MCP Agent Demo: Solving Complex Optimization

# Agent trying to solve manually (struggling)

User: "Optimize my portfolio with the constraints above"

Agent (thinking): "I need to write optimization code. Let me try scipy..."

```python
from scipy.optimize import minimize
import numpy as np

# This is getting complex...
def portfolio_objective(weights):
    # Wait, how do I handle CVaR constraints?
    # I need to calculate CVaR but I'm not sure how...
    portfolio_return = np.dot(weights, expected_returns)
    portfolio_variance = np.dot(weights.T, np.dot(covariance, weights))
    return -portfolio_return / np.sqrt(portfolio_variance)  # Sharpe ratio?

# Constraints are tricky...
constraints = [
    {'type': 'eq', 'fun': lambda w: np.sum(w) - 1.0},
    # How do I enforce CVaR < 12%?
    # How do I handle min/max position limits?
]

# This might not work correctly...
result = minimize(portfolio_objective, x0, bounds=bounds, constraints=constraints)
```

Agent: "I'm having trouble with the CVaR constraint. 
The scipy optimizer doesn't directly support CVaR, and I'm 
not confident my implementation is correct. Also, I'm not 
sure which optimization algorithm to use for this problem..."

# Agent using MCP tools (successful)

User: "Optimize my portfolio with the constraints above"

Agent (via MCP): 
<tool_call>
{
  "tool": "analyze_optimization_problem",
  "arguments": {
    "objective_function": "portfolio_optimization_with_cvar",
    "bounds": [[0.05, 0.30], [0.05, 0.30], [0.05, 0.30], [0.05, 0.30], [0.05, 0.30]],
    "constraints": [
      "sum(weights) == 1.0",
      "target_return >= 0.08",
      "cvar <= 0.12",
      "min_position >= 0.05",
      "max_position <= 0.30"
    ],
    "domain": "financial"
  }
}
</tool_call>

<tool_result>
{
  "problem_type": "constrained_portfolio_optimization",
  "complexity": "high",
  "recommended_strategy": "cma_es_with_constraints",
  "estimated_evaluations": 2000,
  "constraint_handling": "penalty_method",
  "domain_specific_insights": {
    "risk_measure": "CVaR",
    "suitable_algorithms": ["CMA-ES", "Differential Evolution"],
    "common_pitfalls": ["CVaR calculation errors", "constraint violation"]
  }
}
</tool_result>

Agent: "The analysis suggests using CMA-ES with constraint handling. 
Let me optimize using the recommended approach."

<tool_call>
{
  "tool": "optimize_function",
  "arguments": {
    "objective_function": "def portfolio_objective(weights):
    # Calculate portfolio metrics
    portfolio_return = np.dot(weights, expected_returns)
    portfolio_variance = np.dot(weights.T, np.dot(covariance, weights))
    
    # Calculate CVaR (Conditional Value at Risk)
    portfolio_returns_sim = simulate_portfolio_returns(weights, 10000)
    cvar = calculate_cvar(portfolio_returns_sim, confidence=0.95)
    
    # Objective: maximize risk-adjusted return
    sharpe = (portfolio_return - risk_free_rate) / np.sqrt(portfolio_variance)
    
    # Penalty for constraint violations
    penalty = 0
    if np.abs(np.sum(weights) - 1.0) > 0.01:
        penalty += 1000
    if portfolio_return < 0.08:
        penalty += 100 * (0.08 - portfolio_return)
    if cvar > 0.12:
        penalty += 100 * (cvar - 0.12)
    
    return -sharpe + penalty",
    "bounds": [[0.05, 0.30], [0.05, 0.30], [0.05, 0.30], [0.05, 0.30], [0.05, 0.30]],
    "max_evaluations": 2000,
    "domain": "financial",
    "constraints": [
      "sum(weights) == 1.0",
      "target_return >= 0.08",
      "cvar <= 0.12"
    ]
  }
}
</tool_call>

<tool_result>
{
  "success": true,
  "best_parameters": [0.28, 0.22, 0.30, 0.10, 0.10],
  "best_fitness": 1.42,
  "evaluations": 1847,
  "convergence_iterations": 156,
  "explanation": {
    "natural_language": "Optimized portfolio allocation: 28% Tech Stock A, 22% Tech Stock B, 30% Tech Stock C (max), 10% Bonds A, 10% Bonds B. Achieves 8.3% expected return with 11.8% CVaR, satisfying all constraints. The optimizer favored Tech Stock C due to superior risk-adjusted return (Sharpe 1.42).",
    "strategy_used": "CMA-ES with adaptive constraint handling",
    "constraint_satisfaction": "all_constraints_satisfied",
    "risk_metrics": {
      "expected_return": 0.083,
      "cvar": 0.118,
      "sharpe_ratio": 1.42,
      "max_drawdown": 0.15
    }
  }
}
</tool_result>

Agent: "✅ Portfolio optimized successfully!

**Recommended Allocation:**
- Tech Stock A: 28%
- Tech Stock B: 22%  
- Tech Stock C: 30% (maximum allowed)
- Bonds A: 10%
- Bonds B: 10%

**Results:**
- Expected return: 8.3% (exceeds 8% target)
- CVaR: 11.8% (below 12% limit)
- Sharpe ratio: 1.42
- All constraints satisfied

The optimizer used CMA-ES with specialized constraint handling for financial problems, which is more reliable than generic optimization methods for portfolio problems."

# Setting up MCP connection in your agent

from mcp import ClientSession, StdioServerParameters
from mcp.client.stdio import stdio_client

# Connect to Sematryx MCP server
server_params = StdioServerParameters(
    command="python",
    args=["-m", "sematryx.platform_services.integrations.mcp.server"],
    env=None
)

async with stdio_client(server_params) as (read, write):
    async with ClientSession(read, write) as session:
        # Initialize the session
        await session.initialize()
        
        # List available tools
        tools = await session.list_tools()
        print("Available tools:", [t.name for t in tools.tools])
        
        # Call optimization tool
        result = await session.call_tool(
            "optimize_function",
            arguments={
                "objective_function": objective_code,
                "bounds": bounds,
                "domain": "financial",
                "max_evaluations": 2000
            }
        )
        
        print("Optimization result:", result.content)