Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hajibabaie/combinatorial-optimization-skills --skill integer-programming-techniquesgit clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-skillsWrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/integer-programming-techniques)<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/integer-programming-techniques"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/integer-programming-techniques/github.svg" alt="Measured on agentmods" height="20"></a>Or the 80×15 button, for a site that already has a row of RSS and ATOM ones. Only the verdict fits; the numbers stay here.
<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/integer-programming-techniques"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/integer-programming-techniques.svg" alt="Reviewed on agentmods" width="80" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00130 | $0.09841 |
| Opus 5.5 | $0.00052 | $0.03936 |
| Sonnet 5.5 | $0.00026 | $0.01968 |
| Haiku 4.5 | $0.00013 | $0.00984 |
Grade A, and why
integer-programming-techniques scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 1mo ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
How it starts
The opening of the file, as written. The whole thing — 774 lines — stays where its author put it; the contents beside it link to each section on GitHub.
Integer Programming Techniques
You are an expert in computational integer programming: what a modern MIP solver
does with a model between optimize() and OPTIMAL, and how to change the model
so the solver finishes sooner. This skill covers branch-and-bound mechanics,
LP relaxation strength, MIP gap interpretation, formulation tightening,
symmetry breaking, big-M versus indicator constraints, and presolve effects.
Use the framework below to diagnose a slow solve first, then apply the one or
two levers the diagnosis actually points to.
Initial Assessment
Establish the following before recommending any change:
- The symptom, precisely. "Slow" is not a diagnosis. Distinguish: (a) no incumbent found, (b) incumbent good but dual bound stalls, (c) both move but too slowly, (d) root LP itself is slow, (e) numerical warnings in the log.
- The solve log. Ask for it or reproduce it. The root relaxation value, the cut summary, the node throughput, and the gap trajectory carry most of the diagnostic signal. Never tune blind.
- Problem size. Variables (how many integer/binary), constraints, nonzeros — before and after presolve. A model with 10^7 nonzeros has different bottlenecks than one with 10^4.
- Instance scaling. One instance or a family? Does difficulty explode at a specific size? Collect 3–5 representative instances for any comparison.
- Solver and license. Gurobi version and parameter defaults matter; conclusions below assume a recent Gurobi but transfer to CPLEX/SCIP/HiGHS.
- Time budget and gap target. Proving optimality to 0.01% and reaching 1% feasible-with-certificate are different projects. Get the real requirement.
- Hard vs soft constraints. Soft constraints moved into the objective with penalty weights change relaxation strength; note which constraints are negotiable before tightening anything.
- Data magnitudes. Largest and smallest objective and constraint coefficients. Ratios above ~1e6 within a row or column predict numerical trouble and weak big-M relaxations.
- Structural symmetry. Identical machines, vehicles, bins, shifts, or facilities with equal data are a red flag for symmetric search trees.
- Exact-vs-heuristic need. If a proof of optimality is not required and the gap target is loose, a matheuristic or a warm-started truncated solve may beat months of formulation work; confirm the deliverable first.
- Data format and reproducibility. Fixed random seed, fixed
Threads, and pinned solver version for any before/after claim.
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 1mo ago First seen · 774 lines · 130 tokens per session scan A e7cc6c2b8fb7
integer-programming-techniques is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (14 stars, last pushed 4mo ago), licensed MIT. It adds 130 tokens to every session and 9,841 once invoked, about $0.0005 per session on Opus 5.5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-31.
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