AnnealBridge MCP Server

AnnealBridge

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Combinatorial optimization middleware for AI agents. An agent describes what to optimize as structured JSON; AnnealBridge decides how to encode and solve it, checks every answer against the original problem, and returns ranked, verified solutions over MCP, a CLI, or plain Python.

flowchart LR
    U[Natural language] --> A[AI agent]
    A -->|OptimizationProblem JSON<br/>variables · objective · constraints| B
    subgraph B[AnnealBridge]
        direction LR
        V[validate] --> C[compile<br/>BQM / CQM] --> S[solve<br/>local or remote] --> R[re-validate against<br/>the original problem] --> K[rank]
    end
    B -->|SolveResult<br/>ranked, verified solutions| A
    A --> N[Natural-language answer]

Quick start

pip install annealbridge

A 0/1 knapsack: four items, capacity 10, maximize value. No file needed.

from annealbridge.models import OptimizationProblem
from annealbridge.orchestration import OptimizationService

problem = OptimizationProblem.model_validate({
    "version": "1.0",
    "name": "knapsack",
    "variables": [{"name": n, "type": "binary"} for n in ["a", "b", "c", "d"]],
    "objective": {"direction": "maximize", "linear_terms": [
        {"variable": "a", "coefficient": 10}, {"variable": "b", "coefficient": 8},
        {"variable": "c", "coefficient": 7}, {"variable": "d", "coefficient": 6}]},
    "constraints": [{"id": "capacity", "type": "hard", "operator": "<=", "rhs": 10, "terms": [
        {"variable": "a", "coefficient": 6}, {"variable": "b", "coefficient": 5},
        {"variable": "c", "coefficient": 4}, {"variable": "d", "coefficient": 3}]}],
})

result = OptimizationService().solve(problem)
print(result.status)                        # success
print(result.solutions[0].variables)        # {'a': 1, 'b': 0, 'c': 1, 'd': 0}
print(result.solutions[0].objective_value)  # 17.0

Domain failures come back as results, never as exceptions: result.status is one of success, infeasible, invalid_problem, resource_limit_exceeded, backend_unavailable, configuration_error or solver_error. See docs/output-format.md.

Optional extras:

pip install "annealbridge[mcp]"       # + MCP server (annealbridge-mcp)
pip install "annealbridge[dwave]"     # + D-Wave cloud backends
pip install "annealbridge[all]"       # everything
pip install "annealbridge[gpu]"       # + PyTorch, for simulated_bifurcation on CUDA

[gpu] is deliberately not part of [all]: PyTorch is a large download, and on Windows the wheel PyPI serves is the CPU-only build, so a CUDA run needs torch installed from PyTorch's own index first — see docs/backends.md.

Use it from an AI agent (MCP)

With uv installed, add the server to claude_desktop_config.json (or your host's equivalent) and restart the host; where Claude Desktop, Claude Code and Codex keep that configuration is listed in docs/mcp.md. The first run fetches the package into uvx's own cached environment; that download — numpy, dimod, dwave-samplers and the rest — can take tens of seconds, long enough for a host's start-up timeout to show the server as disconnected. Warm the cache once in a terminal first:

uvx --from "annealbridge[mcp]" annealbridge-mcp --version

It resolves the environment and prints the version; from then on the host starts from that cache.

{
  "mcpServers": {
    "annealbridge": {
      "command": "uvx",
      "args": ["--from", "annealbridge[mcp]", "annealbridge-mcp"]
    }
  }
}

Claude Code registers it in one line:

claude mcp add annealbridge -- uvx --from "annealbridge[mcp]" annealbridge-mcp

Optimizing is then an ordinary chat:

You: I can carry 10 kg. Item A is worth 10 and weighs 6, B is worth 8 and weighs 5, C is worth 7 and weighs 4, D is worth 6 and weighs 3. Which ones should I take?

Behind the reply, the agent writes the request as problem JSON and calls solve_optimization. Every solution comes back re-validated against the original constraints, with optimality_proven: true on the exhaustive exact backend; a document the server rejects comes back as invalid_problem with every error and a fix for each, which the agent applies before sending it again. Before solving on a remote backend, or on a large problem, it calls validate_optimization_problem first, so a mistake costs nothing; it calls get_optimization_capabilities when it needs the backend list or the full schema.

Agent: Take A and C: value 17 at exactly 10 kg. The runners-up are A and D (16, at 9 kg) and B and C (15, at 9 kg). This is the proven optimum.

The wording is the agent's; the numbers are the tool result. Another tool, recommend_backend, ranks the backends for a problem and is advisory only; when you did not name a backend and more than one local backend fits, the server instructions tell the agent to show the top entries and ask which to run rather than to decide for you.

If your host lists prompts in its input menu, three of them — pick_subset, assign and schedule_shifts — walk the agent from your own sentence to a problem document of that everyday shape, which it then solves. The server also serves resources: the five example documents under annealbridge://examples/ and the full problem schema at annealbridge://schema, so an agent can read a complete example or the schema itself instead of guessing.

What it is not for. AnnealBridge does not handle continuous (real-valued) variables, non-linear objectives or non-linear constraints. Only exact proves that an answer is optimal or that no feasible one exists, and by default it takes at most 24 compiled variables (slack bits included); the other local backends (simulated_annealing, tabu, simulated_bifurcation) are heuristics whose best answer may not be the optimum. See the Backends table below and docs/limitations.md.

Any stdio-capable MCP host works the same way, a streamable-http transport exists, and pipx or a pip-installed server behind an absolute path work in place of uvx. uvx reuses the environment it resolved on its first run, so a new release reaches an existing install only after uv cache clean annealbridge and a host restart; see docs/mcp.md.

Use it from the command line

Save the problem JSON below as knapsack.json, then:

annealbridge solve knapsack.json

Problem:   knapsack
Backend:   exact
Status:    success
Attempts:  1
Elapsed:   2.7 ms

Best solution (rank 1)
  objective (maximize):  17
  soft violation score:  0
  item_a = 1
  item_b = 0
  item_c = 1
  item_d = 0

Hard constraints: 1 / 1 satisfied
Soft constraints: 0 violations
Optimality proven: yes

Elapsed is the service's own wall clock and varies from run to run. Add --json for the full SolveResult, --backend simulated_annealing to override the backend, or try validate, recommend, capabilities, example and export-schema. See docs/cli.md.

The problem JSON

The document behind the MCP and CLI examples above, the reduced form of examples/knapsack.json:

{
  "version": "1.0",
  "name": "knapsack",
  "variables": [
    {"name": "item_a", "type": "binary"},
    {"name": "item_b", "type": "binary"},
    {"name": "item_c", "type": "binary"},
    {"name": "item_d", "type": "binary"}
  ],
  "objective": {
    "direction": "maximize",
    "linear_terms": [
      {"variable": "item_a", "coefficient": 10},
      {"variable": "item_b", "coefficient": 8},
      {"variable": "item_c", "coefficient": 7},
      {"variable": "item_d", "coefficient": 6}
    ]
  },
  "constraints": [
    {
      "id": "capacity",
      "type": "hard",
      "terms": [
        {"variable": "item_a", "coefficient": 6},
        {"variable": "item_b", "coefficient": 5},
        {"variable": "item_c", "coefficient": 4},
        {"variable": "item_d", "coefficient": 3}
      ],
      "operator": "<=",
      "rhs": 10
    }
  ],
  "solver": {"backend": "exact"}
}

Integer variables ("type": "integer" with bounds, "version": "1.1"), quadratic objective terms, soft constraints with weights and per-backend solver preferences are described in docs/problem-format.md. annealbridge export-schema prints the JSON Schema an agent can use for structured output.

Five ready-to-run examples live in the repository — knapsack, assignment, TSP, integer knapsack and shift scheduling. The installed package carries the same files: annealbridge example lists them and annealbridge example knapsack > knapsack.json saves one (or pipe it straight in with annealbridge example knapsack | annealbridge solve -); the MCP server serves the same five documents as the resources under annealbridge://examples/.

How it works

The agent produces an OptimizationProblem: binary or bounded-integer variables, a linear or quadratic objective, and hard or soft linear constraints. Nothing else. AnnealBridge then, deterministically:

1. validates the problem and collects every error in one pass;
2. compiles it into a BQM or a CQM, computing penalties, slack and integer encodings itself;
3. solves it on a local or remote backend;
4. re-validates every candidate against the original JSON, never trusting solver energy;
5. ranks the feasible solutions and returns the top K with per-constraint evaluations.

An opt-in solver.postprocess step can also repair and locally improve the best samples in the original variables before ranking; what it produces is re-validated like any other candidate and marked by each solution's source. An optional solver.wall_clock_limit_seconds caps how long a solve on a local heuristic backend may take: when it runs out, the result holds what was completed, still re-validated and ranked, and says so (wall_clock_limit_reached). An MCP client that cancels a solve stops it rather than leaving it to run on.

The agent never writes a QUBO matrix, a penalty weight, a slack variable or an integer encoding, and every step is testable without an AI, a network or a vendor account.

Backends

Eight backends sit behind one protocol.

Remote backends need their vendor credential and ANNEALBRIDGE_ALLOW_REMOTE=true; without both they report backend_unavailable. annealbridge recommend ranks the backends for a problem without solving it and never changes the one you asked for. Setup and per-backend behaviour: docs/backends.md.

Design guarantees

• Business-level contract in both directions. Variables, objective and constraints in; ranked solutions with per-constraint evaluations out. No solver internals leak either way.
• Two compiler paths. BQM (automatic penalties, binary slack, encoded integers) for annealers; CQM (native constraints and integers) for the Leap hybrid CQM solver. The backend chooses by declaring what it supports.
• Bounded integers without exposure. "version": "1.1" adds integer variables with the encoding hidden; 1.0 behaviour is pinned by a golden test.
• Structured failures, never exceptions. Every outcome is a SolveResult with a status; every failure carries a stable error code with a recommended_action. infeasible is an answer, not a failure.
• No silent decisions. An unavailable backend is reported, never swapped. An over-limit parameter is rejected, never clamped. An undeclared field is rejected, never ignored. Validator warnings travel with every solve result.
• Safe by default. Remote execution and remote retries are off until enabled; every limit is an environment variable enforced as an error; vendor credentials are redacted from results, logs and error messages. The streamable-http transport has no authentication; keep it on a private network. See docs/security.md and SECURITY.md.
• Enforced architecture. Import boundaries, "no backend names in the orchestration, validation or interface layers", and "a new backend plugs in without touching the pipeline" are tests, not conventions.

Documentation

The pages below live under docs/.

Development

git clone https://github.com/TheTsungYing/AnnealBridge.git
cd AnnealBridge
pip install -e ".[all,dev]"
pytest

pytest runs the full suite with no skip and no xfail and never touches the network; the live vendor tests are opt-in (pytest -m remote). To install the development version without a checkout: pip install "annealbridge[all] @ git+https://github.com/TheTsungYing/AnnealBridge.git". Architecture rules, design principles and the pull-request checklist are in CONTRIBUTING.md.

Version 0.3.0: the problem contract (1.0 / 1.1), the eight backends, the CLI and the MCP tools are complete and covered by tests. What is not supported, by design for now, is listed in docs/limitations.md; changes are in CHANGELOG.md.

License

MIT