I need a general optimization algorithm.?

Question

I'm working on a project for work that requires the solution of a pretty general optimization problem:

It's essentially a resource allocation problem. Imagine x different resource types which are needed to engage in some combination of projects. Each project requires a specific combination of resources and yields a certain profit.

The algorithm must find the resource/project combination that maximizes profitability. Looking for something that is better than exhaustive / brute force optimizations. Thanks!

Answer 1

Brute force though it may be, an x-dimensional linear regression is still your best bet for optimization. If there is a single optimal process, the method will yield it, but you are more likely ro arrive at a number of processes, each optimized, that will yield a maximum profit.

Your other alternative is to optimize each process independently, and then choose the most profitable, but you are likely to discard combinations which may yield a better end result, and you will still need n-dimensional regressions of some sort.

In lieu of dedicated software for the problem, a spreadsheet can be used quite effectively. For x > 7, however, you may need to apply techniques to keep numbers within your computer's ability, although this is not as problematic as it is with polynomial regressions.

Answer 2

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