# Publications

## Using evolutionary algorithms to search for control parameters in a nonlinear partial differential equation.

R.M. Eichler West, E. De Schutter, G.L. Wilcox

*Evolutionary Algorithms 111:33-64 (1999)*

**Abstract - **Many physical systems of interest to scientists and engineers can be modeled using a partial differential equation extended along the dimensions of time and space. These equations are typically nonlinear with real-valued parameters that control the classes of behaviors that the model is able to produce. Unfortunately, these control parameters are often difficult to measure in the physical system. Consequently, the first task in developing a model is usually to search for appropriate parameter values. In a high dimensional system, this task potentially requires a prohibitive number of evaluations and it may be impossible or inappropriate to select a unique solution.
We have applied evolutionary algorithms (EAs) to the problem of parameter selection in models of biologically realistic neurons. Our objective was not to find the best solution, but rather we sought to produce the manifold of high fitness solutions that best accounts for biological variability. The search space was high dimensional (> 100) and each function evaluation required from one minute to several hours of CPU time on high performance computers. Using this model and our goals as an example, we will: 1) review the problem from the neuroscience perspective, 2) discuss high performance computing aspects of the problem, 3) examine the suitability of EAs for the efficient optimization of this class of problems, and 4) describe and justify the specific EA implementation used to solve this problem.