Francesco CARRABS | OPTIMIZATION

cod. 0522200016

OPTIMIZATION

	0522200016
	DIPARTIMENTO DI MATEMATICA
	EQF7
	MATHEMATICS
	2018/2019

CURRICULUM APPLICATIVO

	OBBLIGATORIO
	YEAR OF COURSE 1
	YEAR OF DIDACTIC SYSTEM 2018
	SECONDO SEMESTRE

TEACHING UNITS

	SSD	CFU	HOURS	ACTIVITY	TYPE OF ACTIVITY
	MAT/09	6	48	LESSONS	COMPULSORY SUBJECTS, CHARACTERISTIC OF THE CLASS

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. ABILITY TO APPLY ACQUIRED KNOWLEDGE AND UNDERSTANDING: ABILITY TO RECOGNIZE AND ABILITY TO FORMULATE DECISION-MAKING PROBLEMS OF APPLICATION INTEREST FALLING WITHIN THE CLASS OF LINEAR OPTIMIZATION PROBLEMS WITH INTEGER VARIABLES. ABILITY TO IDENTIFY AND RECOGNIZE MATHEMATICAL PROPERTIES OF THE PROBLEMS UNDER CONSIDERATION AND TO RECOGNIZE THEIR INTRINSIC COMPUTATIONAL COMPLEXITY. KNOWLEDGE OF THE LATEST AND MOST EFFICIENT ALGORITHMS FOR ACCURATE RESOLUTION OF PLI PROBLEMS. KNOWLEDGE OF MAJOR ELEMENTS FOR SOLVING LARGE-SCALE PROBLEMS: LOWER BOUND CALCULATION, HEURISTIC AND META-HEURISTIC ALGORITHMS DESIGN.

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.

ABILITY TO APPLY ACQUIRED KNOWLEDGE AND UNDERSTANDING:
ABILITY TO RECOGNIZE AND ABILITY TO FORMULATE DECISION-MAKING PROBLEMS OF APPLICATION INTEREST FALLING WITHIN THE CLASS OF LINEAR OPTIMIZATION PROBLEMS WITH INTEGER VARIABLES. ABILITY TO IDENTIFY AND RECOGNIZE MATHEMATICAL PROPERTIES OF THE PROBLEMS UNDER CONSIDERATION AND TO RECOGNIZE THEIR INTRINSIC COMPUTATIONAL COMPLEXITY. KNOWLEDGE OF THE LATEST AND MOST EFFICIENT ALGORITHMS FOR ACCURATE RESOLUTION OF PLI PROBLEMS. KNOWLEDGE OF MAJOR ELEMENTS FOR SOLVING LARGE-SCALE PROBLEMS: LOWER BOUND CALCULATION, HEURISTIC AND META-HEURISTIC ALGORITHMS DESIGN.

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

	Contents
	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.

Contents

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.

	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 THE 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 THE THIRTIES.

	Texts
	- CHRISTOS H. PAPADIMITRIOU: COMBINATORIAL OPTIMIZATION: ALGORITHMS AND COMPLEXITY - GEORGE L. NEMHAUSER, LAURENCE A. WOLSEY, INTEGER AND COMBINATORIAL OPTIMIZATION, 1999 - LECTURE NOTES. OTHER RECOMMENDED BOOK: LAURENCE A. WOLSEY, INTEGER PROGRAMMING, 1998.

	More Information
	-THE COURSE LANGUAGE IS ITALIAN. -PARTICIPATION TO THE LECTURES IS STRONGLY RECOMMENDED. -THE EMAIL ADDRESSES OF TEACHERS ARE: RAFFAELE@UNISA.IT, FCARRABS@UNISA.IT

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Francesco CARRABS | OPTIMIZATION