docs(simulation): Optimization concept

src/pages/docs/simulation/concepts/optimization.mdx

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+---
+title: "Optimization"
+description: "Let an algorithm search for a better prompt when hand-fixing isn't enough"
+---
+
+## What optimization is
+
+**Optimization** improves your agent's prompt and configuration automatically, scored by the same evals your simulation runs. Rather than hand-editing the prompt and rerunning, you let an algorithm propose and test many variations and hand you the best one. It's what Fix My Agent is built on: the diagnosis names what is wrong, and an optimization run does the rewriting.
+
+## How a run works
+
+An optimization run is a search for a better prompt, judged by your evals.
+
+<Mermaid chart={`
+%%{init: {"flowchart": {"curve": "linear"}}}%%
+flowchart LR
+    IN["Simulation results<br/>+ eval scores"] --> ALG["Algorithm<br/>proposes candidates"]
+    ALG --> TR["Trials<br/>each candidate run"]
+    TR --> SC["Scores"]
+    SC --> BEST["Best configuration"]
+`} />
+
+Say your refund agent keeps failing a resolution eval. You feed those failing calls in, the algorithm generates candidate prompts, each one is trialed against your scenarios and scored on that same eval, and the best-performing prompt surfaces for you to review and apply. Because the score is your own eval, the winner is the prompt that best satisfies the bar you set.
+
+## The algorithms
+
+You pick the search strategy to match the task and budget:
+
+- **Random Search**, quick variations for a fast baseline
+- **Bayesian**, intelligent selection of few-shot examples and configurations
+- **Meta-Prompt**, analyses failures and rewrites the whole prompt through deeper reasoning
+- **ProTeGi**, critiques failures and applies targeted fixes with beam search
+- **PromptWizard**, mutates across thinking styles, then critiques and refines the top ones
+- **GEPA**, an evolutionary search for production-grade results at the highest cost
+
+The [Optimization](/docs/optimization) product docs cover each algorithm in depth.
+
+## Optimization and Fix My Agent
+
+The two work together. Fix My Agent reads a run and hands you a prioritised list of issues with recommended fixes you apply by hand. An optimization run goes further and executes the improvement automatically, generating and scoring prompts until it finds a better one. Start with Fix My Agent's suggestions, and reach for optimization when manual fixes aren't enough.
+
+## Keep exploring
+
+<CardGroup cols={2}>
+  <Card title="Runs & results" icon="chart-mixed" href="/docs/simulation/concepts/runs-and-results">
+    The results an optimization run learns from
+  </Card>
+  <Card title="Agent definitions & versions" icon="robot" href="/docs/simulation/concepts/agent-definitions">
+    Save the improved prompt as a new version
+  </Card>
+</CardGroup>