Metaheuristics of War

Hill-climbing is a simple metaheuristic algorithm. It exploits a heuristic belief about your space of candidate solutions which is usually true for many problems: that similar solutions tend to behave similarly (and tend to have similar quality), so small modifications will generally result in small, well-behaved changes in quality, allowing us to “climb the hill” of quality up to good solutions. This heuristic belief is one of the central defining features of metaheuristics: indeed, nearly all metaheuristics are essentially elaborate combinations of hill-climbing and random search.

One must use caution. When Clausewitz uses a metaphor, he does so because it helps us understand some dimension of the problem being discussed — not because a Center of Gravity in war maps exactly onto the meaning of the Center of Gravity in physics. Boyd does not make this distinction, and thus is vulnerable to criticisms from those that accurately point out that his interpretation of scientific concepts do not match their original usage. The level of abstraction I am discussing with in this post must be qualified in this respect, as I hope to avoid repeating Boyd’s mistake.

However, the following aspects of metaheuristics are still appealing in abstract. In many real-world problems, we do not know what an optimal solution looks like. We don’t know how to find it. We have a nub of information we can use, but not much more. Most importantly, the space of possible solutions is too large for us to just use brute force search for an answer:

A brute-force approach for the eight queens puzzle would examine all possible arrangements of 8 pieces on the 64-square chessboard, and, for each arrangement, check whether each (queen) piece can attack any other.

While hill-climbing and random-search are inherent in most metaheuristics, there are different types of metaheuristic algorithms for different problems with varying performance in climbing the “hill of quality.” Hence it is customizable and recognizes variation in performance of methods. Some methods will perform well on some problems, but will get stuck at a local optima instead of a peak when faced with others.

One gigantic caveat: the idea of peaks and valleys in the solution space is derived from the assumption of a static, not dynamically evolving, landscape of candidate solutions. A perfect example is the application of the Ant Colony Optimization method to the notoriously hard Traveling Salesman Problem or the use of genetic algorithms to optimize the Starcraft tech tree’s build orders. When the solution space you are searching and climbing evolves in time, algorithms that assume a static landscape run into problems.

However, this is also why (in more mathematically dense language) nailing down principles of war is so perilous.  A solution that you might have used a principle of war to get to is  fine at time T. But it loses validity as we shift to T+1 and tick upwards towards T+k. And should you use a principle that better fits war’s grammar in 1830 than 2013, then you are even more screwed.

The advantage of metaheuristics of war compared to principles of war is that, while both consider solutions to problems with discrete (not continuously shifting) solution landscapes, metaheuristics are about how you find solutions. Hill-climbing is (oversimplified) method of moving through solutions that exploits heuristic information, and random search is  (also oversimplified) “try and see what happens.” The process of a metaheuristic involves a combination of both.

In contrast, principles of war are not really a process as much as a set of general guidelines designed to dramatically and a priori shrink the possible space of solutions to be considered in ways far more sweeping than hill-climbing. They imply a very, very restricted set of solutions while still being too vague to help a practitioner think about how the solutions fit the problem. Principles of war generally say to the practitioner, “generally, you do ___ but how you apply this is up to your specific situation and needs.” It has a broad set of do’s and don’ts that — by definition — foreclose consideration of possible solutions when they conflict with a given principle.

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