column-generation

column-generation is a skill for Claude Code from hajibabaie/combinatorial-optimization-skills. It costs 124 tokens per session (11,844 once invoked), scanned A, original, MIT.

An optimization method for problems with too many variables to list in advance. It repeatedly solves a smaller restricted master problem and searches for new variables, called columns, that could improve the result.

In plain words
What is it for?
Use it for problems involving routes, cutting patterns, crew pairings, machine schedules, or clusters. It covers pricing problems, reduced costs, stabilization, and branching rules compatible with column generation.
Why use it?
It avoids building an enormous model all at once when each variable can be generated from a structured subproblem. The method can provide bounds and can be extended to branch-and-price for integer solutions.

Skill for Claude Code

Written for Claude Code: shipped in a Claude Code plugin. Also seen: positional $N argument.

Part of the combinatorial-optimization plugin — 76 skills shipped together

Good fit Use it for problems involving routes, cutting patterns, crew pairings, machine schedules, or clusters. It covers pricing problems, reduced costs, stabilization, and branching rules compatible with column generation.

Compare 6 skills from other repositories ↓
Install with agentmods
npx agentmods add skills/hajibabaie/combinatorial-optimization-skills/column-generation
Install

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.

Any agent
npx skills add hajibabaie/combinatorial-optimization-skills --skill column-generation
Clone the repo
git clone --depth 1 https://github.com/hajibabaie/combinatorial-optimization-skills

Made for: Claude Code.

Or install combinatorial-optimization, the plugin that ships this one along with the rest of its 76 skills.

Wrote 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.

agentmods badge for column-generation

README.md
[![agentmods](https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/column-generation.svg)](https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/column-generation)
Your own site
<a href="https://agentmods.dev/skills/hajibabaie/combinatorial-optimization-skills/column-generation"><img src="https://agentmods.dev/badge/skills/hajibabaie/combinatorial-optimization-skills/column-generation.svg" alt="Measured on agentmods" height="20"></a>
Per session 124 Skills are progressive disclosure: only the name and description are preloaded; the body loads when the skill is used.
When invoked 11,844 The whole file, excluding the scripts and references it only reads on demand.
Security scan A 0 findings. A grade says what 26 rules found in the file — not that it is safe.
Origin original No closer match found in the catalogue.
Token cost

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.

ModelPer sessionOnce invoked
Fable 5.1 $0.00124 $0.11844
Opus 5 $0.00062 $0.05922
Sonnet 5 $0.00025 $0.02369
Haiku 4.5 $0.00012 $0.01184

Measured 8d ago against content hash 6d1267bb8bbb, method: parsed. Prices are Anthropic first-party input rates as of 2026-09-08, from the pricing page.

Security

Grade A, and why

column-generation 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 8d 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.

skills/column-generation/SKILL.md · 734 lines

How it starts

The opening of the file, as written. The whole thing — 734 lines — stays where its author put it; the contents beside it link to each section on GitHub.

Column Generation

You are an expert in column generation and branch-and-price for large-scale linear and integer programming. This skill covers the restricted master / pricing loop, reduced-cost pricing oracles, convergence and dual bounds, stabilization, heuristic pricing, and branching rules that remain compatible with the pricing problem. Use the framework below to recognize when a problem calls for column generation, implement the loop correctly in gurobipy, and extend it to a full branch-and-price algorithm when the LP bound alone is not enough.

Initial Assessment

Establish the following before writing any code:

  • Why are there too many variables? Identify the combinatorial object a column represents: a cutting pattern, a vehicle route, a crew pairing, a machine schedule, a cluster. If columns cannot be described implicitly by a structured subproblem, column generation does not apply.
  • What is the master structure? Set covering (>=), set partitioning (==), or a general linking system? Covering masters give nonnegative duals and more freedom in pricing; partitioning masters are needed when over-coverage is costed or infeasible.
  • What is the pricing problem and how hard is it? Knapsack (pseudo-polynomial DP), shortest path with resources (labeling), matching, or an NP-hard problem you will solve as a small MIP? Pricing consumes 80-95% of runtime in mature codes; its complexity decides instance reach.
  • LP bound or integer solutions? Decide up front: column generation alone gives the master LP bound plus a heuristic integer solution (price-and-branch). Proven integer optimality requires branch-and-price, which roughly triples implementation effort.
  • Problem size. Number of master rows (items, customers, tasks), expected number of CG iterations (often 1-5x the row count), and pricing instance size. A 1,000-customer routing master with exact elementary pricing is a research project; a 200-item cutting-stock LP solves in seconds.
  • Solver availability. Gurobi or another LP solver with reliable dual values for the master; the pricing solver can be custom code. For true branch-and-price with column generation at every node, check whether SCIP's pricer interface or a framework (Coluna.jl, VRPSolver) saves you from writing tree management yourself.
  • Dual stability risk. Degenerate masters (set partitioning with many ties, identical items) cause oscillating duals and slow convergence. Plan for stabilization if the row count exceeds a few hundred or the master is highly degenerate.
  • Time budget and accuracy. Is a bound within 0.5% in minutes acceptable (stop early via Lagrangian/Farley bounds), or do you need exact LP convergence?
  • Data format. Confirm the instance source (OR-Library cutting stock, Solomon/CVRPLIB routing, custom) and the units of costs and capacities; reduced-cost tolerances must match the cost scale.
  • Validation plan. On small instances, the CG master LP value must match the LP relaxation of the equivalent Dantzig-Wolfe reformulation, and branch-and-price must match a compact MIP solved directly. Build that cross-check first.

Read the full file on GitHub · 734 lines

Changes

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.

  1. 8d ago First seen · 734 lines · 124 tokens per session scan A 6d1267bb8bbb

Subscribe to this mod's changes

column-generation is a skill published in the GitHub repository hajibabaie/combinatorial-optimization-skills (7 stars, last pushed 2mo ago), licensed MIT. It adds 124 tokens to every session and 11,844 once invoked, about $0.0006 per session on Opus 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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