ConstraintBench (Joint Optimality) - Portfolio Optimization: leaderboard
Metric: Joint optimality rate (%): share of the domain's 20 tasks whose solution is feasible and within 0.1 percent of the solver-proven optimum (portfolio optimization domain); ConstraintBench's 200 fully specified constrained-optimization tasks in natural language (20 per operations-research domain, each Gurobi-solved to proven optimality); the model returns a structured solution directly, without a solver, which a deterministic verifier checks against every constraint; one trial per task, OpenAI models at high reasoning effort and Claude with extended thinking (55,000 reasoning tokens), Gemini at its default; higher is better. Source: arxiv.org. Saturation forecast: Around January 2028. 6 models tracked.
Top models
| # | Model | Score | Overall rank |
|---|---|---|---|
| 1 | Claude Opus 4.6 (Thinking) | 25 | #60 (Claude Opus 4.6) |
| 2 | GPT-5.2 (High) | 10 | #105 (GPT-5.2) |
| 3 | Gemini 3 Pro (Preview) | 0 | #64 |
| 4 | Claude Opus 4.5 (Thinking) | 0 | #79 (Claude Opus 4.5) |
| 5 | O4 Mini (High) | 0 | #172 (O4 Mini) |
No result here: #3 Claude Opus 5.5, #5 GPT-6 Astra, #8 Claude Fable 5.1.
Interactive version: theaggregate.ai/benchmark?slug=constraintbench-joint-optimality-portfolio-optimization · How It Works · Data refreshed daily, snapshot 2026-10-11.