Course Scheduling Nikolaos Pothitos, Panagiotis in an Adjustable - PowerPoint PPT Presentation

Course Scheduling in an Adjustable Constraint Propagation Schema Course Scheduling Nikolaos Pothitos, Panagiotis in an Adjustable Constraint Stamatopoulos, Kyriakos Zervoudakis Propagation Schema 1. Introduction 2. Related Work Nikolaos Pothitos Panagiotis Stamatopoulos 3. Contents Kyriakos Zervoudakis 4. Our Course Timetabling Model Department of Informatics and Telecommunications 5. New Random Heuristics University of Athens 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 1

Course Introduction Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos • Course timetabling: an intensive problem. Zervoudakis 1. Introduction • Occurs in schools and academia. 2. Related Work • Often still solved “by hand.” 3. Contents 4. Our Course • Until utilizing Artificial Intelligence tools. Timetabling Model 5. New Random • We design Constraint Programming methodologies. Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 2

Course Related Work: Other Timetabling Scheduling in an Solutions Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis • Artificial Intelligence Paradigms 1. Introduction ◮ Tabu Search 2. Related Work ◮ Genetic Algorithms 3. Contents ◮ Local Search 4. Our Course Timetabling • Other Methodologies Model ◮ Network Flow 5. New Random Heuristics ◮ Clustering to small sub-problems 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 3

Course We Chose Constraint Programming Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, • Constraint Programming incorporates Artificial Kyriakos Zervoudakis Intelligence. 1. Introduction • Also used in other fields. 2. Related Work 3. Contents • Separates the problem declaration phase. . . 4. Our Course Timetabling Model • . . . from the solution search algorithm. 5. New Random Heuristics • A flexible intelligent programming paradigm. 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 4

Course Introduction to Constraint Scheduling in an Satisfaction Problems Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, • Constraint Programming solves Constraint Satisfaction Kyriakos Zervoudakis Problems (CSPs). 1. Introduction 2. Related Work • A CSP is described by: 3. Contents 1. the variables of the problem, 4. Our Course Timetabling ◮ e.g. X , Y , Model 2. the domains of the variables, 5. New Random Heuristics ◮ e.g. D X = { 0 , 1 } , D Y = { 1 , 3 , 4 } , 6. Adjusting 3. the constraints between the variables, Constraint Propagation ◮ e.g. X � = Y . 7. Conclusions – Contributions 5

Course Solving a Constraint Satisfaction Scheduling in an Problem Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis • Assignment: makes a domain singleton. 1. Introduction 2. Related Work • Complete assignment: involves all variables. 3. Contents 4. Our Course • Valid assignment: satisfies the constraints. Timetabling Model • Solution: a valid complete assignment. 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 6

Course Solving Procedure – Search Method Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis • A posteriori constraint enforcement 1. Introduction ◮ Checks constraints after the assignments. 2. Related Work • Constraint Propagation 3. Contents ◮ Done a priori. 4. Our Course Timetabling ◮ Prunes no-good values from domains. Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 7

Course Another CSP: N Queens Scheduling in an Adjustable Constraint Propagation Schema ⋆ Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis ⋆ 1. Introduction 2. Related Work ⋆ 3. Contents ⋆ 4. Our Course Timetabling Model ⋆ 5. New Random Heuristics ⋆ 6. Adjusting Constraint Propagation ⋆ 7. Conclusions – Contributions 8

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis 1. Introduction 2. Related Work 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 9

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 10

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 11

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 12

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 13

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 14

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 15

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 16

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 17

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 18

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 19

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics ⋆ 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 20

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics ⋆ 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 21

Course Constraint Propagation for N Queens Scheduling in an Adjustable Constraint Propagation Schema Nikolaos Pothitos, Panagiotis Stamatopoulos, ⋆ Kyriakos Zervoudakis 1. Introduction 2. Related Work ⋆ 3. Contents 4. Our Course Timetabling Model 5. New Random Heuristics ⋆ 6. Adjusting Constraint Propagation 7. Conclusions – Contributions 22