<p align="center">
<img src=".github/logo.png" width="500px" alt="Constrained Optimization MCP Server">
</p>
# Constrained Optimization MCP Server
A general-purpose Model Context Protocol (MCP) server for solving combinatorial optimization problems with logical and numerical constraints. This server provides a unified interface to multiple optimization solvers, enabling AI assistants to solve complex optimization problems across various domains.
## 🚀 Features
- **Unified Interface**: Single MCP server for multiple optimization backends
- **AI-Ready**: Designed for use with AI assistants through MCP protocol
- **Portfolio Focus**: Specialized tools for portfolio optimization and risk management
- **Extensible**: Modular design for easy addition of new solvers
- **High Performance**: Optimized for large-scale problems
- **Robust**: Comprehensive error handling and validation
## 🛠️ Supported Solvers
* [`Z3`](https://github.com/Z3Prover/z3) - SMT solver for constraint satisfaction problems
* [`CVXPY`](https://www.cvxpy.org/) - Convex optimization solver
* [`HiGHS`](https://highs.dev/) - Linear and mixed-integer programming solver
* [`OR-Tools`](https://developers.google.com/optimization) - Constraint programming solver
## 📦 Installation
```bash
# Install the package
pip install constrained-opt-mcp
# Or install from source
git clone https://github.com/your-org/constrained-opt-mcp
cd constrained-opt-mcp
pip install -e .
```
## 📐 Mathematical Foundations
### Optimization Theory
The Constrained Optimization MCP Server implements solutions for various classes of optimization problems:
#### **Linear Programming (LP)**
$$\min_{x} c^T x \quad \text{subject to} \quad Ax \leq b, \quad x \geq 0$$
#### **Quadratic Programming (QP)**
$$\min_{x} \frac{1}{2}x^T Q x + c^T x \quad \text{subject to} \quad Ax \leq b, \quad x \geq 0$$
#### **Convex Optimization**
$$\min_{x} f(x) \quad \text{subject to} \quad g_i(x) \leq 0, \quad h_j(x) = 0$$
Where $f$ and $g_i$ are convex functions.
#### **Constraint Satisfaction Problems (CSP)**
Find $x \in \mathcal{D}$ such that $C_1(x) \land C_2(x) \land \ldots \land C_k(x)$
#### **Portfolio Optimization (Markowitz)**
$$\max_{w} \mu^T w - \frac{\lambda}{2} w^T \Sigma w \quad \text{subject to} \quad \sum_{i=1}^{n} w_i = 1, \quad w_i \geq 0$$
Where:
- $w$: portfolio weights
- $\mu$: expected returns
- $\Sigma$: covariance matrix
- $\lambda$: risk aversion parameter
### Solver Capabilities
| Problem Type | Solver | Complexity | Mathematical Form |
|--------------|--------|------------|-------------------|
| Constraint Satisfaction | Z3 | NP-Complete | Logical constraints |
| Convex Optimization | CVXPY | Polynomial | Convex functions |
| Linear Programming | HiGHS | Polynomial | Linear constraints |
| Constraint Programming | OR-Tools | NP-Complete | Discrete domains |
## 🚀 Quick Start
### 1. Run Examples
```bash
# Run individual examples
python examples/nqueens.py
python examples/knapsack.py
python examples/portfolio_optimization.py
python examples/job_shop_scheduling.py
python examples/nurse_scheduling.py
python examples/economic_production_planning.py
# Run interactive notebook
jupyter notebook examples/constrained_optimization_demo.ipynb
```
### 2. Start the MCP Server
```bash
constrained-opt-mcp
```
### 3. Connect from AI Assistant
Add the server to your MCP configuration:
```json
{
"mcpServers": {
"constrained-opt-mcp": {
"command": "constrained-opt-mcp",
"args": []
}
}
}
```
### 4. Use the Tools
The server provides the following tools:
- `solve_constraint_satisfaction` - Solve logical constraint problems
- `solve_convex_optimization` - Solve convex optimization problems
- `solve_linear_programming` - Solve linear programming problems
- `solve_constraint_programming` - Solve constraint programming problems
- `solve_portfolio_optimization` - Solve portfolio optimization problems
## 📚 Examples
### Constraint Satisfaction Problem
```python
# Solve a simple arithmetic constraint problem
variables = [
{"name": "x", "type": "integer"},
{"name": "y", "type": "integer"},
]
constraints = [
"x + y == 10",
"x - y == 2",
]
# Result: x=6, y=4
```
### Portfolio Optimization
```python
# Optimize portfolio allocation
assets = ["Stocks", "Bonds", "Real Estate", "Commodities"]
expected_returns = [0.10, 0.03, 0.07, 0.06]
risk_factors = [0.15, 0.03, 0.12, 0.20]
correlation_matrix = [
[1.0, 0.2, 0.6, 0.3],
[0.2, 1.0, 0.1, 0.05],
[0.6, 0.1, 1.0, 0.25],
[0.3, 0.05, 0.25, 1.0],
]
# Result: Optimal portfolio weights and performance metrics
```
### Linear Programming
```python
# Production planning problem
sense = "maximize"
objective_coeffs = [3.0, 2.0] # Profit per unit
variables = [
{"name": "product_a", "lb": 0, "ub": None, "type": "cont"},
{"name": "product_b", "lb": 0, "ub": None, "type": "cont"},
]
constraint_matrix = [
[2, 1], # Labor: 2*A + 1*B <= 100
[1, 2], # Material: 1*A + 2*B <= 80
]
constraint_senses = ["<=", "<="]
rhs_values = [100.0, 80.0]
# Result: Optimal production quantities
```
### Portfolio Examples
- **[Portfolio Optimization](constrained_opt_mcp/examples/financial/portfolio_optimization.py)** - Advanced portfolio optimization strategies including Markowitz, Black-Litterman, and ESG-constrained optimization
- **[Risk Management](constrained_opt_mcp/examples/financial/risk_management.py)** - Risk management strategies including VaR optimization, stress testing, and hedging
#### Enhanced Portfolio Optimization Features
**Equity Portfolio Optimization:**
- Sector diversification constraints (max 25% per sector)
- Market cap constraints (large, mid, small cap allocations)
- ESG (Environmental, Social, Governance) constraints
- Liquidity requirements and individual position limits
- Risk-return optimization with advanced metrics
**Multi-Asset Portfolio Optimization:**
- Asset class constraints (equity, fixed income, alternatives, cash)
- Regional exposure limits (developed vs emerging markets)
- Alternative investment constraints (commodities, real estate, private equity)
- Dynamic rebalancing and risk budgeting
- Multi-period optimization with transaction costs
**Advanced Risk Metrics:**
- Value at Risk (VaR) and Conditional VaR (CVaR)
- Maximum Drawdown and Tail Risk
- Factor exposure analysis and risk attribution
- Stress testing and scenario analysis
- Correlation and concentration risk management
### Comprehensive Examples
#### 🎯 **Combinatorial Optimization**
- **[N-Queens Problem](examples/nqueens.py)** - Classic constraint satisfaction with chessboard visualization
- **[Knapsack Problem](examples/knapsack.py)** - 0/1 and multiple knapsack variants with performance analysis
#### 🏭 **Scheduling & Operations**
- **[Job Shop Scheduling](examples/job_shop_scheduling.py)** - Multi-machine production scheduling with Gantt charts
- **[Nurse Scheduling](examples/nurse_scheduling.py)** - Complex workforce scheduling with fairness constraints
#### 📊 **Quantitative Economics & Finance**
- **[Portfolio Optimization](examples/portfolio_optimization.py)** - Advanced strategies including Markowitz, Black-Litterman, Risk Parity, and ESG-constrained optimization
- **[Economic Production Planning](examples/economic_production_planning.py)** - Multi-period supply chain optimization with inventory management
#### 🧮 **Interactive Learning**
- **[Comprehensive Demo Notebook](examples/constrained_optimization_demo.ipynb)** - Interactive Jupyter notebook with all solver types and visualizations
## 🧪 Testing
Run the comprehensive test suite:
```bash
# Run all tests
pytest
# Run specific test categories
pytest tests/test_z3_solver.py
pytest tests/test_cvxpy_solver.py
pytest tests/test_highs_solver.py
pytest tests/test_ortools_solver.py
pytest tests/test_mcp_server.py
# Run with coverage
pytest --cov=constrained_opt_mcp
```
## 📖 Documentation
- **[API Reference](docs/README.md)** - Complete API documentation
- **[Examples](examples/)** - Comprehensive examples and demos
- **[Jupyter Notebook](examples/constrained_optimization_demo.ipynb)** - Interactive demo notebook
- **[PDF Documentation](docs/constrained_optimization_package.pdf)** - Comprehensive PDF guide with theory, examples, and implementation details
- **[Journal-Style PDF](docs/constrained_optimization_journal.pdf)** - Academic paper format with literature review, mathematics, and research contributions
## 🏗️ Architecture
### Core Components
1. **Core Models** (`constrained_opt_mcp/core/`) - Base classes and problem types
2. **Solver Models** (`constrained_opt_mcp/models/`) - Problem-specific model definitions
3. **Solvers** (`constrained_opt_mcp/solvers/`) - Solver implementations
4. **MCP Server** (`constrained_opt_mcp/server/`) - MCP server implementation
5. **Examples** (`constrained_opt_mcp/examples/`) - Usage examples and demos
### Supported Problem Types
| Problem Type | Solver | Use Cases |
|--------------|--------|-----------|
| Constraint Satisfaction | Z3 | Logic puzzles, verification, planning |
| Convex Optimization | CVXPY | Portfolio optimization, machine learning |
| Linear Programming | HiGHS | Production planning, resource allocation |
| Constraint Programming | OR-Tools | Scheduling, assignment, routing |
| Portfolio Optimization | Multiple | Risk management, portfolio construction |
## 🤝 Contributing
1. Fork the repository
2. Create a feature branch
3. Make your changes
4. Add tests for new functionality
5. Run the test suite
6. Submit a pull request
## 📄 License
This project is licensed under the Apache License 2.0. See the [LICENSE](LICENSE) file for details.
## 🆘 Support
For questions, issues, or contributions, please:
1. Check the [documentation](docs/)
2. Search [existing issues](https://github.com/your-org/constrained-opt-mcp/issues)
3. Create a [new issue](https://github.com/your-org/constrained-opt-mcp/issues/new)
4. Join our [discussions](https://github.com/your-org/constrained-opt-mcp/discussions)
## 📈 Changelog
### Version 1.0.0
- Initial release
- Support for Z3, CVXPY, HiGHS, and OR-Tools
- Portfolio optimization examples
- Comprehensive test suite
- MCP server implementation
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"description": "<p align=\"center\">\n <img src=\".github/logo.png\" width=\"500px\" alt=\"Constrained Optimization MCP Server\">\n</p>\n\n# Constrained Optimization MCP Server\n\nA general-purpose Model Context Protocol (MCP) server for solving combinatorial optimization problems with logical and numerical constraints. This server provides a unified interface to multiple optimization solvers, enabling AI assistants to solve complex optimization problems across various domains.\n\n## \ud83d\ude80 Features\n\n- **Unified Interface**: Single MCP server for multiple optimization backends\n- **AI-Ready**: Designed for use with AI assistants through MCP protocol\n- **Portfolio Focus**: Specialized tools for portfolio optimization and risk management\n- **Extensible**: Modular design for easy addition of new solvers\n- **High Performance**: Optimized for large-scale problems\n- **Robust**: Comprehensive error handling and validation\n\n## \ud83d\udee0\ufe0f Supported Solvers\n\n* [`Z3`](https://github.com/Z3Prover/z3) - SMT solver for constraint satisfaction problems\n* [`CVXPY`](https://www.cvxpy.org/) - Convex optimization solver\n* [`HiGHS`](https://highs.dev/) - Linear and mixed-integer programming solver\n* [`OR-Tools`](https://developers.google.com/optimization) - Constraint programming solver\n\n## \ud83d\udce6 Installation\n\n```bash\n# Install the package\npip install constrained-opt-mcp\n\n# Or install from source\ngit clone https://github.com/your-org/constrained-opt-mcp\ncd constrained-opt-mcp\npip install -e .\n```\n\n## \ud83d\udcd0 Mathematical Foundations\n\n### Optimization Theory\n\nThe Constrained Optimization MCP Server implements solutions for various classes of optimization problems:\n\n#### **Linear Programming (LP)**\n$$\\min_{x} c^T x \\quad \\text{subject to} \\quad Ax \\leq b, \\quad x \\geq 0$$\n\n#### **Quadratic Programming (QP)**\n$$\\min_{x} \\frac{1}{2}x^T Q x + c^T x \\quad \\text{subject to} \\quad Ax \\leq b, \\quad x \\geq 0$$\n\n#### **Convex Optimization**\n$$\\min_{x} f(x) \\quad \\text{subject to} \\quad g_i(x) \\leq 0, \\quad h_j(x) = 0$$\n\nWhere $f$ and $g_i$ are convex functions.\n\n#### **Constraint Satisfaction Problems (CSP)**\nFind $x \\in \\mathcal{D}$ such that $C_1(x) \\land C_2(x) \\land \\ldots \\land C_k(x)$\n\n#### **Portfolio Optimization (Markowitz)**\n$$\\max_{w} \\mu^T w - \\frac{\\lambda}{2} w^T \\Sigma w \\quad \\text{subject to} \\quad \\sum_{i=1}^{n} w_i = 1, \\quad w_i \\geq 0$$\n\nWhere:\n- $w$: portfolio weights\n- $\\mu$: expected returns\n- $\\Sigma$: covariance matrix\n- $\\lambda$: risk aversion parameter\n\n### Solver Capabilities\n\n| Problem Type | Solver | Complexity | Mathematical Form |\n|--------------|--------|------------|-------------------|\n| Constraint Satisfaction | Z3 | NP-Complete | Logical constraints |\n| Convex Optimization | CVXPY | Polynomial | Convex functions |\n| Linear Programming | HiGHS | Polynomial | Linear constraints |\n| Constraint Programming | OR-Tools | NP-Complete | Discrete domains |\n\n## \ud83d\ude80 Quick Start\n\n### 1. Run Examples\n\n```bash\n# Run individual examples\npython examples/nqueens.py\npython examples/knapsack.py\npython examples/portfolio_optimization.py\npython examples/job_shop_scheduling.py\npython examples/nurse_scheduling.py\npython examples/economic_production_planning.py\n\n# Run interactive notebook\njupyter notebook examples/constrained_optimization_demo.ipynb\n```\n\n### 2. Start the MCP Server\n\n```bash\nconstrained-opt-mcp\n```\n\n### 3. Connect from AI Assistant\n\nAdd the server to your MCP configuration:\n\n```json\n{\n \"mcpServers\": {\n \"constrained-opt-mcp\": {\n \"command\": \"constrained-opt-mcp\",\n \"args\": []\n }\n }\n}\n```\n\n### 4. Use the Tools\n\nThe server provides the following tools:\n\n- `solve_constraint_satisfaction` - Solve logical constraint problems\n- `solve_convex_optimization` - Solve convex optimization problems \n- `solve_linear_programming` - Solve linear programming problems\n- `solve_constraint_programming` - Solve constraint programming problems\n- `solve_portfolio_optimization` - Solve portfolio optimization problems\n\n## \ud83d\udcda Examples\n\n### Constraint Satisfaction Problem\n\n```python\n# Solve a simple arithmetic constraint problem\nvariables = [\n {\"name\": \"x\", \"type\": \"integer\"},\n {\"name\": \"y\", \"type\": \"integer\"},\n]\nconstraints = [\n \"x + y == 10\",\n \"x - y == 2\",\n]\n\n# Result: x=6, y=4\n```\n\n### Portfolio Optimization\n\n```python\n# Optimize portfolio allocation\nassets = [\"Stocks\", \"Bonds\", \"Real Estate\", \"Commodities\"]\nexpected_returns = [0.10, 0.03, 0.07, 0.06]\nrisk_factors = [0.15, 0.03, 0.12, 0.20]\ncorrelation_matrix = [\n [1.0, 0.2, 0.6, 0.3],\n [0.2, 1.0, 0.1, 0.05],\n [0.6, 0.1, 1.0, 0.25],\n [0.3, 0.05, 0.25, 1.0],\n]\n\n# Result: Optimal portfolio weights and performance metrics\n```\n\n### Linear Programming\n\n```python\n# Production planning problem\nsense = \"maximize\"\nobjective_coeffs = [3.0, 2.0] # Profit per unit\nvariables = [\n {\"name\": \"product_a\", \"lb\": 0, \"ub\": None, \"type\": \"cont\"},\n {\"name\": \"product_b\", \"lb\": 0, \"ub\": None, \"type\": \"cont\"},\n]\nconstraint_matrix = [\n [2, 1], # Labor: 2*A + 1*B <= 100\n [1, 2], # Material: 1*A + 2*B <= 80\n]\nconstraint_senses = [\"<=\", \"<=\"]\nrhs_values = [100.0, 80.0]\n\n# Result: Optimal production quantities\n```\n\n### Portfolio Examples\n\n- **[Portfolio Optimization](constrained_opt_mcp/examples/financial/portfolio_optimization.py)** - Advanced portfolio optimization strategies including Markowitz, Black-Litterman, and ESG-constrained optimization\n- **[Risk Management](constrained_opt_mcp/examples/financial/risk_management.py)** - Risk management strategies including VaR optimization, stress testing, and hedging\n\n#### Enhanced Portfolio Optimization Features\n\n**Equity Portfolio Optimization:**\n- Sector diversification constraints (max 25% per sector)\n- Market cap constraints (large, mid, small cap allocations)\n- ESG (Environmental, Social, Governance) constraints\n- Liquidity requirements and individual position limits\n- Risk-return optimization with advanced metrics\n\n**Multi-Asset Portfolio Optimization:**\n- Asset class constraints (equity, fixed income, alternatives, cash)\n- Regional exposure limits (developed vs emerging markets)\n- Alternative investment constraints (commodities, real estate, private equity)\n- Dynamic rebalancing and risk budgeting\n- Multi-period optimization with transaction costs\n\n**Advanced Risk Metrics:**\n- Value at Risk (VaR) and Conditional VaR (CVaR)\n- Maximum Drawdown and Tail Risk\n- Factor exposure analysis and risk attribution\n- Stress testing and scenario analysis\n- Correlation and concentration risk management\n\n### Comprehensive Examples\n\n#### \ud83c\udfaf **Combinatorial Optimization**\n- **[N-Queens Problem](examples/nqueens.py)** - Classic constraint satisfaction with chessboard visualization\n- **[Knapsack Problem](examples/knapsack.py)** - 0/1 and multiple knapsack variants with performance analysis\n\n#### \ud83c\udfed **Scheduling & Operations**\n- **[Job Shop Scheduling](examples/job_shop_scheduling.py)** - Multi-machine production scheduling with Gantt charts\n- **[Nurse Scheduling](examples/nurse_scheduling.py)** - Complex workforce scheduling with fairness constraints\n\n#### \ud83d\udcca **Quantitative Economics & Finance**\n- **[Portfolio Optimization](examples/portfolio_optimization.py)** - Advanced strategies including Markowitz, Black-Litterman, Risk Parity, and ESG-constrained optimization\n- **[Economic Production Planning](examples/economic_production_planning.py)** - Multi-period supply chain optimization with inventory management\n\n#### \ud83e\uddee **Interactive Learning**\n- **[Comprehensive Demo Notebook](examples/constrained_optimization_demo.ipynb)** - Interactive Jupyter notebook with all solver types and visualizations\n\n## \ud83e\uddea Testing\n\nRun the comprehensive test suite:\n\n```bash\n# Run all tests\npytest\n\n# Run specific test categories\npytest tests/test_z3_solver.py\npytest tests/test_cvxpy_solver.py\npytest tests/test_highs_solver.py\npytest tests/test_ortools_solver.py\npytest tests/test_mcp_server.py\n\n# Run with coverage\npytest --cov=constrained_opt_mcp\n```\n\n## \ud83d\udcd6 Documentation\n\n- **[API Reference](docs/README.md)** - Complete API documentation\n- **[Examples](examples/)** - Comprehensive examples and demos\n- **[Jupyter Notebook](examples/constrained_optimization_demo.ipynb)** - Interactive demo notebook\n- **[PDF Documentation](docs/constrained_optimization_package.pdf)** - Comprehensive PDF guide with theory, examples, and implementation details\n- **[Journal-Style PDF](docs/constrained_optimization_journal.pdf)** - Academic paper format with literature review, mathematics, and research contributions\n\n## \ud83c\udfd7\ufe0f Architecture\n\n### Core Components\n\n1. **Core Models** (`constrained_opt_mcp/core/`) - Base classes and problem types\n2. **Solver Models** (`constrained_opt_mcp/models/`) - Problem-specific model definitions \n3. **Solvers** (`constrained_opt_mcp/solvers/`) - Solver implementations\n4. **MCP Server** (`constrained_opt_mcp/server/`) - MCP server implementation\n5. **Examples** (`constrained_opt_mcp/examples/`) - Usage examples and demos\n\n### Supported Problem Types\n\n| Problem Type | Solver | Use Cases |\n|--------------|--------|-----------|\n| Constraint Satisfaction | Z3 | Logic puzzles, verification, planning |\n| Convex Optimization | CVXPY | Portfolio optimization, machine learning |\n| Linear Programming | HiGHS | Production planning, resource allocation |\n| Constraint Programming | OR-Tools | Scheduling, assignment, routing |\n| Portfolio Optimization | Multiple | Risk management, portfolio construction |\n\n## \ud83e\udd1d Contributing\n\n1. Fork the repository\n2. Create a feature branch\n3. Make your changes\n4. Add tests for new functionality\n5. Run the test suite\n6. Submit a pull request\n\n## \ud83d\udcc4 License\n\nThis project is licensed under the Apache License 2.0. See the [LICENSE](LICENSE) file for details.\n\n## \ud83c\udd98 Support\n\nFor questions, issues, or contributions, please:\n\n1. Check the [documentation](docs/)\n2. Search [existing issues](https://github.com/your-org/constrained-opt-mcp/issues)\n3. Create a [new issue](https://github.com/your-org/constrained-opt-mcp/issues/new)\n4. Join our [discussions](https://github.com/your-org/constrained-opt-mcp/discussions)\n\n## \ud83d\udcc8 Changelog\n\n### Version 1.0.0\n- Initial release\n- Support for Z3, CVXPY, HiGHS, and OR-Tools\n- Portfolio optimization examples\n- Comprehensive test suite\n- MCP server implementation\n",
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