gurddy-mcp 0.1.6

MCP (Model Context Protocol) server for Gurddy optimization library - CSP, LP, and SciPy integration for advanced optimization

Gurddy MCP Server

A comprehensive Model Context Protocol (MCP) server for solving Constraint Satisfaction Problems (CSP), Linear Programming (LP), Minimax optimization, and SciPy-powered advanced optimization problems. Built on the gurddy optimization library with SciPy integration, it supports solving various classic problems through two MCP transports: stdio (for IDE integration) and HTTP/SSE (for web clients).

🚀 Quick Start (Stdio): pip install gurddy_mcp then configure in your IDE

🌐 Quick Start (HTTP): docker run -p 8080:8080 gurddy-mcp or see deployment guide

📦 PyPI Package: https://pypi.org/project/gurddy_mcp

Main Features

🎯 CSP Problem Solving

• N-Queens Problem: Place N queens on an N×N chessboard with no attacks
• Graph Coloring: Assign colors to vertices so adjacent vertices differ
• Map Coloring: Color geographic regions with adjacent regions differing
• Sudoku Solver: Solve standard 9×9 Sudoku puzzles
• Logic Puzzles: Einstein's Zebra puzzle and custom logic problems
• Scheduling: Course scheduling, meeting scheduling, resource allocation
• General CSP Solver: Support for custom constraint satisfaction problems

📊 LP/Optimization Problems

• Linear Programming: Continuous variable optimization with linear constraints
• Mixed Integer Programming: Optimization with integer and continuous variables
• Production Planning: Resource-constrained production optimization with sensitivity analysis
• Portfolio Optimization: Investment allocation under risk constraints
• Transportation Problems: Supply chain and logistics optimization

🎮 Minimax/Game Theory

• Zero-Sum Games: Solve two-player games (Rock-Paper-Scissors, Matching Pennies, Battle of Sexes)
• Mixed Strategy Nash Equilibria: Find optimal probabilistic strategies
• Robust Optimization: Minimize worst-case loss under uncertainty
• Maximin Decisions: Maximize worst-case gain (conservative strategies)
• Security Games: Defender-attacker resource allocation
• Robust Portfolio: Minimize maximum loss across market scenarios
• Production Planning: Conservative production decisions (maximize minimum profit)
• Advertising Competition: Market share games and competitive strategies

🔬 SciPy Integration

• Nonlinear Portfolio Optimization: Quadratic risk models with SciPy optimization
• Statistical Parameter Estimation: Distribution fitting with constraints (MLE, quantile matching)
• Signal Processing Optimization: FIR filter design with frequency response optimization
• Hybrid CSP-SciPy: Discrete facility selection + continuous capacity optimization
• Numerical Integration: Optimization problems involving integrals and complex functions

🧮 Classic Math Problems

• 24-Point Game: Find arithmetic expressions to reach 24 using four numbers
• Chicken-Rabbit Problem: Classic constraint problem with heads and legs
• Mini Sudoku: 4×4 Sudoku solver using CSP techniques
• 4-Queens Problem: Simplified N-Queens for educational purposes
• 0-1 Knapsack: Classic optimization problem with weight and value constraints

🔌 MCP Protocol Support

• Stdio Transport: Local IDE integration (Kiro, Claude Desktop, Cline, etc.)
• HTTP/SSE Transport: Web clients and remote access
• Unified Interface: Same tools across both transports
• JSON-RPC 2.0: Full protocol compliance
• Auto-approval: Configure trusted tools for seamless execution

Installation

From PyPI (Recommended)

# Install the latest stable version
pip install gurddy_mcp

# Or install with development dependencies
pip install gurddy_mcp[dev]

From Source

# Clone the repository
git clone https://github.com/novvoo/gurddy-mcp.git
cd gurddy-mcp

# Install in development mode
pip install -e .

Verify Installation

# Test MCP stdio server
echo '{"jsonrpc":"2.0","id":1,"method":"tools/list","params":{}}' | gurddy-mcp

Usage

1. MCP Stdio Server (Primary Interface)

The main gurddy-mcp command is an MCP stdio server that can be integrated with tools like Kiro.

Option A: Using uvx (Recommended - Always Latest Version)

Using uvx ensures you always run the latest published version without manual installation.

Configure in ~/.kiro/settings/mcp.json or .kiro/settings/mcp.json:

Recommended: Explicit latest version

{
  "mcpServers": {
    "gurddy": {
      "command": "uvx",
      "args": ["gurddy-mcp@latest"],
      "env": {},
      "disabled": false,
      "autoApprove": [
        "run_example",
        "info",
        "install",
        "solve_n_queens",
        "solve_sudoku",
        "solve_graph_coloring",
        "solve_map_coloring",
        "solve_lp",
        "solve_production_planning",
        "solve_minimax_game",
        "solve_minimax_decision"
      ]
    }
  }
}

Alternative: Without version specifier (also uses latest)

{
  "mcpServers": {
    "gurddy": {
      "command": "uvx",
      "args": ["gurddy-mcp"],
      "env": {},
      "disabled": false,
      "autoApprove": [
        "run_example", "info", "install", "solve_n_queens", "solve_sudoku", 
        "solve_graph_coloring", "solve_map_coloring", "solve_lp", 
        "solve_production_planning", "solve_minimax_game", "solve_minimax_decision"
      ]
    }
  }
}

Pin to specific version (if needed)

{
  "mcpServers": {
    "gurddy": {
      "command": "uvx",
      "args": ["gurddy-mcp==0.1.6"],
      "env": {},
      "disabled": false,
      "autoApprove": [
        "run_example", "info", "install", "solve_n_queens", "solve_sudoku", 
        "solve_graph_coloring", "solve_map_coloring", "solve_lp", 
        "solve_production_planning", "solve_minimax_game", "solve_minimax_decision"
      ]
    }
  }
}

Why use uvx?

• ✅ Always runs the latest published version automatically
• ✅ No manual installation or upgrade needed
• ✅ Isolated environment per execution
• ✅ No dependency conflicts with your system Python

Prerequisites: Install uv first:

# macOS/Linux
curl -LsSf https://astral.sh/uv/install.sh | sh

# Or using pip
pip install uv

# Or using Homebrew (macOS)
brew install uv

Option B: Using Direct Command (After Installation)

If you've already installed gurddy-mcp via pip:

{
  "mcpServers": {
    "gurddy": {
      "command": "gurddy-mcp",
      "args": [],
      "env": {},
      "disabled": false,
      "autoApprove": [
        "run_example", "info", "install", "solve_n_queens", "solve_sudoku", 
        "solve_graph_coloring", "solve_map_coloring", "solve_lp", 
        "solve_production_planning", "solve_minimax_game", "solve_minimax_decision"
      ]
    }
  }
}

Available MCP tools (13 total):

• info - Get gurddy MCP server information and capabilities
• install - Install or upgrade the gurddy package
• run_example - Run example programs (n_queens, graph_coloring, minimax, scipy_optimization, classic_problems, etc.)
• solve_n_queens - Solve N-Queens problem for any board size
• solve_sudoku - Solve 9×9 Sudoku puzzles using CSP
• solve_graph_coloring - Solve graph coloring with configurable colors
• solve_map_coloring - Solve map coloring problems (e.g., Australia, USA)
• solve_lp - Solve Linear Programming (LP) or Mixed Integer Programming (MIP)
• solve_production_planning - Production optimization with optional sensitivity analysis
• solve_minimax_game - Two-player zero-sum games (find Nash equilibria)
• solve_minimax_decision - Robust optimization (minimize max loss or maximize min gain)

Test the MCP server:

# Test initialization
echo '{"jsonrpc":"2.0","id":1,"method":"initialize","params":{"protocolVersion":"2024-11-05","capabilities":{},"clientInfo":{"name":"test","version":"1.0"}}}' | gurddy-mcp

# Test listing tools
echo '{"jsonrpc":"2.0","id":2,"method":"tools/list","params":{}}' | gurddy-mcp

2. MCP HTTP Server

Start the HTTP MCP server (MCP protocol over HTTP/SSE):

Local Development:

uvicorn mcp_server.mcp_http_server:app --host 127.0.0.1 --port 8080

Docker:

# Build the image
docker build -t gurddy-mcp .

# Run the container
docker run -p 8080:8080 gurddy-mcp

Access the server:

• Root: http://127.0.0.1:8080/
• Health check: http://127.0.0.1:8080/health
• SSE endpoint: http://127.0.0.1:8080/sse
• Message endpoint: http://127.0.0.1:8080/message (POST)

Test the HTTP MCP server:

# List available tools
curl -X POST http://127.0.0.1:8080/message \
  -H "Content-Type: application/json" \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/list","params":{}}'

# Call a tool
curl -X POST http://127.0.0.1:8080/message \
  -H "Content-Type: application/json" \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"info","arguments":{}}}'

Python Client Example: See examples/http_mcp_client.py for a complete example of how to interact with the HTTP MCP server.

MCP Tools

The server provides the following MCP tools:

info

Get information about the gurddy package.

{
  "name": "info",
  "arguments": {}
}

install

Install or upgrade the gurddy package.

{
  "name": "install",
  "arguments": {
    "package": "gurddy",
    "upgrade": false
  }
}

run_example

Run a gurddy example.

{
  "name": "run_example",
  "arguments": {
    "example": "n_queens"
  }
}

Available examples: lp, csp, n_queens, graph_coloring, map_coloring, scheduling, logic_puzzles, optimized_csp, optimized_lp, minimax, scipy_optimization, classic_problems

solve_n_queens

Solve the N-Queens problem.

{
  "name": "solve_n_queens",
  "arguments": {
    "n": 8
  }
}

solve_sudoku

Solve a 9x9 Sudoku puzzle.

{
  "name": "solve_sudoku",
  "arguments": {
    "puzzle": [[5,3,0,...], [6,0,0,...], ...]
  }
}

solve_graph_coloring

Solve graph coloring problem.

{
  "name": "solve_graph_coloring",
  "arguments": {
    "edges": [[0,1], [1,2], [2,0]],
    "num_vertices": 3,
    "max_colors": 3
  }
}

solve_map_coloring

Solve map coloring problem.

{
  "name": "solve_map_coloring",
  "arguments": {
    "regions": ["A", "B", "C"],
    "adjacencies": [["A", "B"], ["B", "C"]],
    "max_colors": 2
  }
}

solve_lp

Solve a Linear Programming (LP) or Mixed Integer Programming (MIP) problem using PuLP.

{
  "name": "solve_lp",
  "arguments": {
    "profits": {
      "ProductA": 30,
      "ProductB": 40
    },
    "consumption": {
      "ProductA": {"Labor": 2, "Material": 3},
      "ProductB": {"Labor": 3, "Material": 2}
    },
    "capacities": {
      "Labor": 100,
      "Material": 120
    },
    "integer": true
  }
}

solve_production_planning

Solve a production planning optimization problem with optional sensitivity analysis.

{
  "name": "solve_production_planning",
  "arguments": {
    "profits": {
      "ProductA": 30,
      "ProductB": 40
    },
    "consumption": {
      "ProductA": {"Labor": 2, "Material": 3},
      "ProductB": {"Labor": 3, "Material": 2}
    },
    "capacities": {
      "Labor": 100,
      "Material": 120
    },
    "integer": true,
    "sensitivity_analysis": false
  }
}

solve_minimax_game

Solve a two-player zero-sum game using minimax (game theory).

{
  "name": "solve_minimax_game",
  "arguments": {
    "payoff_matrix": [
      [0, -1, 1],
      [1, 0, -1],
      [-1, 1, 0]
    ],
    "player": "row"
  }
}

Returns the optimal mixed strategy and game value for the specified player.

solve_minimax_decision

Solve a minimax decision problem under uncertainty (robust optimization).

{
  "name": "solve_minimax_decision",
  "arguments": {
    "scenarios": [
      {"A": -0.2, "B": -0.1, "C": 0.05},
      {"A": 0.3, "B": 0.2, "C": -0.02},
      {"A": 0.05, "B": 0.03, "C": -0.01}
    ],
    "decision_vars": ["A", "B", "C"],
    "budget": 100.0,
    "objective": "minimize_max_loss"
  }
}

Objectives: minimize_max_loss (robust portfolio) or maximize_min_gain (conservative production)

Docker Deployment

Build and Run

# Build the image
docker build -t gurddy-mcp .

# Run the container
docker run -p 8080:8080 gurddy-mcp

# Or with environment variables
docker run -p 8080:8080 -e PORT=8080 gurddy-mcp

Docker Compose

version: '3.8'
services:
  gurddy-mcp:
    build: .
    ports:
      - "8080:8080"
    environment:
      - PYTHONUNBUFFERED=1
    restart: unless-stopped

Example Output

N-Queens Problem

POST /solve-n-queens
{
"n": 8
}

Project Structure

mcp_server/
├── handlers/
│   └── gurddy.py           # Core solver implementation
├── tools/                  # MCP tool wrappers
├── examples/               # Rich Problem Examples
│   ├── n_queens.py         # N-Queens Problem
│   ├── graph_coloring.py   # Graph Coloring Problem
│   ├── map_coloring.py     # Map Coloring Problem
│   ├── logic_puzzles.py    # Logic Puzzles
│   ├── scheduling.py       # Scheduling Problem
│   ├── scipy_optimization.py # SciPy Integration Examples
│   └── classic_problems.py # Classic Math Problems
├── mcp_stdio_server.py     # MCP Stdio Server (for IDE integration)
└── mcp_http_server.py      # MCP HTTP Server (for web clients)

examples/
└── http_mcp_client.py      # Example HTTP MCP client

Dockerfile                  # Docker configuration for HTTP server

MCP Transports

Transport	Command	Protocol	Use Case
Stdio	gurddy-mcp	MCP over stdin/stdout	IDE integration (Kiro, Claude Desktop, etc.)
HTTP	uvicorn mcp_server.mcp_http_server:app	MCP over HTTP/SSE	Web clients, remote access, Docker deployment

Both transports implement the same MCP protocol and provide identical tools.

Example Output

N-Queens Problem

$ gurddy-mcp-cli run-example n_queens

Solving 8-Queens problem...

8-Queens Solution:
+---+---+---+---+---+---+---+---+
| Q |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
|   |   |   |   | Q |   |   |   |
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   | Q |
+---+---+---+---+---+---+---+---+
|   |   |   |   |   | Q |   |   |
+---+---+---+---+---+---+---+---+
|   |   | Q |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   | Q |   |
+---+---+---+---+---+---+---+---+
|   | Q |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+
|   |   |   | Q |   |   |   |   |
+---+---+---+---+---+---+---+---+
Queen positions: (0,0), (1,4), (2,7), (3,5), (4,2), (5,6), (6,1), (7,3)

Logic Puzzles

$ python -m mcp_server.server run-example logic_puzzles

Solving Simple Logic Puzzle:
Solution:
Position 1: Alice has Cat in Green house
Position 2: Bob has Dog in Red house  
Position 3: Carol has Fish in Blue house

Solving the Famous Zebra Puzzle (Einstein's Riddle)...
ANSWERS:
Who owns the zebra? Ukrainian (House 5)
Who drinks water? Japanese (House 2)

HTTP API Examples

Classic Problem Solving

Australian Map Coloring

import requests

response = requests.post("http://127.0.0.1:8080/solve-map-coloring", json={ 
"regions": ['WA', 'NT', 'SA', 'QLD', 'NSW', 'VIC', 'TAS'], 
"adjacencies": [ 
['WA', 'NT'], ['WA', 'SA'], ['NT', 'SA'], ['NT', 'QLD'], 
['SA', 'QLD'], ['SA', 'NSW'], ['SA', 'VIC'], 
['QLD', 'NSW'], ['NSW', 'VIC'] 
], 
"max_colors": 4
})

8-Queens Problem

response = requests.post("http://127.0.0.1:8080/solve-n-queens",
json={"n": 8})

Available Examples

All examples can be run using gurddy-mcp run-example <name> or python -m mcp_server.server run-example <name>:

CSP Examples ✅

• n_queens - N-Queens problem (4, 6, 8 queens with visual board display)
• graph_coloring - Graph coloring (Triangle, Square, Petersen graph, Wheel graph)
• map_coloring - Map coloring (Australia, USA Western states, Europe)
• scheduling - Scheduling problems (Course scheduling, meeting scheduling, resource allocation)
• logic_puzzles - Logic puzzles (Simple logic puzzle, Einstein's Zebra puzzle)
• optimized_csp - Advanced CSP techniques (Sudoku solver)

LP Examples ✅

• lp / optimized_lp - Linear programming examples:
  • Portfolio optimization with risk constraints
  • Transportation problem (supply chain optimization)
  • Constraint relaxation analysis
  • Performance comparison across problem sizes

Minimax Examples ✅

• minimax - Minimax optimization and game theory:
  • Rock-Paper-Scissors (zero-sum game)
  • Matching Pennies (coordination game)
  • Battle of the Sexes (mixed strategy equilibrium)
  • Robust portfolio optimization (minimize maximum loss)
  • Production planning (maximize minimum profit)
  • Security resource allocation (defender-attacker game)
  • Advertising competition (market share game)

SciPy Integration Examples ✅

• scipy_optimization - Advanced optimization with SciPy:
  • Nonlinear portfolio optimization with quadratic risk models
  • Statistical parameter estimation (distribution fitting with constraints)
  • Signal processing optimization (FIR filter design)
  • Hybrid CSP-SciPy facility location (discrete + continuous optimization)
  • Numerical integration in optimization objectives

Classic Math Problems ✅

• classic_problems - Educational math problem solving:
  • 24-Point Game (arithmetic expressions to reach 24)
  • Chicken-Rabbit Problem (classic constraint satisfaction)
  • 4×4 Mini Sudoku (simplified CSP demonstration)
  • 4-Queens Problem (educational N-Queens variant)
  • 0-1 Knapsack Problem (classic optimization)

Supported Problem Types

🧩 CSP Problems

• N-Queens: Classic N-Queens problem for any board size (N=4 to N=100+)
• Graph Coloring: Vertex coloring for arbitrary graphs (triangle, Petersen, wheel, etc.)
• Map Coloring: Geographic region coloring (Australia, USA, Europe maps)
• Sudoku: Standard 9×9 Sudoku puzzles with constraint propagation
• Logic Puzzles: Einstein's Zebra puzzle and custom logical reasoning problems
• Scheduling: Course scheduling, meeting rooms, resource allocation with time constraints

📈 Optimization Problems

• Linear Programming: Continuous variable optimization with linear constraints
• Integer Programming: Discrete variable optimization (production quantities, assignments)
• Mixed Integer Programming: Combined continuous and discrete variables
• Production Planning: Multi-product resource-constrained optimization
• Portfolio Optimization: Investment allocation with risk and return constraints
• Transportation: Supply chain optimization (warehouses to customers)

🎲 Game Theory & Robust Optimization

• Zero-Sum Games: Rock-Paper-Scissors, Matching Pennies, Battle of Sexes
• Mixed Strategy Nash Equilibria: Optimal probabilistic strategies for both players
• Minimax Decisions: Minimize worst-case loss across uncertainty scenarios
• Maximin Decisions: Maximize worst-case gain (conservative strategies)
• Robust Portfolio: Minimize maximum loss across market scenarios
• Security Games: Defender-attacker resource allocation problems

🔬 SciPy-Powered Advanced Optimization

• Nonlinear Portfolio Optimization: Quadratic risk models with Sharpe ratio maximization
• Statistical Parameter Estimation: MLE and quantile-based distribution fitting with constraints
• Signal Processing: FIR filter design with frequency response optimization
• Hybrid Optimization: Combine Gurddy CSP with SciPy continuous optimization
• Numerical Integration: Optimization problems involving complex mathematical functions

🧮 Classic Educational Problems

• 24-Point Game: Find arithmetic expressions using four numbers to reach 24
• Chicken-Rabbit Problem: Classic constraint satisfaction with heads and legs
• Mini Sudoku: 4×4 Sudoku solving using CSP techniques
• N-Queens Variants: Educational versions of the classic problem
• Knapsack Problems: 0-1 knapsack optimization with weight and value constraints

Performance Features

• Fast Solution: Millisecond response for small-medium problems (N-Queens N≤12, graphs <50 vertices)
• Scalable: Handles large problems (N-Queens N=100+, LP with 1000+ variables)
• Memory Efficient: Backtracking search and constraint propagation minimize memory usage
• Extensible: Custom constraints, objective functions, and problem types
• Concurrency-Safe: HTTP API supports concurrent request processing
• Production Ready: Docker deployment, health checks, error handling

Performance Benchmarks

Typical execution times on standard hardware:

• CSP Examples: 0.4-0.5s (N-Queens, Graph Coloring, Logic Puzzles)
• LP Examples: 0.8-0.9s (Portfolio, Transportation, Production Planning)
• Minimax Examples: 0.3-0.5s (Game solving, Robust optimization)
• SciPy Examples: 0.5-1.2s (Nonlinear optimization, Statistical fitting)
• Classic Problems: 0.1-0.3s (24-point, Chicken-rabbit, Mini sudoku)
• Sudoku: <0.1s for standard 9×9 puzzles
• Large N-Queens: ~2-3s for N=100

Troubleshooting

Common Errors

• "gurddy package not available": Install with python -m mcp_server.server install
• "No solution found": No solution exists under given constraints; try relaxing constraints
• "Invalid input types": Check the data types of input parameters
• "Unknown example": Use python -m mcp_server.server run-example --help to see available examples

Installation Issues

# install individually
pip install gurddy>=0.1.8 pulp>=2.6.0 scipy>=1.9.0 numpy>=1.21.0

# Check installation
python -c "import gurddy, pulp, scipy, numpy; print('All dependencies installed')"

Example Debugging

Run examples directly for debugging:

# After installing gurddy_mcp
python -c "from mcp_server.examples import n_queens; n_queens.main()"

# Or from source
python mcp_server/examples/n_queens.py
python mcp_server/examples/graph_coloring.py
python mcp_server/examples/logic_puzzles.py
python mcp_server/examples/scipy_optimization.py
python mcp_server/examples/classic_problems.py

SciPy Integration Requirements

The SciPy integration examples require additional dependencies:

# Install SciPy and NumPy 
pip install scipy>=1.9.0 numpy>=1.21.0

# Verify SciPy integration
python -c "import scipy.optimize, numpy; print('SciPy integration ready')"

SciPy Examples Include:

• Nonlinear Portfolio Optimization: Quadratic risk models with Sharpe ratio maximization
• Statistical Parameter Estimation: Distribution fitting with MLE and quantile methods
• Signal Processing: FIR filter design with frequency response optimization
• Hybrid CSP-SciPy: Facility location combining discrete and continuous optimization
• Numerical Integration: Complex optimization problems involving integrals

Extension Development

Adding a New CSP Problem

1. In mcp_server/examples/ Create a problem implementation in mcp_server/handlers/gurddy.py
2. Add the solver function in mcp_server/handlers/gurddy.py
3. Add the API endpoint in mcp_server/mcp_http_server.py

Custom Constraints

# Define a custom constraint in gurddy
def custom_constraint(var1, var2):
return var1 + var2 <= 10

model.addConstraint(gurddy.FunctionConstraint(custom_constraint, (var1, var2)))

License

This project is licensed under an open source license. Please see the LICENSE file for details.