by *Goldberg, D. E., Sastry, K., and Llorà X. (2007)*. Complexity, 12(3), 27—29. Link to the PDF.

**Abstract:**

The push for better understanding and design of complex systems requires the solution of challenging optimization problems with large numbers of decision variables. This note presents principled results demonstrating the scalable solution of a difficult test function on instances over a billion variables using a parallel implementation of a genetic algorithm (GA). The problem addressed is a noisy, blind problem over a vector of binary decision variables. Noise is added equaling a tenth of the deterministic objective function variance of the problem, thereby making it difficult for simple hillclimbers to find the optimal solution. The genetic algorithm used - the compact GA - is able to find the optimum in the presence of noise quickly, reliably, and accurately, and the solution scalability follows known convergence theories. These results on noisy problem together with other results on problems involving varying modularity, hierarchy, and overlap foreshadow routine solution of billion-variable problems across the landscape of complexity science.