picoGA: A Vectorized Implementation of a Genetic Algorithm in Matlab

This document describes picoGA, our submission to the Tiny GA programming competition at GECCO 2006. picoGA is optimized to have small code size and a small memory footprint. It is implemented in the Matlab programming language. Matlab is an interpretted language that is optimized for performing operations on arrays. Loops, especially nested loops, tend to run slowly in Matlab. It is possible however to significantly improve the performance of Matlab programs by converting loops into array operations. This process is called vectorization (see [1] for further information). Matlab provides a rich set of functions, and many expressive indexing schemes that make it possible to vectorize code. Vectorized code not only runs faster, it also requires fewer lines of code. A drawback of vectorization is that it sometimes results in the consumption of more memory. Another drawback is that vectorized code can be harder to understand for users who are new to Matlab programming. In our submission we have sought to create a GA implementation that balances the costs and benefits of vectorization. There are some loops that we could have been vectorized to reduce the number of lines of code and to improve the performance of picoGA, however because the vectorization of these loops would have resulted in a drastic increase in the memory footprint, and because performance is not one of the criteria of the competition we decided to leave these loops unchanged. We will point out places where we made such decisions, and show what the vectorized code might have been in each case. In other places vectorization allowed for a big reduction in program size without drastically affecting the memory footprint. In such cases we have vectorized the code. For sophisticated users of Matlab, vectorization oftentimes improves the clarity of code, however it can make matters more difficult for others. Hence, in this document, we will explain how our vectorized code works. In the next section we describe features of our code that are relevant to the Tiny GA competition. In the following section we visit places in the code where we have implemented vectorization, and other places where we have avoided it. We will assume that readers are familiar with the vector indexing and logical indexing syntax of Matlab. For an introduction to this syntax see [2]