Constrained Optimization MCP Server
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
Click on "Install Server".
Wait a few minutes for the server to deploy. Once ready, it will show a "Started" state.
In the chat, type
@followed by the MCP server name and your instructions, e.g., "@Constrained Optimization MCP Serveroptimize my investment portfolio with 70% stocks, 20% bonds, and 10% real estate, maximizing returns while keeping risk below 15%"
That's it! The server will respond to your query, and you can continue using it as needed.
Here is a step-by-step guide with screenshots.
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.
๐ 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
Related MCP server: MCP Optimizer
๐ ๏ธ Supported Solvers
Z3- SMT solver for constraint satisfaction problemsCVXPY- Convex optimization solverHiGHS- Linear and mixed-integer programming solverOR-Tools- Constraint programming solver
๐ฆ Installation
# 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 .๐ 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 |
๐ Quick Start
1. Run Examples
# 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.ipynb2. Start the MCP Server
constrained-opt-mcp3. Connect from AI Assistant
Add the server to your MCP configuration:
{
"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 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
๐ Examples
Constraint Satisfaction Problem
# 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=4Portfolio Optimization
# 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 metricsLinear Programming
# 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 quantitiesPortfolio 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
๐ฏ Combinatorial Optimization
N-Queens Problem - Classic constraint satisfaction with chessboard visualization
Knapsack Problem - 0/1 and multiple knapsack variants with performance analysis
๐ญ Scheduling & Operations
Job Shop Scheduling - Multi-machine production scheduling with Gantt charts
Nurse Scheduling - Complex workforce scheduling with fairness constraints
๐ 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
๐งฎ Interactive Learning
Comprehensive Demo Notebook - Interactive Jupyter notebook with all solver types and visualizations
๐งช Testing
Run the comprehensive test suite:
# 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_mcp๐ 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
๐๏ธ 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 |
๐ค Contributing
Fork the repository
Create a feature branch
Make your changes
Add tests for new functionality
Run the test suite
Submit a pull request
๐ License
This project is licensed under the Apache License 2.0. See the LICENSE file for details.
๐ Support
For questions, issues, or contributions, please:
Check the documentation
Search existing issues
Create a new issue
Join our discussions
๐ Changelog
Version 1.0.0
Initial release
Support for Z3, CVXPY, HiGHS, and OR-Tools
Portfolio optimization examples
Comprehensive test suite
MCP server implementation
Available Tools
5 toolssolve_constraint_programmingA
Solve constraint programming problems using OR-Tools.
This tool is ideal for combinatorial optimization problems, scheduling,
assignment problems, and constraint satisfaction with discrete variables.
Args:
variables: List of variable definitions with 'name', 'type', and optional 'domain'/'shape'
constraints: List of constraint expressions as strings
objective: Optional objective definition with 'type' and 'expression'
parameters: Dictionary of solver parameters
description: Optional problem description
Returns:
Solution results including variable values and feasibility status
Example:
variables = [
{"name": "x", "type": "integer", "domain": [0, 10]},
{"name": "y", "type": "boolean"}
]
constraints = [
"x + y >= 5",
"x - y <= 3"
]
objective = {"type": "minimize", "expression": "x + y"}
| Name | Required | Description | Default |
|---|---|---|---|
| variables | Yes | ||
| constraints | Yes | ||
| objective | No | ||
| parameters | No | ||
| description | No |
TDQS
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must fully disclose behavioral traits. It mentions OR-Tools as the solver and defines parameters, but lacks details on side effects, authentication, error handling, or limitations. The return description is minimal ('variable values and feasibility status').
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is well-structured with a summary, Args, Returns, and an example. It is front-loaded with the core purpose. However, it is somewhat verbose; slight trimming could improve conciseness without losing clarity.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the tool's complexity (nested objects, no output schema, 5 params), the description covers inputs, outputs, and usage example. It explains the objective and parameters. However, it does not detail the constraint expression syntax, which may be unfamiliar to users.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description must compensate. It provides a detailed Args section explaining each parameter, including types and optional fields, plus a concrete example. This adds significant meaning beyond the raw schema, which only has titles and types.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool solves constraint programming problems using OR-Tools and lists typical use cases like combinatorial optimization and scheduling. However, it does not explicitly differentiate from the sibling tool 'solve_constraint_satisfaction', which could cause confusion.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description indicates when the tool is ideal (e.g., combinatorial optimization, scheduling) but does not provide guidance on when not to use it or suggest alternative tools. Usage is implied from the domain listing, but no explicit exclusions or comparisons are given.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
solve_constraint_satisfactionB
Solve constraint satisfaction problems using Z3 SMT solver.
This tool is ideal for logical reasoning, puzzle solving, and constraint satisfaction
problems where you need to find values that satisfy a set of logical constraints.
Args:
variables: List of variable definitions with 'name' and 'type' fields
constraints: List of constraint expressions as strings
description: Optional problem description
timeout: Optional timeout in milliseconds
Returns:
Solution results including variable values and satisfiability status
Example:
variables = [
{"name": "x", "type": "integer"},
{"name": "y", "type": "integer"}
]
constraints = [
"x + y == 10",
"x - y == 2"
]
| Name | Required | Description | Default |
|---|---|---|---|
| variables | Yes | ||
| constraints | Yes | ||
| description | No | ||
| timeout | No |
TDQS
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must carry the full burden. It mentions using the Z3 SMT solver and a timeout parameter, but does not disclose behavioral traits like side effects, error handling, or whether it modifies state. The description adds minimal behavioral context beyond basic usage.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is well-structured with a summary, usage statement, parameter list, return description, and example. It is front-loaded with the core purpose. Minor verbosity in the 'ideal for' sentence could be trimmed, but overall it is efficient and clear.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
The description includes a helpful example and parameter explanations, but lacks details on return value format (e.g., sat/unsat, variable values) and does not address edge cases or error behavior. Given the tool's complexity and absence of output schema and annotations, more context would be beneficial.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description compensates well by explaining each parameter in the 'Args' section and providing a concrete example. The explanation of 'variables' having 'name' and 'type' fields, and 'constraints' as expressions, adds meaning that the schema alone lacks.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states the tool solves constraint satisfaction problems using the Z3 SMT solver, and mentions its applicability to logical reasoning and puzzles. However, it does not explicitly differentiate from sibling tools like solve_constraint_programming or solve_linear_programming, leaving some ambiguity about when to choose this specific solver.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description says the tool is 'ideal for' certain problem types but provides no guidance on when not to use it or how it compares to sibling tools (e.g., constraint programming, convex optimization). Without explicit exclusions or alternatives, an AI agent lacks the context to choose correctly.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
solve_convex_optimizationA
Solve convex optimization problems using CVXPY.
This tool is ideal for mathematical optimization problems with convex objectives
and constraints, including linear programming, quadratic programming, and
semidefinite programming.
Args:
variables: List of variable definitions with 'name' and 'shape'
objective_type: Either 'minimize' or 'maximize'
objective_expr: The objective function expression as a string
constraints: List of constraint expressions as strings
parameters: Dictionary of parameter values (e.g., matrices A, b)
description: Optional problem description
Returns:
Solution results including variable values and objective value
Example:
variables = [{"name": "x", "shape": 2}]
objective_type = "minimize"
objective_expr = "cp.sum_squares(x)"
constraints = ["x >= 0", "cp.sum(x) == 1"]
| Name | Required | Description | Default |
|---|---|---|---|
| variables | Yes | ||
| objective_type | Yes | ||
| objective_expr | Yes | ||
| constraints | Yes | ||
| parameters | No | ||
| description | No |
TDQS
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description carries the full burden. It briefly mentions CVXPY but does not disclose behavioral traits such as side effects, authorization needs, or performance characteristics. The description is minimal in this regard.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is well-structured with a one-liner, a clarifying paragraph, parameter documentation, return info, and an example. It is front-loaded and each part serves a purpose, though the example could be more integrated.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given the absence of an output schema and annotations, the description covers input parameters well but falls short on return value details (only 'solution results including variable values and objective value'). The example helps, but more specifics on result structure are needed.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
The input schema has 0% description coverage, but the tool description includes a detailed parameter list with explanations (e.g., 'variables: List of variable definitions with name and shape') and an example. This adds significant meaning beyond the schema, though some details (e.g., shape format) could be clearer.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states that the tool solves convex optimization problems using CVXPY, and lists specific problem types (linear, quadratic, semidefinite programming). This distinguishes it from sibling tools like solve_constraint_satisfaction.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
The description says it is 'ideal for convex optimization problems' which implies usage context, but it does not explicitly state when not to use it or mention alternative sibling tools. There is no direct guidance on choosing among similar tools.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
solve_linear_programmingA
Solve linear and mixed-integer programming problems using HiGHS.
This tool is ideal for linear programming, mixed-integer linear programming,
and large-scale optimization problems with linear constraints.
Args:
sense: Optimization sense, either "minimize" or "maximize"
objective_coeffs: List of objective function coefficients
variables: List of variable definitions with optional bounds and types
constraint_matrix: 2D list representing the constraint matrix (dense format)
constraint_senses: List of constraint directions ("<=", ">=", "=")
rhs_values: List of right-hand side values for constraints
options: Optional solver options dictionary
description: Optional problem description
Returns:
Solution results including variable values and objective value
Example:
sense = "minimize"
objective_coeffs = [1.0, 2.0, 3.0]
variables = [
{"name": "x1", "lb": 0, "ub": 10, "type": "cont"},
{"name": "x2", "lb": 0, "ub": None, "type": "int"},
{"name": "x3", "lb": 0, "ub": 1, "type": "bin"}
]
constraint_matrix = [[1, 1, 0], [0, 1, 1]]
constraint_senses = ["<=", ">="]
rhs_values = [5, 3]
| Name | Required | Description | Default |
|---|---|---|---|
| sense | Yes | ||
| objective_coeffs | Yes | ||
| variables | Yes | ||
| constraint_matrix | Yes | ||
| constraint_senses | Yes | ||
| rhs_values | Yes | ||
| options | No | ||
| description | No |
TDQS
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations provided, so description carries full burden. It describes solving behavior, variable types, and input format, but doesn't mention side effects, error handling, or performance characteristics. Adequate but not detailed.
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
Well-structured: purpose sentence, ideal-use sentence, Args list, Returns line, and example. Slightly verbose due to extensive example, but example is highly valuable for understanding parameter usage.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
Given 8 parameters (6 required), nested objects, and no output schema, the description covers all parameters with explanations, an example, and return description. It is complete and actionable for an agent.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, but the description provides a detailed Args section with explanations for all parameters and a comprehensive example, adding significant meaning beyond the bare schema.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states 'Solve linear and mixed-integer programming problems using HiGHS', specifying the exact type of problems (linear, MILP, large-scale with linear constraints). This differentiates it from siblings like solve_constraint_programming and solve_convex_optimization.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
It says 'ideal for linear programming, mixed-integer linear programming, and large-scale optimization problems with linear constraints', guiding when to use. However, it does not explicitly state when not to use or mention alternatives, though sibling names imply distinction.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
solve_portfolio_optimizationA
Solve portfolio optimization problems using modern portfolio theory.
This tool implements Markowitz mean-variance optimization to find optimal
asset allocations that maximize expected return while constraining risk.
Args:
assets: List of asset names
expected_returns: List of expected returns for each asset
risk_factors: List of risk factors (standard deviations) for each asset
correlation_matrix: Correlation matrix between assets
max_allocations: Optional maximum allocation limits for each asset
risk_budget: Optional maximum portfolio risk (variance)
description: Optional problem description
Returns:
Optimal portfolio weights and performance metrics
Example:
assets = ["Bonds", "Stocks", "RealEstate", "Commodities"]
expected_returns = [0.08, 0.12, 0.10, 0.15]
risk_factors = [0.02, 0.15, 0.08, 0.20]
correlation_matrix = [[1.0, 0.2, 0.3, 0.1], [0.2, 1.0, 0.6, 0.7], ...]
max_allocations = [0.4, 0.6, 0.3, 0.2]
risk_budget = 0.01
| Name | Required | Description | Default |
|---|---|---|---|
| assets | Yes | ||
| expected_returns | Yes | ||
| risk_factors | Yes | ||
| correlation_matrix | Yes | ||
| max_allocations | No | ||
| risk_budget | No | ||
| description | No |
TDQS
Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?
No annotations are provided, so the description must bear the full burden. It describes the optimization goal (maximize return, constrain risk) and mentions returns, but lacks details on computational assumptions, error handling, or prerequisites (e.g., positive semidefinite correlation matrix).
Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.
Is the description appropriately sized, front-loaded, and free of redundancy?
The description is well-structured with a clear purpose statement, followed by an Args list, Returns, and Example. Every sentence adds value; no redundant information. It is concise yet comprehensive.
Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.
Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?
The description covers the tool's purpose, parameters, and returns. However, without an output schema, the return format is vague ('weights and performance metrics'). Missing details on error conditions or validation. Given complexity, it is mostly complete for basic usage.
Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.
Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?
Schema description coverage is 0%, so the description compensates well by listing each parameter with its meaning (e.g., 'List of expected returns', 'Optional maximum allocation limits') and providing a concrete example. It does not specify shape constraints or validation rules, but the example illustrates usage.
Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.
Does the description clearly state what the tool does and how it differs from similar tools?
The description clearly states it solves portfolio optimization problems using modern portfolio theory (Markowitz mean-variance). The verb 'solve' and resource 'portfolio optimization' are specific and distinct from sibling tools like solve_convex_optimization or solve_linear_programming.
Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.
Does the description explain when to use this tool, when not to, or what alternatives exist?
There is no explicit guidance on when to use this tool versus alternatives like solve_convex_optimization. The example implies usage for asset allocation, but no criteria for when not to use or what alternatives are available.
Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.
TDQS
Each tool targets a distinct optimization paradigm or solver (OR-Tools, Z3, CVXPY, HiGHS, Markowitz), but there is slight overlap between constraint programming and constraint satisfaction, and convex optimization encompasses linear programming. Descriptions clarify differences.
All tools follow the consistent pattern 'solve_<descriptive_noun>', using snake_case and clear terminology for the optimization type.
With 5 tools covering major constrained optimization paradigms, the count is well-scoped for the server's purpose. It covers a broad range without being overwhelming.
The set covers constraint programming, satisfaction, convex, linear, and portfolio optimization. Missing non-convex nonlinear optimization and stochastic optimization, but major paradigms are present.
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