Raffaele CERULLI | OPTIMIZATION
Raffaele CERULLI OPTIMIZATION
cod. 0522200016
OPTIMIZATION
| 0522200016 | |
| DEPARTMENT OF MATHEMATICS | |
| EQF7 | |
| MATHEMATICS | |
| 2023/2024 |
| OBBLIGATORIO | |
| YEAR OF COURSE 1 | |
| YEAR OF DIDACTIC SYSTEM 2018 | |
| SPRING SEMESTER |
| SSD | CFU | HOURS | ACTIVITY | |
|---|---|---|---|---|
| MAT/09 | 6 | 48 | LESSONS |
| 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. |
| Prerequisites | |
|---|---|
| THE OPERATIONS RESEARCH COURSE IS OFFICIALLY REQUIRED TO ATTEND THIS COURSE. |
| Contents | |
|---|---|
| 1. LINEAR PROGRAMMING (PL) (LECTURES 6 HOURS; EXERCISE 2H) - RECALLS OF THE MAIN RESULTS OF LINEAR PROGRAMMING; - PATHOLOGIC CASE OF THE SIMPLEX METHOD: KLEE E MINTY CUBE; - ELLIPSOID METHOD; - SIMPLEX TABLEAU. 2. ALTERNATIVE ALGORITHMS TO THE SIMPLEX METHOD (LECTURES 6 HOURS; EXERCISE 2H) - DUAL-SIMPLEX METHOD; - PRIMAL-DUAL ALGORITHM; - DELAYED COLUMN GENERATION ALGORITHM. 3. INTEGER LINEAR PROGRAMMING (PLI) (LECTURES 14 HOURS; EXERCISE 2H) - COMPLEXITY THEORY: CLASSIFICATION OF THE OPTIMIZATION PROBLEMS ACCORDING TO THEIR DIFFICULTY; - LOGIC VARIABLES AND CONSTRAINTS; MULTI-OBJECTIVE PROBLEMS; - CLASSICAL COMBINATORIAL OPTIMIZATION PROBLEMS; - LAGRANGIAN RELAXATION; - VALID INEQUALITIES. 4 EXACT APPROACHES (LECTURES 6 HOURS; EXERCISE 2H) - BRANCH AND BOUND; - CUTTING PLANE; - BRANCH AND CUT. 5 HEURISTIC APPROACHES (LECTURES 6 HOURS; EXERCISE 2H) - 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 ASSESSMENT LEVEL (18) IS AWARDED WHEN THE STUDENT SHOWS A FRAGMENTARY KNOWLEDGE OF THEORETICAL CONTENTS AND A LIMITED ABILITY TO FORMULATE OPTIMIZATION PROBLEMS AND TO APPLY ALGORITHMS TO SOLVE THEM. THE MAXIMUM ASSESSMENT LEVEL (30) IS ATTRIBUTED WHEN THE STUDENT SHOWS A COMPLETE AND IN-DEPTH KNOWLEDGE OF THE COURSE TOPICS AND A REMARKABLE ABILITY TO IDENTIFY THE MOST APPROPRIATE METHODS TO SOLVE THE OPTIMIZATION PROBLEMS FACED. 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, K. STEIGLITZ: COMBINATORIAL OPTIMIZATION: ALGORITHMS AND COMPLEXITY, 1998; - M.S. BAZARAA, J.J. JARVIS & H.D. SHERALI, LINEAR PROGRAMMING AND NETWORK FLOWS, FOURTH EDITION, JOHN WILEY, 2010; - GEORGE L. NEMHAUSER, LAURENCE A. WOLSEY, INTEGER AND COMBINATORIAL OPTIMIZATION, 1999. - LECTURE NOTES PROVIDED BY THE TEACHER. OTHER RECOMMENDED BOOK: LAURENCE A. WOLSEY, INTEGER PROGRAMMING, 1998. |
| More Information | |
|---|---|
| - EMAIL: RAFFAELE@UNISA.IT, FCARRABS@UNISA.IT - THE COURSE LANGUAGE IS ITALIAN; - THE ATTENDANCE OF THE LESSONS IS HIGHLY RECOMMENDED; - OFFICE HOURS FOR STUDENTS ARE AVAILABLE ON THE WEBPAGE: HTTPS://DOCENTI.UNISA.IT/001227/HOME |
BETA VERSION Data source ESSE3 [Ultima Sincronizzazione: 2024-11-05]
