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Little models, big results

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illigal 2009-05-19 11:35:33 Publish:

I am in my 25th year as a genetic algorithmist. In September 1980, I sat in John Holland's course, Introduction to Adaptive Systems, wondering what all the genetics stuff had to do with adaptive systems. Shortly thereafter, I proposed applying genetic algorithms to gas pipeline optimization and rule learning, did so, and went on to take my first teaching job at the University of Alabama. Although I had succeeded in applying GAs in my problem domain, my doing so left me with as many questions as I answered. And although I had used GAs to help solve interesting engineering problems, I was unhappy with GAs--and my own lack of understanding of GAs--as engineered objects.

That experience on my thesis left me with a thirst to better understand genetic algorithms, how they work, and how to make them work better. And that thirst led me to try difference equations, Markov chains, transform methods, anything that I could get my hands on, to help me do a better job in GA analysis and design. At first, my studies took me toward more esoteric and sophisticated tools, but then my training in fluid mechanics kicked (somewhere between my leaving Alabama and coming to Illinois), and I turned to the methodology of little models, including facetwise models, and patchquilt integration using dimensional analysis.

My 2002 book, The Design of Innovation, tells the long version of this story, but the basic idea of little modeling is to construct models for various effects in isolation (selection alone, crossover alone, mutation alone), and use dimensional analysis to create models for complex phenomena from pairs of simpler models. For example, we might create a model for convergence time under selection alone, combine this with a model for mixing under crossover alone, and consider the pairwise effect as a dimensionless ratio of the two times. This approach, though algebraically simple, is remarkably powerful in helping sort out experimental results and organize a researcher's thinking.

More recently, Ali Yassine, Tian-Li Yu, and I have carried the little modeling approach over to organizational theory here. We are still exploring the possibilities for this kind of study, but we believe the approach that has worked so well for GAs will help shine light on some of the complexity of large human organizations.

Interestingly, the approach from the modeling middle is almost universally criticized by both theoreticians (who believe it to be too simplistic) and practitioners (who find theory of any sort abhorrent). Aristotle was rather partial to the golden mean, and I find this middling type of analysis just the ticket, especially when approaching a poorly understood phenomenon without a well trodden body of accepted theory. Little models give great bang for the buck, and I urge every serious genetic algorithmist on the planet to become acquainted with the array of mixing, schema theorem, population-sizing, and convergence time models IlliGAL members and others have used to understand and design modern GAs. Without some analytical guidance, our understanding would have been too meager, but with more sophisticated models our ability to design would have been non-existent. The right balance of accuracy and model simplicity has been crucial to the advance of our art.

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