Raffaele CERULLI | OPTIMIZATION METHODS

cod. 0522500054

OPTIMIZATION METHODS

	0522500054
	DIPARTIMENTO DI INFORMATICA
	EQF7
	COMPUTER SCIENCE
	2020/2021

CURRICULUM DATA SCIENCE & MACHINE LEARNING

	YEAR OF COURSE 2
	YEAR OF DIDACTIC SYSTEM 2016
	SECONDO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/09	6	48	LESSONS	SUPPLEMENTARY COMPULSORY SUBJECTS

PROFESSORS

	RAFFAELE CERULLI T Curriculum
	FRANCESCO CARRABS Curriculum

	Objectives
	KNOWLEDGE AND UNDERSTANDING THE COURSE AIMS TO DEEPEN AND BROADEN THE KNOWLEDGE ON THE INTEGER LINEAR PROGRAMMING PROBLEMS INTRODUCED DURING THE COURSE OF OPERATIONAL RESEARCH, WITH PARTICULAR REGARD TO CLASSES OF PROBLEMS OF SIGNIFICANT APPLICATION INTEREST. KNOWLEDGE WILL BE GAINED ON THE METHODS OF SOLVING LINEAR PROGRAMMING PROBLEMS WITH A VERY HIGH NUMBER OF VARIABLES OR CONSTRAINTS. WITH REGARD TO THE LINEAR OPTIMIZATION PROBLEMS WITH INTEGER AND BINARY VARIABLES, THE COURSE AIMS TO TEACH THE MAIN FOUNDATIONS OF MATHEMATICAL MODELLING OF COMBINATORIAL OPTIMIZATION PROBLEMS AND TO TEACH THE MAIN ALGORITHMS, BOTH OF THE EXACT TYPE AND OF THE APPROXIMATE TYPE, FOR SOLVING PROBLEMS OF OPTIMIZATION TO INTEGER OR BINARY VARIABLES. APPLYING KNOWLEDGE AND UNDERSTANDING ABILITY TO RECOGNIZE AND ABILITY TO FORMULATE DECISION-MAKING PROBLEMS OF APPLICATION INTEREST WITHIN THE CLASS OF LINEAR OPTIMIZATION PROBLEMS AND INTEGER OPTIMIZATION PROBLEMS. ABILITY TO IDENTIFY AND RECOGNIZE MATHEMATICAL PROPERTIES OF THE PROBLEMS UNDER CONSIDERATION AND TO RECOGNIZE THEIR INTRINSIC COMPUTATIONAL COMPLEXITY AND THE MOST EFFICIENT ALGORITHMS FOR THEIR SOLUTION. ABILITY TO DESIGN HEURISTIC ALGORITHMS TO FIND GOOD FEASIBLE SOLUTION IN A SHORT TIME FOR THE PROBLEM UNDER STUDY.

KNOWLEDGE AND UNDERSTANDING
THE COURSE AIMS TO DEEPEN AND BROADEN THE KNOWLEDGE ON THE INTEGER LINEAR PROGRAMMING PROBLEMS INTRODUCED DURING THE COURSE OF OPERATIONAL RESEARCH,
WITH PARTICULAR REGARD TO CLASSES OF PROBLEMS OF SIGNIFICANT APPLICATION INTEREST. KNOWLEDGE WILL BE GAINED ON THE METHODS OF SOLVING LINEAR PROGRAMMING PROBLEMS
WITH A VERY HIGH NUMBER OF VARIABLES OR CONSTRAINTS. WITH REGARD TO THE LINEAR OPTIMIZATION PROBLEMS WITH INTEGER AND BINARY VARIABLES,
THE COURSE AIMS TO TEACH THE MAIN FOUNDATIONS OF MATHEMATICAL MODELLING OF COMBINATORIAL OPTIMIZATION PROBLEMS AND TO TEACH THE MAIN ALGORITHMS, BOTH OF THE EXACT TYPE AND OF THE APPROXIMATE TYPE, FOR SOLVING PROBLEMS OF OPTIMIZATION TO INTEGER OR BINARY VARIABLES.

APPLYING KNOWLEDGE AND UNDERSTANDING
ABILITY TO RECOGNIZE AND ABILITY TO FORMULATE DECISION-MAKING PROBLEMS OF APPLICATION INTEREST WITHIN THE CLASS OF LINEAR OPTIMIZATION PROBLEMS AND INTEGER OPTIMIZATION PROBLEMS.
ABILITY TO IDENTIFY AND RECOGNIZE MATHEMATICAL PROPERTIES OF THE PROBLEMS UNDER CONSIDERATION AND TO RECOGNIZE THEIR INTRINSIC
COMPUTATIONAL COMPLEXITY AND THE MOST EFFICIENT ALGORITHMS FOR THEIR SOLUTION. ABILITY TO DESIGN HEURISTIC ALGORITHMS TO FIND GOOD FEASIBLE SOLUTION IN A SHORT TIME FOR THE PROBLEM UNDER STUDY.

	Prerequisites
	THE OPERATIONS RESEARCH COURSE IS OFFICIALLY REQUIRED TO ATTEND THIS COURSE.

	Contents
	1. LINEAR PROGRAMMING (PL) PATHOLOGIC CASE OF THE SIMPLEX METHOD: KLEE E MINTY CUBE; ELLIPSOID METHOD; SIMPLEX TABLEAU; DUAL-SIMPLEX METHOD; PRIMAL-DUAL ALGORITHM; DELAYED COLUMN GENERATION ALGORITHM; 2. INTEGER LINEAR PROGRAMMING (PLI) LOGIC VARIABLES AND CONSTRAINTS; MULTI-OBJECTIVE PROBLEMS; CLASSICAL COMBINATORIAL PROBLEMS; LAGRANGIAN RELAXATION; BENDERS DECOMPOSITION; VALID INEQUALITIES; EXACT APPROACHES: BRANCH AND BOUND, CUTTING PLANE, BRANCH AND CUT. HEURISTIC METHODS: LOCAL SEARCH, GREEDY ALGORITHM, TABU SEARCH, SIMULATED ANNEALING, GENETIC ALGORITHM;

Contents

1. LINEAR PROGRAMMING (PL)
PATHOLOGIC CASE OF THE SIMPLEX METHOD: KLEE E MINTY CUBE; ELLIPSOID METHOD; SIMPLEX TABLEAU; DUAL-SIMPLEX METHOD; PRIMAL-DUAL ALGORITHM; DELAYED COLUMN GENERATION ALGORITHM;

2. INTEGER LINEAR PROGRAMMING (PLI)
LOGIC VARIABLES AND CONSTRAINTS; MULTI-OBJECTIVE PROBLEMS;
CLASSICAL COMBINATORIAL PROBLEMS; LAGRANGIAN RELAXATION; BENDERS DECOMPOSITION; VALID INEQUALITIES; EXACT APPROACHES: BRANCH AND BOUND, CUTTING PLANE, BRANCH AND CUT. HEURISTIC METHODS: LOCAL SEARCH, GREEDY ALGORITHM, TABU SEARCH, SIMULATED ANNEALING, GENETIC ALGORITHM;

	Teaching Methods
	FRONTAL LESSONS FOR A TOTAL DURATION OF 48 HOURS (6 CFUS), WHICH TAKE PLACE IN THE CLASSROOM WITH THE AID OF PROJECTIONS. AT THE END OF THE PRESENTATION OF A TOPIC, VARIOUS APPLICATION EXAMPLES AND EXERCISES WILL BE PROVIDED.

	Verification of learning
	THE FINAL EXAM IS DESIGNED TO EVALUATE AS A WHOLE: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED IN THE COURSE, AS WELL AS THE ABILITY TO APPLY SUCH KNOWLEDGE FOR THE RESOLUTION OF OPTIMIZATION PROBLEMS. THE ORAL EXAMINATION WILL COVER ALL THE TOPICS OF THE COURSE AND ASSESSMENT WILL TAKE INTO ACCOUNT THE KNOWLEDGE DEMONSTRATED BY THE STUDENT CONCERNING BOTH THE THEORETICAL AND APPLICATIVE ASPECTS FOR THE RESOLUTION OF THE OPTIMIZATION PROBLEMS. THE EVALUATION OF THE ORAL EXAMINATION IS EXPRESSED IN THIRTIES.

Verification of learning

THE FINAL EXAM IS DESIGNED TO EVALUATE AS A WHOLE: THE KNOWLEDGE AND UNDERSTANDING OF THE CONCEPTS PRESENTED IN THE COURSE, AS WELL AS THE ABILITY TO APPLY SUCH KNOWLEDGE FOR THE RESOLUTION OF OPTIMIZATION PROBLEMS.

THE ORAL EXAMINATION WILL COVER ALL THE TOPICS OF THE COURSE AND ASSESSMENT WILL TAKE INTO ACCOUNT THE KNOWLEDGE DEMONSTRATED BY THE STUDENT CONCERNING BOTH THE THEORETICAL AND APPLICATIVE ASPECTS FOR THE RESOLUTION OF THE OPTIMIZATION PROBLEMS. THE EVALUATION OF THE ORAL EXAMINATION IS EXPRESSED IN THIRTIES.

	Texts
	- CHRISTOS H. PAPADIMITRIOU: COMBINATORIAL OPTIMIZATION: ALGORITHMS AND COMPLEXITY - GEORGE L. NEMHAUSER, LAURENCE A. WOLSEY, INTEGER AND COMBINATORIAL OPTIMIZATION, 1999 - LECTURE NOTES

	More Information
	-THE COURSE LANGUAGE IS ITALIAN. -PARTICIPATION TO THE LECTURES IS STRONGLY RECOMMENDED. -THE EMAIL ADDRESS OF TEACHER IS: RAFFAELE@UNISA.IT

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Raffaele CERULLI | OPTIMIZATION METHODS