What does "Column Generation" mean?

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Column generation is a technique used to solve large problems in a methodical way. Instead of trying to solve the entire problem all at once, it breaks the problem down into smaller parts. This method works by focusing on a part of the problem, called a subproblem, and solving that first.

Once the subproblem is solved, the results help to create new parts (or columns) that can improve the solution. This process continues, cycling back to the subproblem, until the best possible solution to the main problem is found.

One challenge with column generation is that the values used to guide the process can change a lot during each cycle. This fluctuation can slow things down. To make the process faster, scientists have developed ways to stabilize these values. Recent improvements include using machine learning to better predict the outcomes and make adjustments that help the process move along quicker.

Overall, column generation is a powerful tool for tackling complex problems by working on them step by step, refining the solution as more information becomes available.