1. CSCI 5240 Combinatorial Search and Optimization with Constraints
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2. Administrative Tidbits
Instructor: Jimmy Lee, SHB 1009, x38426,
Tutor: Zichen Zhu, SHB 1005, x38422,
Course information dissemination and discussion: newsgroup <cuhk.cse.csci5240> and homepage <
Evaluation criteria: assignments (60%) and project (40%)
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3. Learning Outcomes
To model applications as Constraint Satisfaction/Optimization Problems
To understand various search-based constraint solving algorithms
To program and use state-of-the-art constraint solver
To read and write mathematics, understand research papers, and do research
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4. The Graph Coloring Problem
Color the following graph using {R,G,B} so that no neighbouring nodes share the same color
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5. Crytarithmetic Puzzles
S E N D D O N A L D
+) M O R E ) G E R A L D
M O N E Y R O B E R T
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6. Solution of Numerical Systems
Real variables
3X1 + 4X2 + 6X3 > 5
12X1 - 6X2 + 7X3 = 67
X12 + X22 >= 7
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7. SAT and Boolean Systems
Variables are of Boolean type
X1X2 + X2X3 + X3X4 + X4X5 = T
X1X2X3 + X2X3X4 = F
X1X3X4 + X1X2 + X5 = T
X2X4 + X5X1 = T
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8. Scene Labelling Probably the first constraint satisfaction problem
Recognize objects in 3D scene by interpreting lines in 2D drawings + -
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9. Interactive Graphics
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10. Scheduling Problems Production scheduling (InSol Ltd.)
Well-activity scheduling (Saga Petroleum)
Planning production of jets (Dassault Aviation)
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11. Car Sequencing
Sequence the cars on production conveyer belt, satisfying various resource constraints
Posed as a challenge to the AI community in 1986
Breakthrough using constraints in 1988
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12. Application Domains - 1
Timetabling, resource allocation, spatial and temporal reasoning, binpacking
Airport counter allocation, Nurse rostering, Ship berth allocation, Flight crew rostering, Train rescheduling, Basketball league scheduling
Network management and configuration
Telecommunication networks cabling planning, Optimal placement of base stations in wireless networks
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13. Application Domains - 2 Molecular biology: DNA sequencing
Scene labeling, manufacturing, AI planning
Finite element analysis, linear programming
Analog and digital circuit design
VLSI CAD, circuit simulation
Satellite camera scheduling
More …
What do the examples share in common?
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14. Constraint Satisfaction Problems
A finite set of unknowns, each of which is associated with a set of feasible values
Problem-specific conditions are imposed on the unknowns to limit the combinations of values that the unknowns can take
The aim is to find a “consistent” assignment of values to the unknowns
Extremely difficult to solve!!!!
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15. Constraint Programming - 1
A C program for converting Fahrenheit (F) to Celsius (C) would contain:
C := (F - 32) * 5/9
How about converting Celcius to Fahrenheit?
F := /5 * C
How about converting temperatures to and from Kelvin (K) as well?
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16. Constraint Programming - 2
K := C - 273
C := K + 273
K := /9*F
F := /5*K
Wouldn’t it be nice if we can simply state the following relationship ?
C = (F - 32) * 5/9
K = C - 273
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17. Constraint Programming - 3
Constraint Programming is
declarative: programmer states the relations between a set of objects and the constraint solver finds a solution satisfying the relations
multimodal: the ability to solve many different problems with the same program, even if they were not anticipated when the program was written
extensible: easy to modify and extend
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18. Course Outline - 1 Constraint Satisfaction Techniques
Basic terminologies and definitions
Examining various constraint domains
Algorithms for constraint satisfaction and optimization
Mathematical programming
Systematic and local search
Finite domain constraints and combinatorial problems
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19. Course Outline - 2 Programming with Constraints
Use of Constraint Programming systems
CP = Modeling + Search
Simple modeling techniques
Controlling search
Model search
Solution search
Modeling with finite domain constraints
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20. Constraint programming represents one of the closest approaches computer science has yet made to the Holy Grail of programming: the user states the problem, the computer solves it.
Eurgene C. Freuder, 1997
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21. Summary
An emergent software technology with strong theoretical foundation and widespread commercial interest
Identified in 1997 by ACM as one of the strategic directions in computing research
Read the success stories of 4C in the course page
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22. Mystery Shoppers Problem
Details of the problem available at the course homepage
A well-known cosmetic company wants to evaluate the performance of her 35 salesladies, who station at the company's counters at 19 department stores in 4 different geographical regions. For this purpose, the company has hired 40 secret agents of different categories (age, professions, etc) to disguise as shoppers to visit the salesladies. Each shopper has to visit 3 to 4 salesladies and each saleslady has to be visited by 4 shoppers. Two of these visits must be in the first two weeks. The visits must be scheduled in such a way that each saleslady must be visited by shoppers of different varieties, and that shoppers should visit salesladies in different geographic regions. The assessment period is 4 weeks.
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23. Acknowledgement
With the consent of Roman Bartak, I have shamelessly adopted and adapted a number of slides produced by him for use in this presentation
I am solely responsible, however, for any errors therein
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