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USolver

A best-effort universal logic and numerical solver interface using MCP. Implements the "LLM sandwich" model where a query is interpreted by the LLM, calls out to a dedicated efficient solver fit for the problem, and then verbalizes the result. And the solver solutions can be chained together to solve more complex problems that require multi-step approaches.

Exposes minimal solvers for the following software packages:

• ortools - Combinatorial optimization solver
• cvxpy - Convex optimization solver
• z3 - SMT solver over booleans, integers, reals, and strings

To install run the install.py script. This will install the MPC server for Claude Desktop and/or Cursor.

uv run install.py

Examples

To run the individual solver examples. You can invoke the individual examples. Below are example prompts that you can feed to the language model for these specific problems.

uv run examples/example_z3.py
uv run examples/example_cvxpy.py
uv run examples/example_ortools.py
uv run examples/example_z3_simple.py

Z3

A chemical engineering example:

Use usolver to design a water transport pipeline with the following requirements:

* Volumetric flow rate: 0.05 m³/s
* Pipe length: 100 m
* Water density: 1000 kg/m³
* Maximum allowable pressure drop: 50 kPa
* Flow continuity: Q = π(D/2)² × v
* Pressure drop: ΔP = f(L/D)(ρv²/2), where f ≈ 0.02 for turbulent flow
* Practical limits: 0.05 ≤ D ≤ 0.5 m, 0.5 ≤ v ≤ 8 m/s
* Pressure constraint: ΔP ≤ 50,000 Pa
* Find: optimal pipe diameter and flow velocity

CVXPY

A simple convex optimization problem minimizing the 2-norm of a linear system:

Use usolver to solve the following convex optimization problem:

Minimize: ||Ax - b||₂²
Subject to: 0 ≤ x ≤ 1
where 
  A = [1.0, -0.5; 0.5, 2.0; 0.0, 1.0] 
  b = [2.0, 1.0, -1.0]

OR-Tools

A classic worker shift scheduling problem:

Use usolver to solve a nurse scheduling problem with the following requirements:

* Schedule 4 nurses (Alice, Bob, Charlie, Diana) across 3 shifts over (Monday, Tuesday, Wednesday)
* Shifts: Morning (7AM-3PM), Evening (3PM-11PM), Night (11PM-7AM)
* Each shift must be assigned to exactly one nurse each day
* Each nurse works at most one shift per day
* Distribute shifts evenly (2-3 shifts per nurse over the period)
* Charlie can't work on Tuesday.

Chained Examples

A chained example that uses both OR-Tools to optimize for table layout and CVXPY to optimize for staff scheduling.

Use usolver to optimize a restaurant's layout and staffing with the following requirements in two parts. Use combinatorial optimization to optimize for table layout and convex optimization to optimize for staff scheduling.

* Part 1: Optimize table layout
  - Mix of 2-seater, 4-seater, and 6-seater tables
  - Maximum floor space: 150 m²
  - Space requirements: 4m² (2-seater), 6m² (4-seater), 9m² (6-seater)
  - Maximum 20 tables total
  - Minimum mix: 2× 2-seaters, 3× 4-seaters, 1× 6-seater
  - Objective: Maximize total seating capacity

* Part 2: Optimize staff scheduling using Part 1's capacity
  - 12-hour operating day
  - Each staff member can handle 20 seats
  - Minimum 2 staff per hour
  - Maximum staff change between hours: 2 people
  - Variable demand: 40%-100% of capacity
  - Objective: Minimize labor cost ($25/hour per staff)