTTING PLANE, BRANCH AND PRICE. LOCAL SEARCH ALGORITHMS AND METAHEURISTICS.

Contents

MATHEMATICAL PROGRAMMING AND OPTIMALITY CONDITIONS. DUALITY THEORY. MAIN ELEMENTS OF THE
ELLIPSOID METHOD. DUAL SIMPLEX. SOLUTION ALGORITHMS FOR LARGE SIZE PROBLEMS: COLUMN GENERATION METHOD. PRIMAL-DUAL METHOD.
DISCRETE OPTIMIZATION: NETWORK FLOW PROBLEMS. MAIN CLASSES OF COMBINATORIAL PROBLEMS. VALID
INEQUALITIES. RELAXATIONS. BENDERS DECOMPOSITION. EXACT SOLUTION METHODS: BRANCH AND BOUND,
BRANCH AND CUT, CUTTING PLANE, BRANCH AND PRICE. LOCAL SEARCH ALGORITHMS AND METAHEURISTICS.