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# Constraint Programming

### Overview

Today more than ever, the optimal use of resources has become a very important issue. Many decision problems (logistics, production, space, etc.) aiming at an optimal use of resources can be formulated as constraint combinatorial optimization problems. Unfortunately, these problems are difficult to solve mainly for two reasons :

1. They require complex algorithms to design and develop,
2. Finding an optimal solution can be computationally intensive.

In this course, we will learn the basics of constraint programming: a paradigm that aims to reduce the cost of developing and solving combinatorial problems through extensive reuse of code, whose design is open-ended, but also through pruning techniques of the search space by reasoning at the level of constraints.

During the proposed projects, you will develop your own constraint programming solver in Java that we will gradually extend in functionality in order to solve more and more complex combinatorial problems, especially in scheduling and vehicle routing. You will also develop global constraints, implement search strategies, model problems, and measure the impact of modeling choices on the efficiency of the solution.

Each module first introduces the concepts through videos, then a programming project is proposed to put these concepts into practice.

### Syllabus

Module 1: From Backtracking Search to the Constraint Programming Paradigm
Starting from a custom backtracking search algorithm for the N-Queens Problem, we will make the approach gradually more generic until the introduction of a purely declarative approach and the design a first tiny CP library.

Module 2: Introduction to Mini-CP
The design and internals (variables, domains, state restoration, etc.) of Mini-CP, the constraint programming library that is used along the course and that is extended in each assignment.

Module 3: The sum and element global constraints
Two constraints that occur for solving most of the CP problems. Design of their filtering algorithms, study of their properties and implementation.

Module 4: The extensional table constraint
Introduction to the table constraint, the most generic one can imagine in CP. Study of some of its application, and filtering algorithms for this constraint.

Module 5: The alldifferent constraint
Study of the alldifferent global constraint as an illustration of an elegant reuse of well-known graph algorithms embedded into the filtering of constraints.

Module 6: The Circuit constraint and Vehicle Routing Problems (VRP)
Introduction to solving VRP with CP using the successor model and the circuit global constraint. Introduction to solving optimization problems with CP and Large Neighborhood search.

Module 7: Cumulative Scheduling Problems
Introduction to Scheduling with CP and the cumulative constraint, instrumental for scheduling non preemptive tasks with resource requirements.

Module 8: Disjunctive Scheduling Problems
A specific case of scheduling problems is the one of disjunctive resource where activities cannot overlap in time. We will study specific filtering and search techniques and apply it to solve the well kownknown job-shop problem.

Module 9: Blackbox Search
Introduction to efficient search heuristics independent of the problem to solve. All these searches are declinations of the well-known first-fail principle.

Module 10: Modeling
Introduction to advanced modeling techniques to boost the solving of your problems, including redundant constraints, and symmetry breaking.

### Taught by

Pierre Schaus, Laurent Michel and Pascal Van Hentenryck

## Reviews

5.0 rating, based on 1 Class Central review

Start your review of Constraint Programming

• Ilya Kudryavtsev
Great intro to the modern CSP! Using the project-based approach makes sense. You start with the CSP solver implemented in Java and improve it every week.

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