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 streamable HTTP (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.)
• Streamable HTTP Transport: Web clients and remote access with optional streaming
• 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",
        "solve_24_point_game",
        "solve_chicken_rabbit_problem",
        "solve_scipy_portfolio_optimization",
        "solve_scipy_statistical_fitting",
        "solve_scipy_facility_location"
      ]
    }
  }
}

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",
        "solve_24_point_game", "solve_chicken_rabbit_problem", 
        "solve_scipy_portfolio_optimization", "solve_scipy_statistical_fitting", 
        "solve_scipy_facility_location"
      ]
    }
  }
}

Pin to specific version (if needed)

{
  "mcpServers": {
    "gurddy": {
      "command": "uvx",
      "args": ["gurddy-mcp==<VERSION>"],
      "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",
        "solve_24_point_game", "solve_chicken_rabbit_problem", 
        "solve_scipy_portfolio_optimization", "solve_scipy_statistical_fitting", 
        "solve_scipy_facility_location"
      ]
    }
  }
}

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",
        "solve_24_point_game", "solve_chicken_rabbit_problem", 
        "solve_scipy_portfolio_optimization", "solve_scipy_statistical_fitting", 
        "solve_scipy_facility_location"
      ]
    }
  }
}

Available MCP tools (16 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)
• solve_24_point_game - Solve 24-point game with four numbers using arithmetic operations
• solve_chicken_rabbit_problem - Solve classic chicken-rabbit problem with heads and legs constraints
• solve_scipy_portfolio_optimization - Solve nonlinear portfolio optimization using SciPy
• solve_scipy_statistical_fitting - Solve statistical parameter estimation using SciPy
• solve_scipy_facility_location - Solve facility location problem using hybrid CSP-SciPy approach

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

# Test info tools
echo '{"jsonrpc":"2.0","id":10,"method":"tools/call","params":{"name":"info","arguments":{"":""}}}' | gurddy-mcp |jq 

# Test run example tools
echo '{"jsonrpc":"2.0","id":10,"method":"tools/call","params":{"name":"run_example","arguments":{"example":"n_queens"}}}' | gurddy-mcp |jq

# Test sudoku tools
cat <<EOF | tr -d '\n'|gurddy-mcp|jq
{"jsonrpc":"2.0","id":123,"method":"tools/call","params":{
  "name":"solve_sudoku",
  "arguments":{
    "puzzle":[
      [5,3,0,0,7,0,0,0,0],
      [6,0,0,1,9,5,0,0,0],
      [0,9,8,0,0,0,0,6,0],
      [8,0,0,0,6,0,0,0,3],
      [4,0,0,8,0,3,0,0,1],
      [7,0,0,0,2,0,0,0,6],
      [0,6,0,0,0,0,2,8,0],
      [0,0,0,4,1,9,0,0,5],
      [0,0,0,0,8,0,0,7,9]
    ]
  }
}}
EOF

2. MCP HTTP Server

Start the HTTP MCP server (MCP protocol over streamable HTTP):

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
• HTTP transport: http://127.0.0.1:8080/mcp/http (POST - supports both regular and streaming)

Test the HTTP MCP server:

HTTP Transport (non-streaming):

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

HTTP Transport (streaming with Accept header):

# List tools with streaming response
curl -X POST http://127.0.0.1:8080/mcp/http \
  -H "Content-Type: application/json" \
  -H "Accept: text/event-stream" \
  -d '{"jsonrpc":"2.0","id":1,"method":"tools/list","params":{}}'

# Call a tool with streaming response
curl -X POST http://127.0.0.1:8080/mcp/http \
  -H "Content-Type: application/json" \
  -H "Accept: text/event-stream" \
  -d '{"jsonrpc":"2.0","id":2,"method":"tools/call","params":{"name":"solve_n_queens","arguments":{"n":4}}}'

HTTP Transport (streaming with X-Stream header):

# Alternative way to enable streaming
curl -X POST http://127.0.0.1:8080/mcp/http \
  -H "Content-Type: application/json" \
  -H "X-Stream: true" \
  -d '{"jsonrpc":"2.0","id":3,"method":"tools/call","params":{"name":"info","arguments":{}}}'

Python Client Example:

• examples/streamable_http_client.py - HTTP transport client with streaming examples

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)

solve_24_point_game

Solve the 24-point game with four numbers using arithmetic operations.

{
  "name": "solve_24_point_game",
  "arguments": {
    "numbers": [1, 2, 3, 4]
  }
}

Finds arithmetic expressions using +, -, *, / and parentheses to reach exactly 24.

solve_chicken_rabbit_problem

Solve the classic chicken-rabbit problem with heads and legs constraints.

{
  "name": "solve_chicken_rabbit_problem",
  "arguments": {
    "total_heads": 35,
    "total_legs": 94
  }
}

Determines the number of chickens (2 legs) and rabbits (4 legs) given total heads and legs.

solve_scipy_portfolio_optimization

Solve nonlinear portfolio optimization using SciPy with quadratic risk models.

{
  "name": "solve_scipy_portfolio_optimization",
  "arguments": {
    "expected_returns": [0.12, 0.18, 0.15],
    "covariance_matrix": [
      [0.04, 0.01, 0.02],
      [0.01, 0.09, 0.03],
      [0.02, 0.03, 0.06]
    ],
    "risk_tolerance": 1.0
  }
}

Optimizes portfolio weights to maximize return minus risk penalty using mean-variance optimization.

solve_scipy_statistical_fitting

Solve statistical parameter estimation using SciPy with distribution fitting.

{
  "name": "solve_scipy_statistical_fitting",
  "arguments": {
    "data": [1.2, 2.3, 1.8, 2.1, 1.9, 2.4, 1.7, 2.0],
    "distribution": "normal"
  }
}

Fits statistical distributions ("normal", "exponential", "uniform") to data and provides goodness-of-fit tests.

solve_scipy_facility_location

Solve facility location problem using hybrid CSP-SciPy approach.

{
  "name": "solve_scipy_facility_location",
  "arguments": {
    "customer_locations": [[0, 0], [10, 10], [5, 15]],
    "customer_demands": [100, 150, 80],
    "facility_locations": [[2, 3], [8, 12], [6, 8]],
    "max_facilities": 2,
    "fixed_cost": 100.0
  }
}

Combines discrete facility selection (CSP) with continuous capacity optimization (SciPy) to minimize total cost.

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 (16 MCP tools)
│                          # - solve_24_point_game, solve_chicken_rabbit_problem
│                          # - solve_scipy_portfolio_optimization, solve_scipy_statistical_fitting
│                          # - solve_scipy_facility_location, and 11 other solvers
├── 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
│   │                      # - Portfolio optimization, statistical fitting, facility location
│   ├── classic_problems.py # Classic Math Problems
│   │                      # - 24-point game, chicken-rabbit problem, mini sudoku
│   ├── optimized_csp.py    # Advanced CSP techniques
│   ├── optimized_lp.py     # Linear programming examples
│   └── minimax.py          # Game theory and robust optimization
├── 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

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

HTTP Transport Features

HTTP Transport (/mcp/http endpoint):

• Single request-response pattern
• Optional streaming: Add Accept: text/event-stream or X-Stream: true header
• Simpler for one-off requests
• Compatible with standard HTTP clients
• No connection state to manage
• Supports both regular JSON responses and SSE-formatted streaming responses

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 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 - CSP examples
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/optimized_csp.py

# LP and optimization examples
python mcp_server/examples/optimized_lp.py

# Game theory and minimax examples
python mcp_server/examples/minimax.py

# SciPy integration examples (includes portfolio, statistical fitting, facility location)
python mcp_server/examples/scipy_optimization.py

# Classic math problems (includes 24-point game, chicken-rabbit problem)
python mcp_server/examples/classic_problems.py

# Test individual MCP tools directly
python -c "from mcp_server.handlers.gurddy import solve_24_point_game; print(solve_24_point_game([1,2,3,4]))"
python -c "from mcp_server.handlers.gurddy import solve_chicken_rabbit_problem; print(solve_chicken_rabbit_problem(35, 94))"
python -c "from mcp_server.handlers.gurddy import solve_scipy_portfolio_optimization; print(solve_scipy_portfolio_optimization([0.12, 0.18], [[0.04, 0.01], [0.01, 0.09]]))"

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

Development

Architecture

The project uses a centralized tool registry with auto-generated schemas to ensure consistency between stdio and HTTP servers:

• Tool Definitions: mcp_server/tool_definitions.py (basic metadata only)
• Auto-Generated Registry: mcp_server/tool_registry.py (schemas generated from function signatures)
• Stdio Server: mcp_server/mcp_stdio_server.py (for IDE integration)
• HTTP Server: mcp_server/mcp_http_server.py (for web clients)
• Handlers: mcp_server/handlers/gurddy.py (tool implementations)
• Schema Generator: scripts/generate_registry.py (auto-generates schemas from function signatures)

Adding a New Tool

1. Implement handler in mcp_server/handlers/gurddy.py:

   def my_new_tool(param1: str, param2: int = 10) -> Dict[str, Any]:
       """Tool implementation with proper type hints."""
       return {"result": "success"}

1. Add basic metadata in mcp_server/tool_definitions.py:

   {
       "name": "my_new_tool",
       "function": "my_new_tool",
       "description": "Description of what the tool does",
       "category": "optimization",
       "module": "handlers.gurddy"
   }

1. Generate schemas and verify:

   # Auto-generate schemas from function signatures
   python scripts/generate_registry.py
   
   # Verify consistency
   python scripts/verify_consistency.py
   pytest tests/test_consistency.py -v

That's it! The schema is automatically generated from your function's type hints, and both stdio and HTTP servers will pick up the new tool.

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)))

Testing

# Run all tests
pytest

# Run specific test suites
pytest tests/test_consistency.py -v
pytest tests/test_tool_registry.py -v

# Verify tool registry consistency
python scripts/verify_consistency.py

License

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