Add cuopt-multi-objective-exploration skill (Pareto frontier)

[cafzal]

Description

Adds cuopt-multi-objective-exploration — a concept skill for problems with two or more objectives and no fixed weighting, where the user wants to see the tradeoff instead of accepting one weighted answer. It turns repeated single-objective cuOpt solves into a Pareto frontier (payoff table → ε-constraint / weighted-sum sweep → filter dominated) and supplies the discipline to read it: exchange rates, knee points, deferring the final choice. It adds no solver features and invents no API; it sits above the api-* and formulation skills, orchestrating the solves they already cover.

cuOpt-specific correctness points

• ε-constraining is most natural on linear objectives, so a quadratic objective (risk xᵀΣx) can simply stay the objective. A convex one can also be ε-constrained directly: cuOpt routes xᵀQx ≤ ε through the barrier solver as a second-order cone.
• PDLP warm-start is LP-only; MILP frontier points are optimal to the gap you set, since each solve gets a time limit.
• A hard constraint (coverage floor, budget, fairness cap) is often a latent objective — promote it to a swept ε-constraint (when its level was an assumption, not a firm limit).

User testing

Used the skill to enrich two existing examples and confirmed it drove the right calls — companion PR NVIDIA/cuopt-examples#151:

• Workforce (MILP) — promoted two hard constraints into tradeoffs (coverage → cost vs. coverage; the max_shifts cap → cost vs. fairness), chose ε-constraint over weighted-sum, anchored objective ranges, filtered dominated points, capped each solve, and reported no MILP duals.
• Portfolio (QP) — recognized the base notebook's hand-coded target-return loop as ε-constraint and added what it omits: the return-constraint dual (shadow price d(variance)/d(return)), with the PDLP-tolerance caveat.

The skill drives the method; runnable code still needs cuopt-numerical-optimization-api-python plus the worked notebooks, which are Colab-GPU validated (T4, clean end-to-end).

Validation & gating

Registered in AGENTS.md + marketplace.json; ci/utils/validate_skills.sh passes. The contribution is SKILL.md + evals/evals.json — BENCHMARK.md, the skill card, and skill.oms.sig are generated by the NVSkills onboarding pipeline. The official NVSkills-Eval is the gate (PENDING).

Checklist

• I am familiar with the Contributing Guidelines.
• Testing
  • New or existing tests cover these changes
  • Added tests
  • Created an issue to follow-up
  • NA
• Documentation
  • The documentation is up to date with these changes
  • Added new documentation
  • NA

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[rgsl888prabhu]

@cafzal Thank you for the draft PR, do you have access to push PR branch to main repo? Currently there is a requirement for skill related PRs to be made available in main repo to trigger CI pipe line.

Once you have done that, pipeline will validate and eval. It will also create BENCHMARK.md and skill card.

[cafzal]

Thank you for the draft PR, do you have access to push PR branch to main repo? Currently there is a requirement for skill related PRs to be made available in main repo to trigger CI pipe line.

Once you have done that, pipeline will validate and eval. It will also create BENCHMARK.md and skill card.

@rgsl888prabhu I don't have write access to NVIDIA/cuopt (push: false), so I've been working from my own fork.

Could you either:

1. Push this PR's branch to the main repo on your end so the skill CI can run; or
2. Add me as a collaborator (write access) and I'll push it up.

Either works for me. Thanks.

[rgsl888prabhu]

Thank you for the draft PR, do you have access to push PR branch to main repo? Currently there is a requirement for skill related PRs to be made available in main repo to trigger CI pipe line.
Once you have done that, pipeline will validate and eval. It will also create BENCHMARK.md and skill card.

@rgsl888prabhu I don't have write access to NVIDIA/cuopt (push: false), so I've been working from my own fork.

Could you either:

1. Push this PR's branch to the main repo on your end so the skill CI can run; or
2. Add me as a collaborator (write access) and I'll push it up.

Either works for me. Thanks.

Hmm, even if I create a branch, don't think you will be able to push changes to that. And the CI requires elevated access to run. So for now, lets review and merge this PR through this. And I will create another PR once it is merged to trigger to create new skill card and BENCHMARK.md.

[cafzal]

Sounds good @rgsl888prabhu . I marked this PR as ready for review:

Waiting on code owner review from NVIDIA/cuopt-infra-codeowners

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📝 Walkthrough

Walkthrough

This PR adds a new cuopt-multi-objective-exploration skill registered in the marketplace, documents a stepwise Pareto-frontier exploration workflow, supplies evaluation cases for multi-objective reasoning, and cross-references the new skill from numerical optimization formulation guidance.

Changes

Multi-objective Exploration Skill

Layer / File(s)	Summary
Skill registration and agent documentation .claude-plugin/marketplace.json, AGENTS.md	The new skill is registered in the marketplace manifest pointing to ./skills/cuopt-multi-objective-exploration and added to the agent skills listing as a concept-level skill for Pareto-frontier exploration.
Pareto frontier exploration workflow and evaluation skills/cuopt-multi-objective-exploration/SKILL.md, skills/cuopt-multi-objective-exploration/evals/evals.json	Comprehensive documentation defines the complete workflow: frontmatter, core Pareto concepts, four practical steps (payoff-table construction, scalarization method selection with weighted-sum vs ε-constraint tradeoffs, sweep/collection with warm-start and MILP guidance, and result interpretation with knee-point and tradeoff reporting). Evaluation cases validate multi-objective reasoning and correctly reject single-objective hard-constraint problems.
Cross-reference in formulation skill skills/cuopt-numerical-optimization-formulation/SKILL.md	The existing formulation skill is updated to direct users to the new multi-objective skill when objectives conflict without fixed priority, recommending ε-constraint or weighted-sum Pareto sweeps for non-dominated solution filtering.

🎯 2 (Simple) | ⏱️ ~12 minutes

🚥 Pre-merge checks | ✅ 5

✅ Passed checks (5 passed)

Check name	Status	Explanation
Title check	✅ Passed	The title directly and clearly describes the main change: adding a new skill for multi-objective exploration using Pareto frontier methodology, which is the core objective of the PR.
Docstring Coverage	✅ Passed	No functions found in the changed files to evaluate docstring coverage. Skipping docstring coverage check.
Linked Issues check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Out of Scope Changes check	✅ Passed	Check skipped because no linked issues were found for this pull request.
Description check	✅ Passed	The PR description provides comprehensive context about the skill, its methodology, cuOpt-specific considerations, user testing, and validation status, clearly relating to all changes in the changeset.

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✨ Finishing Touches

🧪 Generate unit tests (beta)

• Create PR with unit tests

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[coderabbitai]

Actionable comments posted: 1

Caution

Some comments are outside the diff and can’t be posted inline due to platform limitations.

⚠️ Outside diff range comments (1)

skills/cuopt-multi-objective-exploration/SKILL.md (1)

1-136: ⚠️ Potential issue | 🟠 Major | ⚡ Quick win

Block merge until NVSkills CI maintainer validation is present.

This PR modifies skills/**, but the provided context states NVSkills-Eval is still pending. Per policy, merge should wait for a maintainer /nvskills-ci validation comment.

As per coding guidelines skills/**: “PRs that change content under 'skills/' must be validated by NVSkills CI with maintainer '/nvskills-ci' comment before merge”.

🤖 Prompt for AI Agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

In `@skills/cuopt-multi-objective-exploration/SKILL.md` around lines 1 - 136, The
PR modifies content under skills/ (the skill named
"cuopt-multi-objective-exploration" in SKILL.md) but lacks the required NVSkills
CI maintainer validation; before merging, add or request the maintainer
'/nvskills-ci' validation comment (or otherwise obtain NVSkills CI approval) so
the CI gate for skills/** is satisfied and the change can be merged.

🤖 Prompt for all review comments with AI agents

Verify each finding against current code. Fix only still-valid issues, skip the
rest with a brief reason, keep changes minimal, and validate.

Inline comments:
In `@skills/cuopt-multi-objective-exploration/SKILL.md`:
- Around line 48-53: Update all fenced code blocks in SKILL.md to include a
language identifier (e.g., add "text" after the opening triple backticks) so
markdownlint MD040 is satisfied; specifically, change fences that currently
start with ``` to ```text for blocks containing the table ("f1 f2 f3" grid), the
weighted-objective line ("minimize  w1·f1(x) + w2·f2(x) + ..."), the
ε-constrained example ("minimize  f1(x) subject to  f2(x) ≤ ε2 ..."), and the
pseudocode block beginning with "frontier = []" (and any other similar fenced
sections at the noted locations). Ensure each opening fence has the language
token while leaving the block contents unchanged.

---

Outside diff comments:
In `@skills/cuopt-multi-objective-exploration/SKILL.md`:
- Around line 1-136: The PR modifies content under skills/ (the skill named
"cuopt-multi-objective-exploration" in SKILL.md) but lacks the required NVSkills
CI maintainer validation; before merging, add or request the maintainer
'/nvskills-ci' validation comment (or otherwise obtain NVSkills CI approval) so
the CI gate for skills/** is satisfied and the change can be merged.

🪄 Autofix (Beta)

Fix all unresolved CodeRabbit comments on this PR:

• Push a commit to this branch (recommended)
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---

ℹ️ Review info

⚙️ Run configuration

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Review profile: CHILL

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Run ID: af2492a4-3014-4982-adde-ccd81d315e52

📥 Commits

Reviewing files that changed from the base of the PR and between c4e878d and 7b70227.

📒 Files selected for processing (5)

• .claude-plugin/marketplace.json
• AGENTS.md
• skills/cuopt-multi-objective-exploration/SKILL.md
• skills/cuopt-multi-objective-exploration/evals/evals.json
• skills/cuopt-numerical-optimization-formulation/SKILL.md

[cafzal]

Ready on my side. Once it's on a non-fork branch, two things clear the checks:

1. NVSkills CI - /nvskills-ci for eval
2. Label Checker to add add improvement + non-breaking

Thanks!

[rgsl888prabhu]

@mlubin may I get your review on this PR ?

[mlubin]

I can see this skill being useful, thanks for the contribution.

[cafzal]

Thanks @mlubin , I addressed your review comments and lightly revamped the workflow steps for clarity and consistency.

[rgsl888prabhu]

/ok to test abbafe7

[rgsl888prabhu]

@cafzal Thank you for the awesome skill, once CI passes, will merge it and then create a new PR for eval

[rgsl888prabhu]

/merge