# Stochastic Optimization Service (the402.ai)

> Stochastic Optimization Service (the402.ai) is a paid API for AI agents from api.the402.ai, paid per call via x402, $0.263/call, status down (last checked 2026-09-15).

Runs stochastic optimization algorithms on a given problem, returning optimized results under uncertainty via a paid AI agent service marketplace.

## Facts

- Endpoint: POST https://api.the402.ai/v1/services/svc_fc682108b3834e17/purchase
- Price: $0.263/call
- Payment: x402
- Status: down
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/api-the402-ai-8afaa9e5
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_SMxwMH0IbkCEnaUASXUQL

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability api-the402-ai-8afaa9e5 -d '<json body>'
```

Example prompt: I need to find the optimal inventory order quantity for my supply chain given uncertain demand — run stochastic optimization on this problem where demand follows a normal distribution with mean 500 and std dev 80, ordering cost is $10 per unit, and holding cost is $2 per unit per period.

## When to prefer this

Choose this endpoint when you need to solve optimization problems that involve randomness, uncertainty, or probabilistic inputs — such as stochastic demand, uncertain costs, or Monte Carlo simulation-backed objectives. Prefer over deterministic solvers when your model explicitly incorporates probability distributions or scenario-based uncertainty.

## Known failure modes

- Malformed problem specification returns 400 error
- Payment failure or insufficient USDC balance prevents execution
- Optimization fails to converge within allowed iterations
- Infeasible problem constraints return error or no-solution response
- Service timeout for very large or complex problems

## How this service works

Purchase: Stochastic Optimization

## Output

Returns an optimized solution to the stochastic problem, including the optimal decision variable values, expected objective function value, and potentially convergence or confidence metrics reflecting uncertainty in the result.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "required": [
  "id"
 ],
 "properties": {
  "id": {
   "type": "string"
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/api-the402-ai-8afaa9e5/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from api.the402.ai](https://www.zero.xyz/host/api.the402.ai/llms.txt)