Constrained Optimization MCP Server

# Constrained Optimization Examples This directory contains comprehensive examples demonstrating the capabilities of the Constrained Optimization MCP Server across various domains. ## 📊 **Quantitative Economics & Finance** ### Portfolio Optimization (`portfolio_optimization.py`) - **Markowitz mean-variance optimization** - **Black-Litterman model** with investor views - **Risk parity optimization** for balanced risk allocation - **ESG-constrained optimization** for sustainable investing - **Efficient frontier analysis** and strategy comparison - **Advanced risk metrics** and performance attribution ### Financial Examples (`constrained_opt_mcp/examples/financial/`) - **Portfolio Optimization** (`portfolio_optimization.py`) - Advanced portfolio strategies - **Risk Management** (`risk_management.py`) - VaR optimization and stress testing ## 🏭 **Scheduling & Operations** ### Job Shop Scheduling (`job_shop_scheduling.py`) - **Multi-machine scheduling** with operation sequences - **Makespan minimization** for production efficiency - **Resource allocation** and timing constraints - **Gantt chart visualization** of optimal schedules - **Performance analysis** across different problem sizes ### Nurse Scheduling (`nurse_scheduling.py`) - **Workforce scheduling** with complex constraints - **Shift coverage requirements** and fairness considerations - **Nurse preferences** and soft constraints - **Weekend coverage** and consecutive shift limits - **Schedule quality analysis** and visualization ## 🎯 **Combinatorial Optimization** ### N-Queens Problem (`nqueens.py`) - **Constraint satisfaction** problem solving - **Classic algorithmic challenge** with visualization - **Performance analysis** across different board sizes - **Solution visualization** on chessboard - **Complexity analysis** and benchmarking ### Knapsack Problem (`knapsack.py`) - **0/1 knapsack** and multiple knapsack variants - **Binary decision variables** and integer programming - **Value maximization** under weight constraints - **Multiple knapsack** resource allocation - **Performance analysis** and visualization ## 🏭 **Economic Production Planning** ### Economic Production Planning (`economic_production_planning.py`) - **Multi-period production planning** with inventory management - **Demand forecasting** and capacity constraints - **Cost minimization** across production, holding, and shortage costs - **Resource allocation** and supply chain optimization - **Strategy comparison** (Just-in-Time vs Safety Stock vs Balanced) - **Economic efficiency analysis** and performance metrics ## 🧮 **Mathematical Optimization** ### Interactive Demo (`constrained_optimization_demo.ipynb`) - **Comprehensive Jupyter notebook** with all solver types - **Interactive visualizations** and performance analysis - **Mathematical theory** and formulations - **Portfolio optimization** with advanced constraints - **Real-time examples** and demonstrations ## 🚀 **Getting Started** ### Prerequisites ```bash pip install constrained-opt-mcp ``` ### Running Examples ```bash # Run individual examples python examples/nqueens.py python examples/knapsack.py python examples/job_shop_scheduling.py python examples/nurse_scheduling.py python examples/portfolio_optimization.py python examples/economic_production_planning.py # Run interactive notebook jupyter notebook examples/constrained_optimization_demo.ipynb ``` ### Example Structure Each example follows a consistent structure: 1. **Problem Definition** - Clear description of the optimization problem 2. **Mathematical Formulation** - Complete mathematical model 3. **Implementation** - Code using the MCP server 4. **Visualization** - Charts and graphs for results 5. **Analysis** - Performance metrics and insights 6. **Comparison** - Different strategies or approaches ## 📈 **Key Features Demonstrated** ### Solver Integration - **Z3** - Constraint satisfaction and logical reasoning - **CVXPY** - Convex optimization and portfolio problems - **HiGHS** - Linear programming and production planning - **OR-Tools** - Constraint programming and scheduling ### Problem Types - **Linear Programming** - Production planning, resource allocation - **Convex Optimization** - Portfolio optimization, risk management - **Constraint Satisfaction** - N-Queens, scheduling problems - **Integer Programming** - Knapsack, assignment problems - **Mixed-Integer Programming** - Complex scheduling and planning ### Visualization & Analysis - **Interactive plots** and charts - **Performance benchmarking** across problem sizes - **Strategy comparison** and sensitivity analysis - **Economic metrics** and efficiency analysis - **Real-time optimization** results ## 🎯 **Use Cases** ### Financial Services - Portfolio optimization and risk management - Asset allocation and rebalancing - ESG investing and sustainable finance - Risk budgeting and factor investing ### Manufacturing & Operations - Production planning and scheduling - Resource allocation and capacity planning - Supply chain optimization - Inventory management ### Healthcare & Services - Nurse and staff scheduling - Resource allocation in hospitals - Appointment scheduling - Workforce optimization ### Research & Education - Algorithm benchmarking and comparison - Optimization theory demonstration - Mathematical modeling examples - Performance analysis and visualization ## 📚 **Documentation** - **[API Reference](../docs/README.md)** - Complete API documentation - **[PDF Guide](../docs/constrained_optimization_package.pdf)** - Comprehensive user guide - **[Academic Paper](../docs/constrained_optimization_journal.pdf)** - Journal-style research paper - **[Interactive Demo](constrained_optimization_demo.ipynb)** - Jupyter notebook with examples ## 🤝 **Contributing** We welcome contributions! Please see the main README for guidelines on: - Adding new examples - Improving existing examples - Adding new problem types - Enhancing visualizations - Performance optimization ## 📄 **License** This project is licensed under the Apache License 2.0 - see the [LICENSE](../LICENSE) file for details.