DE-path : a differential-evolution-based method for computing energy-minimizing paths on surfaces

Abstract

Computing energy-minimizing paths that are general for different energy forms is a common task in science and engineering. Conventional methods adopt numerical solvers, such as conjugate gradient or quasi-Newton. While these are efficient, the results are highly sensitive with respect to the initial paths. In this paper we develop a method based on differential evolution (DE) for computing optimal solutions. We propose a simple strategy to encode paths and define path operations, such as addition and scalar multiplication, so that the discrete paths can fit into the DE framework. We demonstrate the effectiveness of our method on three applications: (1) computing discrete geodesic paths on surfaces with non-uniform density function; (2) finding a smooth path that follows a given vector field as much as possible; and (3) finding a curve on a terrain with (near-) constant slope.