As a community, we focus a lot on the heuristics available to solve a problem. But my experience in the field is that we don’t spend much time on the heuristics themselves: the cost function will get most of the work.

## Incrementality

When solving a problem using a metaheuristic, it is important to quickly evaluate incumbent solutions. When the number of variables is small, it is possible to compute the cost of a solution from scratch, but, if the problem has millions of variables, even a linear time-complexity will become limiting.

This is where incremental evaluation comes into play: for many cost functions, we can compute the result quickly for a small change of inputs. This is perfect for local search, which can now scale to very large problems.

## Rolling your own

If you need incremental evaluation for your problem, you are going to roll your own. It is quite easy at first: evaluating sums, maxs and products incrementally is not very difficult.

But in practice requirements change: you’ll need to implement a slightly different cost function and add new features to it. Before you know it, this incremental cost function prevents you from experimenting as much as you’d like to. It may even have become a maintenance issue! Moreover, we have more important stuff to do, and it’s rarely on par with what you could obtain with more optimizations and preprocessing.

## Any framework?

I sometimes feel the need for a library that would make incremental evaluation smoother. I know of one good framework for the metaheuristics part (ParadisEO), but I dont know of any framework to implement incremental evaluation of the cost function. When tackling some large scale problems, this is where the work is spent (both for the humans and the computer).

If you know one such framework, I’d like to hear from you!

Full disclosure: I am going to work at LocalSolver starting in November. A powerful modeling language makes modeling much easier, but generic solvers do not allow you to plug your own search engine: sometimes I’d like the best of both worlds.

There’s all the work around Self-Adjusting Computation:

http://www.umut-acar.org/self-adjusting-computation

See also Matthew Hammer’s homepage.

Thanks!

That’s much more generic and powerful than what I had in mind. Food for thought ðŸ™‚

I’ll benchmark CEAL if I need incremental computation for a new project.