Evolving Smoothing Kernels for Global Optimization

摘要

The Diffusion-Equation Method (DEM) - sometimes synonymously called the Continuation Method - is a well-known natural computation approach in optimization. The DEM continuously transforms the objective function by a (Gaussian) kernel technique to reduce barriers separating local and global minima. Now, the DEM can successfully solve problems of small sizes. Here, we present a generalization of the DEM to use convex combinations of smoothing kernels in Fourier space. We use a genetic algorithm to incrementally optimize the (meta-)combinatorial problem of finding better performing kernels for later optimization of an objective function. For two test applications we derive and show their transferability to larger problems. Most strikingly, the original DEM failed on a number of the test instances to find the global optimum while our transferable kernels - obtained via evolutionary computations - were able to find the global optimum.