Francesco CARRABS | OPTIMIZATION

cod. 0522200016

OPTIMIZATION

	0522200016
	DIPARTIMENTO DI MATEMATICA
	EQF7
	MATHEMATICS
	2020/2021

CURRICULUM APPLICATION-ORIENTED MATHEMATICS

	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

	FRANCESCO CARRABS T Curriculum
	CIRIACO D'AMBROSIO 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 THE 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 THE 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 A 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
THE 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 THE 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 A 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) (LECTURES 12H; EXERCISE 4H) 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) (LECTURES 26H; EXERCISE 6H) - 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) (LECTURES 12H; EXERCISE 4H)
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) (LECTURES 26H; EXERCISE 6H)
- 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
	THE COURSE IS ORGANIZED IN 48 HOURS OF FRONTAL LESSONS (6 CFU), USING PROJECTED SLIDES. AT THE END OF EACH TOPIC, SOME EXAMPLES AND CLASSROOM EXERCISES ARE PRESENTED. THE SOLUTION OF THE EXERCISE, WHICH IS CARRIED OUT UNDER THE SUPERVISION OF THE TEACHER, SEEKS TO DEVELOP AND STRENGTHEN THE STUDENT CAPACITY OF IDENTIFYING THE MOST APPROPRIATE TECHNIQUES TO SOLVE IT.

	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 ORAL, EXPRESSED IN THIRTIES, TAKES INTO ACCOUNT THE ABILITY TO DESCRIBE THE OPTIMIZATION ALGORITHMS AND THE OTHER CONCEPTS, PRESENTED IN THE COURSE, IN A CLEAR AND CONCISE MANNER. THE MINIMUM GRADE (18/30) IS ATTRIBUTED WHEN THE STUDENT DEMONSTRATES UNCERTAINTIES IN THE PRESENTATION OF THE CONCEPTS AND OPTIMIZATION ALGORITHMS, PRESENTED IN THE COURSE, AND LOW EXPOSITORY CAPACITY. THE MAXIMUM LEVEL (30/30) IS ATTRIBUTED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND THOROUGH KNOWLEDGE OF THE OPTIMIZATION ALGORITHMS AND SHOWS A REMARKABLE ABILITY TO IDENTIFY THE MORE APPROPRIATE METHOD TO USE IN ORDER TO SOLVE THE OPTIMIZATION PROBLEMS STUDIED. THE LAUDE IS ATTRIBUTED WHEN THE CANDIDATE SHOWS A SIGNIFICANT MASTERY OF THE THEORETICAL AND OPERATIONAL CONTENTS AND SHOWS THE ABILITY TO PRESENT THE TOPICS WITH REMARKABLE PROPERTIES OF LANGUAGE AND AUTONOMOUS PROCESSING CAPACITY EVEN IN CONTEXTS DIFFERENT FROM THOSE PROPOSED BY THE TEACHER.

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 ORAL, EXPRESSED IN THIRTIES, TAKES INTO ACCOUNT THE ABILITY TO DESCRIBE THE OPTIMIZATION ALGORITHMS AND THE OTHER CONCEPTS, PRESENTED IN THE COURSE, IN A CLEAR AND CONCISE MANNER.

THE MINIMUM GRADE (18/30) IS ATTRIBUTED WHEN THE STUDENT DEMONSTRATES UNCERTAINTIES IN THE PRESENTATION OF THE CONCEPTS AND OPTIMIZATION ALGORITHMS, PRESENTED IN THE COURSE, AND LOW EXPOSITORY CAPACITY.

THE MAXIMUM LEVEL (30/30) IS ATTRIBUTED WHEN THE STUDENT DEMONSTRATES A COMPLETE AND THOROUGH KNOWLEDGE OF THE OPTIMIZATION ALGORITHMS AND SHOWS A REMARKABLE ABILITY TO IDENTIFY THE MORE APPROPRIATE METHOD TO USE IN ORDER TO SOLVE THE OPTIMIZATION PROBLEMS STUDIED.

THE LAUDE IS ATTRIBUTED WHEN THE CANDIDATE SHOWS A SIGNIFICANT MASTERY OF THE THEORETICAL AND OPERATIONAL CONTENTS AND SHOWS THE ABILITY TO PRESENT THE TOPICS WITH REMARKABLE PROPERTIES OF LANGUAGE AND AUTONOMOUS PROCESSING CAPACITY EVEN IN CONTEXTS DIFFERENT FROM THOSE PROPOSED BY THE TEACHER.

	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. - THE ATTENDANCE OF THE LESSONS IS HIGHLY RECOMMENDED. - OFFICE HOURS FOR STUDENTS ARE AVAILABLE HERE: HTTPS://DOCENTI.UNISA.IT/001227/HOME HTTPS://DOCENTI.UNISA.IT/020511/HOME

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Francesco CARRABS | OPTIMIZATION