Licensed under Apache License 2.0 for open source distribution and usage
Provides source code hosting and collaboration features for the constrained optimization project
Supports running interactive optimization examples and demonstrations through Jupyter notebooks for educational and prototyping purposes
Includes comprehensive test suite using pytest for validating solver implementations and ensuring reliability of optimization solutions
Implements optimization solvers and examples in Python, providing access to mathematical optimization capabilities through Python-based tools
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
- SMT solver for constraint satisfaction problemsCVXPY
- Convex optimization solverHiGHS
- Linear and mixed-integer programming solverOR-Tools
- Constraint programming solver
📦 Installation
📐 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
2. Start the MCP Server
3. Connect from AI Assistant
Add the server to your MCP configuration:
4. Use the Tools
The server provides the following tools:
solve_constraint_satisfaction
- Solve logical constraint problemssolve_convex_optimization
- Solve convex optimization problemssolve_linear_programming
- Solve linear programming problemssolve_constraint_programming
- Solve constraint programming problemssolve_portfolio_optimization
- Solve portfolio optimization problems
📚 Examples
Constraint Satisfaction Problem
Portfolio Optimization
Linear Programming
Portfolio Examples
Portfolio Optimization - Advanced portfolio optimization strategies including Markowitz, Black-Litterman, and ESG-constrained optimization
Risk Management - 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 - Classic constraint satisfaction with chessboard visualization
Knapsack Problem - 0/1 and multiple knapsack variants with performance analysis
🏭 Scheduling & Operations
Job Shop Scheduling - Multi-machine production scheduling with Gantt charts
Nurse Scheduling - Complex workforce scheduling with fairness constraints
📊 Quantitative Economics & Finance
Portfolio Optimization - Advanced strategies including Markowitz, Black-Litterman, Risk Parity, and ESG-constrained optimization
Economic Production Planning - Multi-period supply chain optimization with inventory management
🧮 Interactive Learning
Comprehensive Demo Notebook - Interactive Jupyter notebook with all solver types and visualizations
🧪 Testing
Run the comprehensive test suite:
📖 Documentation
API Reference - Complete API documentation
Examples - Comprehensive examples and demos
Jupyter Notebook - Interactive demo notebook
PDF Documentation - Comprehensive PDF guide with theory, examples, and implementation details
Journal-Style PDF - Academic paper format with literature review, mathematics, and research contributions
🏗️ Architecture
Core Components
Core Models (
constrained_opt_mcp/core/
) - Base classes and problem typesSolver Models (
constrained_opt_mcp/models/
) - Problem-specific model definitionsSolvers (
constrained_opt_mcp/solvers/
) - Solver implementationsMCP Server (
constrained_opt_mcp/server/
) - MCP server implementationExamples (
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
Fork the repository
Create a feature branch
Make your changes
Add tests for new functionality
Run the test suite
Submit a pull request
📄 License
This project is licensed under the Apache License 2.0. See the LICENSE file for details.
🆘 Support
For questions, issues, or contributions, please:
Check the documentation
Search existing issues
Create a new issue
Join our 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
hybrid server
The server is able to function both locally and remotely, depending on the configuration or use case.
Tools
Enables solving complex combinatorial optimization problems with logical and numerical constraints through multiple solvers (Z3, CVXPY, HiGHS, OR-Tools). Specializes in portfolio optimization, scheduling, resource allocation, and constraint satisfaction problems.