Proxy Benders Decomposition: A Smarter Way to Optimize Large-Scale Problems

Optimization can feel like an endless puzzle, especially when dealing with large-scale mixed-integer problems. Traditional Benders decomposition has been a go-to method, yet it often gets bogged down by its repetitive nature and sluggish convergence. Enter Proxy Benders Decomposition (Proxy-BD), a breath of fresh air for anyone tired of solving the same subproblems repeatedly.

Breaking Down Proxy-BD

Proxy-BD isn't your typical optimization tool. Instead of relying on exact solutions for subproblems, it uses certified optimization proxies. These proxies follow a self-supervised predict-project-and-complete approach. In simple terms, they guess, check, and refine solutions to produce Benders cuts that aren't just valid but also efficient.

Why does this matter? Think of it like having a GPS that not only predicts traffic but also offers an unerring shortcut each time. The real magic lies in its certification layer, which ensures that even if a prediction is off, the method self-corrects. This makes Proxy-BD both reliable and flexible, adapting to modern decomposition schemes like branch-and-Benders-cut algorithms.

Impressive Numbers Speak for Themselves

Let's talk numbers. Proxy-BD has shown its prowess on large-scale facility location and network design problems. For instance, in uncapacitated facility location instances up to 2000x2000, the tool achieved median optimality gaps below 0.5%. If you think that's impressive, consider the speed: up to 161x faster than traditional methods and with over 240x fewer generated cuts on the largest instances. That's not just progress. it's a quantum leap.

This brings us to the heart of the matter: efficiency. As problems scale, Proxy-BD scales even better. It thrives on complexity, showing that when faced with intricate problems, smarter isn't just better, it's essential.

Why Should You Care?

In a world where time is money, the ability to solve large-scale problems faster and more efficiently isn't just nice to have. it's critical. If you're in the field of optimization, Proxy-BD could be your new best friend. But here's the real kicker: what traditional methods see as a barrier, Proxy-BD sees as an opportunity.

The gap between the keynote and the cubicle is enormous, and Proxy-BD might just bridge it. Imagine the potential savings in industries where optimization dictates the bottom line. So the question isn't whether Proxy-BD works, but rather, can you afford to ignore it?