# Ingegneria Gestionale | OPTIMIZATION ALGORITHMS

## Ingegneria Gestionale OPTIMIZATION ALGORITHMS

 0622600026 DIPARTIMENTO DI INGEGNERIA INDUSTRIALE EQF7 MANAGEMENT ENGINEERING 2022/2023

 YEAR OF COURSE 2 YEAR OF DIDACTIC SYSTEM 2018 AUTUMN SEMESTER
SSD CFU HOURS ACTIVITY TYPE OF ACTIVITY MAT/09 6 60 LESSONS SUPPLEMENTARY COMPULSORY SUBJECTS
 CIRIACO D'AMBROSIO T FEDERICA LAUREANA
ExamDate
ALGORITMI DI OTTIMIZZAZIONE06/02/2023 - 09:00
ALGORITMI DI OTTIMIZZAZIONE06/02/2023 - 09:00
Objectives
KNOWLEDGE AND UNDERSTANDING:

THE COURSE AIMS TO DEEPEN AND BROADEN THE KNOWLEDGE OF LINEAR AND INTEGER PROGRAMMING PROBLEMS INTRODUCED DURING THE COURSE OF OPERATIONAL RESEARCH, WITH PARTICULAR REGARD TO CLASSES OF PROBLEMS OF SIGNIFICANT APPLICATION INTEREST. IN PARTICULAR, ALTERNATIVE ALGORITHMS TO THE SIMPLEX METHOD FOR SOLVING CONTINUOUS LINEAR PROGRAMMING PROBLEMS WITH A VERY HIGH NUMBER OF CONSTRAINTS AND VARIABLES WILL BE PRESENTED. 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.

APPLYING KNOWLEDGE AND UNDERSTANDING:

THE ABILITY TO FORMULATE DECISION-MAKING PROBLEMS THROUGH MATHEMATICAL MODELS WITH CONTINUOUS OR INTEGER VARIABLES ACCORDING TO THE REQUIREMENTS;

THE ABILITY TO RECOGNIZE THE INTRINSIC COMPUTATIONAL COMPLEXITY OF THE PROBLEM UNDER CONSIDERATION AND TO IDENTIFY THE MOST EFFICIENT ALGORITHMS FOR ITS SOLUTION.

THE 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 8 HOURS; EXERCISE 4H)
- 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 4H)
- DUAL-SIMPLEX METHOD;
- DELAYED COLUMN GENERATION ALGORITHM.
3. INTEGER LINEAR PROGRAMMING (PLI) (LECTURES 12 HOURS; EXERCISE 4H)
- 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 8 HOURS; EXERCISE 4H)
- BRANCH AND BOUND;
- CUTTING PLANE;
- BRANCH AND CUT.
5. HEURISTIC APPROACHES (LECTURES 8 HOURS; EXERCISE 2H)
- LOCAL SEARCH;
- GREEDY ALGORITHM;
- TABU SEARCH;
- SIMULATED ANNEALING;
- GENETIC ALGORITHM.
Teaching Methods
THE COURSE IS ORGANIZED IN 60 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.