Harmonic Oscillator based Particle Swarm Optimization

Abstract

Numerical optimization techniques are widely used in a broad area of science and technology, from finding the minimal energy of systems in Physics or Chemistry to finding optimal routes in logistics or optimal strategies for high speed trading. In general, a set of parameters (parameter space) is tuned to find the lowest value of a function depending on these parameters (cost function). In most cases the parameter space is too big to be completely searched and the most efficient techniques combine stochastic elements (randomness included in the starting setting and decision making during the optimization process) with well designed deterministic process. Thus there is nothing like a universal best optimization method; rather than that, different methods and their settings are more or less efficient in different contexts. Here we present a method that integrates Particle Swarm Optimization (PSO), a highly effective and successful algorithm inspired by the collective behavior of a flock of birds searching for food, with the principles of Harmonic Oscillators. This physics-based approach introduces the concept of energy, enabling a smoother and a more controlled convergence throughout the optimization process. We test our method on a standard set of test functions and show that in most cases it can outperform its natural competitors including the original PSO as well as the broadly used COBYLA and Differential Evolution optimization methods.