MCP Solver: Crush Constraints, Scale Solutions Effortlessly

MCP Solver

A Model Context Protocol (MCP) server that exposes MiniZinc constraint solving capabilities to Large Language Models.

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Overview

The MCP Solver integrates MiniZinc constraint programming with LLMs through the Model Context Protocol, enabling AI models to:

• Create, edit, and validate constraint models
• Execute constraint solving operations
• Access and update solution knowledge
• Manage solver insights through a memo system

For a detailed description of the system architecture and theoretical foundations, see the accompanying research paper: Stefan Szeider, "MCP-Solver: Integrating Language Models with Constraint Programming Systems", arXiv:2501.00539, 2024.

Feedback

You can provide feedback to the author via this form.

Features

• Finite domain and global constraint support
• Asynchronous solving with configurable timeouts
• Item-based model editing
• Solution state management
• Knowledge base maintenance

Available Tools

Model modification has transitioned in this version from a line-based to an item-based editing approach, which improves robustness by validating each item independently. Each model modification operation returns the current model with numbered items in truncated form, ensuring consistent tracking of items and their indices. Line-based editing remains for handling the memo.

Tool Name	Description
get_model	Get current model content with numbered items
add_item	Add new item at specific index
delete_item	Delete item at index
replace_item	Replace item at index
clear_model	Clear all items in the model
solve_model	Solve the model with the Chuffed constraint solver
get_solution	Get specific variable value from solution with optional array indices
get_solve_time	Get last solve execution time
get_memo	Get current knowledge base
edit_memo	Edit knowledge base

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System Requirements

• Python 3.11+
  (Note: Python 3.11 is required to support the use of asyncio.timeout in the solver code.)
• MiniZinc with the Chuffed solver
• Operating systems:
  • macOS
  • Windows
  • Linux (with appropriate adaptations)

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Installation

1. Install an MCP-compatible client (e.g., Claude web interface or desktop app)

2. Install the MCP Solver:

   git clone https://github.com/szeider/mcp-solver.git

cd mcp-solver
uv pip install -e .

3. Create the configuration file:

For macOS/Linux:

Create the configuration file at:

    ~/Library/Application/Support/Claude/claude_desktop_config.json

Add the following content:

    {
  "mcpServers": {
    "MCP Solver": {
      "command": "uv",
      "args": [
        "--directory", 
        "/absolute/path/to/mcp-solver",  // Use full path to mcp-solver directory
        "run", 
        "mcp-solver"
      ]
    }
  }
}

For Windows:

Create the configuration file at:

    %APPDATA%\Claude\claude_desktop_config.json

Add the following content:

    {
  "mcpServers": {
    "MCP Solver": {
      "command": "cmd.exe",
      "args": [
        "/C",
        "cd C:\\absolute\\path\\to\\mcp-solver && uv run mcp-solver"
      ]
    }
  }
}

4. The memo file location defaults to the standard configuration directory for your operating system. The default can be overridden in pyproject.toml.

5. The setup can be tested with:

   uv run test-setup

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Lite Mode

The MCP Solver also supports a Lite Mode , which provides a streamlined interface with only the essential tools. In Lite Mode, the available tools are limited to:

• clear_model
• add_item
• replace_item
• delete_item
• solve_model
• get_model

In this mode:

• solve_model returns the status of the solution—if the model is satisfiable (SAT), it also returns the solution; otherwise, only the status (UNSAT or TIMEOUT) is provided.
• The instructions prompt is loaded from instructions_prompt_lite.md instead of the full instructions_prompt.md.

To run the MCP Solver in Lite Mode, add the --lite flag to your command. For example, update your configuration file as follows (similar for Windows):

{
  "mcpServers": {
    "MCP Solver": {
      "command": "uv",
      "args": [
        "--directory",
        "/absolute/path/to/mcp-solver",
        "run",
        "mcp-solver",
        "--lite"
      ]
    }
  }
}

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Examples

Casting

This is based on an example by George Johnson (NYT, July 13, 1999).

User

Suppose that a theatrical director feels obligated to cast either his ingenue, Actress Alvarez, or his nephew, Actor Cohen, in a production. But Miss Alvarez won't be in a play with Mr. Cohen (her former lover), and she demands that the cast include her new flame, Actor Davenport. The producer, with her own favors to repay, insists that Actor Branislavsky have a part. But Mr. Branislavsky won't be in any play with Miss Alvarez or Mr. Davenport. Can the director cast the play?

LLM

Let me model this casting problem using MiniZinc. We'll use boolean variables to represent whether each actor is cast.

System: clear_model

Model cleared

System: add_item (multiple)

var bool: alvarez;
var bool: cohen;
var bool: branislavsky;
var bool: davenport;
constraint alvarez \/ cohen;                          % Must cast either Alvarez or Cohen
constraint not (alvarez /\ cohen);                    % Alvarez won't work with Cohen
constraint alvarez -> davenport;                      % If Alvarez is cast, Davenport must be cast
constraint branislavsky;                              % Branislavsky must be cast
constraint not (branislavsky /\ alvarez);             % Branislavsky won't work with Alvarez
constraint not (branislavsky /\ davenport);           % Branislavsky won't work with Davenport
solve satisfy;

System: solve_model

{'status': 'SAT', 'solution': Solution(alvarez=False, cohen=True, branislavsky=True, davenport=False, _checker=''), 'solve_time': 0.0}

LLM

The problem has a solution: cast Cohen and Branislavsky, but not Alvarez or Davenport. Let's verify:

1. Either Alvarez or Cohen must be cast ✓ (Cohen is cast)
2. Alvarez and Cohen can't both be cast ✓ (only Cohen is cast)
3. If Alvarez is cast, Davenport must be cast ✓ (Alvarez isn't cast)
4. Branislavsky must be cast ✓ (Branislavsky is cast)
5. Branislavsky won't work with Alvarez ✓ (Alvarez isn't cast)
6. Branislavsky won't work with Davenport ✓ (Davenport isn't cast)

The director can cast the play with Cohen and Branislavsky.

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N-Queens

This example shows how the same model can be solved with different parameter values, and the solving times can be obtained.

User

Check whether you can place n Queens on an nxn chessboard. Try n=10,20,30,40 and compare the solving times

LLM

Let me create a model for the N-Queens problem and test different sizes.

System: clear_model

Model cleared

System: add_item (multiple)

int: n = 10;
array[1..n] of var 1..n: queens;
constraint alldifferent(queens);
constraint alldifferent([queens[i] + i | i in 1..n]);
constraint alldifferent([queens[i] - i | i in 1..n]);
solve satisfy;

LLM

Testing n=10:

System: solve_model

{'status': 'SAT', 'solution': Solution(queens=[3, 6, 9, 1, 8, 4, 2, 7, 5, 10], _checker=''), 'solve_time': 0.001}

LLM

Testing n=20:

System: edit_model

int: n = 20;

System: solve_model

{'status': 'SAT', 'solution': Solution(queens=[4, 18, 16, 11, 13, 1, 3, 19, 8, 12, 17, 2, 10, 15, 6, 14, 9, 7, 5, 20], _checker=''), 'solve_time': 0.005}

LLM

Testing n=30:

System: edit_model

int: n = 30;

System: solve_model

{'status': 'SAT', 'solution': Solution(queens=[17, 23, 9, 18, 2, 13, 8, 1, 24, 21, 6, 22, 11, 26, 5, 25, 19, 14, 10, 3, 29, 27, 15, 4, 12, 20, 16, 7, 28, 30], _checker=''), 'solve_time': 0.04}

LLM

Testing n=40:

System: edit_model

int: n = 40;

System: solve_model

{'status': 'SAT', 'solution': Solution(queens=[12, 34, 23, 8, 20, 31, 15, 27, 18, 33, 5, 2, 26, 10, 16, 32, 4, 11, 14, 3, 9, 25, 28, 30, 35, 6, 1, 17, 21, 37, 13, 29, 24, 19, 7, 22, 39, 36, 38, 40], _checker=''), 'solve_time': 0.043}

LLM

Solve times comparison: n=10: 0.001s n=20: 0.005s n=30: 0.040s n=40: 0.043s

Solutions exist for all tested board sizes. Time complexity increases non-linearly but remains manageable up to n=40.

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TSP

User

A saleswoman based in Vienna needs to plan her upcoming tour through Austria, visiting each province capital once. Help find the shortest route. Distances in km: 1=Vienna, 2=St. Pölten, 3=Eisenstadt, 4=Linz, 5=Graz, 6=Klagenfurt, 7=Salzburg, 8=Innsbruck, 9=Bregenz

| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9
---|---|---|---|---|---|---|---|---|---
1 | 0 | 65 | 60 | 184 | 195 | 319 | 299 | 478 | 631
2 | 65 | 0 | 125 | 119 | 130 | 254 | 234 | 413 | 566
3 | 60 | 125 | 0 | 184 | 157 | 281 | 261 | 440 | 593
4 | 184 | 119 | 184 | 0 | 208 | 252 | 136 | 315 | 468
5 | 195 | 130 | 157 | 208 | 0 | 136 | 280 | 459 | 629
6 | 319 | 254 | 281 | 252 | 136 | 0 | 217 | 391 | 566
7 | 299 | 234 | 261 | 136 | 280 | 217 | 0 | 188 | 343
8 | 478 | 413 | 440 | 315 | 459 | 391 | 188 | 0 | 157
9 | 631 | 566 | 593 | 468 | 629 | 566 | 343 | 157 | 0

LLM

I'll model this as a Traveling Salesperson Problem using a circuit constraint.

System: add_item (multiple)

include "globals.mzn";
int: n = 9;
array[1..n,1..n] of int: dist = [|0,65,60,184,195,319,299,478,631|65,0,125,119,130,254,234,413,566|60,125,0,184,157,281,261,440,593|184,119,184,0,208,252,136,315,468|195,130,157,208,0,136,280,459,629|319,254,281,252,136,0,217,391,566|299,234,261,136,280,217,0,188,343|478,413,440,315,459,391,188,0,157|631,566,593,468,629,566,343,157,0|];
array[1..n] of var 1..n: succ;
var int: total_dist = sum(i in 1..n)(dist[i,succ[i]]);
constraint circuit(succ);
solve minimize total_dist;

System: solve_model

{'status': 'SAT', 'solution': Solution(objective=1564, succ=[2, 4, 1, 7, 3, 5, 9, 6, 8], _checker=''), 'solve_time': 0.002}

LLM

Optimal route found: Vienna → St. Pölten → Linz → Salzburg → Bregenz → Innsbruck → Klagenfurt → Graz → Eisenstadt → Vienna

Total distance: 1,564 km

Route verification:

• Each city visited exactly once: ✓ (circuit constraint)
• Distance calculation correct: ✓
• Starting/ending in Vienna (city 1): ✓

User

Assume the road between Vienna and Eisenstadt is blocked, what is now the shortest tour?

LLM

I'll modify the distance matrix to make the Vienna-Eisenstadt route impossible (infinite distance).

System: add_item

array[1..n,1..n] of int: dist = [|0,65,9999,184,195,319,299,478,631|65,0,125,119,130,254,234,413,566|9999,125,0,184,157,281,261,440,593|184,119,184,0,208,252,136,315,468|195,130,157,208,0,136,280,459,629|319,254,281,252,136,0,217,391,566|299,234,261,136,280,217,0,188,343|478,413,440,315,459,391,188,0,157|631,566,593,468,629,566,343,157,0|];

System: solve_model

{'status': 'SAT', 'solution': Solution(objective=1694, succ=[4, 1, 2, 7, 3, 5, 9, 6, 8], _checker=''), 'solve_time': 0.003}

LLM

Optimal route: Vienna → Linz → St. Pölten → Salzburg → Bregenz → Innsbruck → Klagenfurt → Graz → Eisenstadt → Vienna

Total distance: 1,694 km (+130 km compared to unblocked route)

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Disclaimer

This MCP Solver is in its prototype stage and should be used with caution. Users are encouraged to experiment, but any use in critical environments is at their own risk.

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Changelog

See the CHANGELOG.md for details on version history and changes.

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License

This project is licensed under the MIT License - see the LICENSE file for details.

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