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What is constraint programming?

by Stephen M. Walker II, Co-Founder / CEO

What is constraint programming?

Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. It is a form of declarative programming that uses mathematical constraints to define the rules that must be met. In constraint programming, users declaratively state the constraints on the feasible solutions for a set of decision variables.

This approach is particularly effective for tackling issues such as scheduling, resource allocation, verification, diagnosis, product configuration, and planning. Its versatility has led to successful implementations in diverse areas including operations research, computer graphics, natural language processing, database systems, molecular biology, business applications, electrical engineering, and circuit design.

To solve these constraints, a variety of methods are employed. Standard techniques include chronological backtracking and constraint propagation, but problem-specific branching heuristics and other customized code may also be used. In some cases, constraint programming serves as a heuristic for finding solutions to mixed integer programs.

Users must also specify a method for solving the constraints. While standard methods are often used, customized code can provide a more tailored solution. The roots of constraint programming can be traced back to constraint logic, which integrates constraints into a logic program.

Constraint logic programming, an extended version of logic programming, often incorporates constraint programming. This approach includes literal requirements and comparisons of variables, and extends to include constraints, providing a comprehensive and flexible framework for problem-solving.

What are the benefits of constraint programming?

  1. Intuitive Modeling Language — Constraint programming allows for a more flexible modeling language, which is more intuitive and closer to natural language.

  2. Efficient Search — Constraint programming provides the ability to move flexibly throughout the search space and to backtrack when early choices turn out to be dead ends.

  3. Global Constraints — Constraint programming's idea of global constraints can exploit substructure in the problem, which can significantly speed up the solution process.

  4. Quickly Finds Feasible Solutions — Constraint programming can quickly find feasible solutions, which is particularly useful in multi-model architectures such as column generation.

What are some common applications of constraint programming?

Constraint programming has been successfully applied in a variety of fields:

  1. Scheduling and Resource Allocation — Constraint programming is particularly effective for scheduling and resource allocation problems, including timetabling for hospitals and industry scheduling.

  2. Planning — Constraint programming has been used in planning applications, where constraints can naturally describe the problem.

  3. Verification — Constraint programming has been used in applications to verification, both of circuits and of real-time control systems.

  4. Graphical Interface Design — Constraints are used for graphical interface design and implementation.

What are some common constraint programming algorithms?

Constraint programming uses a variety of algorithms, including:

  1. Constraint Propagation — This is a fundamental technique in constraint programming that reduces the domain of variables based on constraints.

  2. Backtracking Search — This is a common search strategy used in constraint programming, where the algorithm explores the search space and backtracks when it encounters a dead end.

  3. Global Constraints — These are highly structured sets of constraints that can significantly speed up the solution process.

What are some common issues with constraint programming?

Despite its benefits, constraint programming also has some challenges:

  1. Problem Translation — One of the big issues with constraint programming is translating your problem into constraints.

  2. Highly Constrained Problems — While constraint programming is often said to be more effective for "highly-constrained" problems, making a problem highly constrained by placing a tight bound on a cost function can make the problem intractable for constraint programming.

  3. Implementation Technology — There are challenges related to improvements in implementation technology, including the use of global analysis-based optimization and debugging facilities.

  4. Distributed and Network-Wide Programming — Another challenge for constraint programming systems is related to the role of such systems in distributed and network-wide programming.

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