Efficient algorithms for multidimensional global optimization in genetic mapping of complex traits

Kajsa Ljungberg1, Kateryna Mishchenko2, Sverker Holmgren11Division of Scientific Computing, Department of Information Technology, Uppsala University, Uppsala, Sweden; 2Department of Mathematics and Physics, M lardalen University College, V ster s, SwedenAbstract: We present a two-phase strategy for optimizing a multidimensional, nonconvex function arising during genetic mapping of quantitative traits. Such traits are believed to be affected by multiple so called QTL, and searching for d QTL results in a d-dimensional optimization problem with a large number of local optima. We combine the global algorithm DIRECT with a number of local optimization methods that accelerate the final convergence, and adapt the algorithms to problem-specific features. We also improve the evaluation of the QTL mapping objective function to enable exploitation of the smoothness properties of the optimization landscape. Our best two-phase method is demonstrated to be accurate in at least six dimensions and up to ten times faster than currently used QTL mapping algorithms.Keywords: global optimization, QTL mapping, DIRECT