Adaptive Artificial Physics Optimization Using Proportional Derivative Controllers

Abstract

APO (Artificial Physics Optimization) is a physicomimetics-inspired population-based global search and optimization heuristic that can be modeled as a second-order dynamical system. A central concept of physicomimetics is that the tools and techniques of modern physics and engineering may be applied directly to optimization algorithms such as APO. The extended algorithms described in this paper are a realization of this concept. Using the state-space Z-transform, APO’s performance is improved by introducing backward and forward PDCs (Proportional Derivative Controllers). Algorithm APO-PD1 employs a backward PDC architecture that allows each particle to predict its location in the optimization landscape based on its then current state of motion. An error signal computed from the distance between the particle’s predicted position and the swarm-weighted position is used to adjust the particle’s velocity through the decision space (DS) with the result that APO-PD1 is measurably better than APO. APO-PD2 further improves APO by utilizing the same error signal in a forward PDC architecture in which both the particle’s current state of motion and its trajectory history are used to predict its future location. This modification improves performance even more by allowing the swarm’s particles to change trajectories more quickly. Numerical experiments on a suite of widely employed high-dimensionality benchmarks show that APO-PD2 outperforms both APO-PD1 and APO.