constraint-programming

What it does

Instructs the agent to solve complex combinatorial problems (scheduling, allocation, sequencing, assignment) using constraint programming, leveraging propagation, global constraints, and intelligent search strategies. It focuses on problems where MIP struggles or where logical constraints are prominent, and it provides two example domains: Job Shop Scheduling and Nurse Scheduling with CP.

How it works

The skill begins with an initial assessment rubric for understanding the problem characteristics, purpose of constraint programming, problem size, and the technical environment. It then outlines core CP concepts: Variables with discrete domains, Constraints, Propagation, and Search. It provides an explicit implementation example for Job Shop Scheduling using OR-Tools CP-SAT, including model construction (variables for starts, ends, and intervals; precedence and disjunctive constraints; makespan objective), solving (CpSolver with time limit and workers), and optional Gantt plotting. It then presents a second CP example for Nurse Scheduling with global constraints, defining boolean decision variables per nurse/day/shift, and constraints for coverage, single shift per day, rest periods, fair distribution, and weekend/off constraints. The skill shows how to encode the problem and obtain a solution, including feasible/optimal statuses and extracted schedules.

When to use it

Use when the user describes scheduling or allocation problems with complex or logical constraints, disjunctive resources, or all-different/global constraints, or when CP-SAT is appropriate and MIP is insufficient. Trigger keywords include constraint programming, CP-SAT, constraint satisfaction, all-different constraint, global constraints, propagation, search strategies, or complex logical constraints.

What it can touch

The skill relies on explicit code blocks and uses theOR-Tools CP-SAT solver (imported as from ortools.sat.python import cp_model). It creates and manipulates variables, constraints, and objective functions, and can generate a schedule (list of job/operation/machine/start/end/duration) and a Gantt plot. It references plotting utilities (matplotlib) for visualization in the Job Shop example and uses standard Python data structures for schedules.

Caveats

License: MIT. The skill demonstrates example usage and may require adapting to specific problem instances and environment constraints (solver availability, time limits, and performance considerations). It uses a heuristic with a fixed number of search workers and a time limit, which may affect optimality depending on instance hardness. It includes domain-specific assumptions (e.g., horizon computation, machine indexing) that must align with user data.