A Model-Free Approach for Online Optimization of Nonlinear Systems

Abstract

This paper proposes a strategy to search optimal control parameters of a complex nonlinear system using a metaheuristic optimization algorithm in a computationally efficient manner. The proposed algorithm, called BAS-swarm (Beetle Antennae Search-swarm), is a gradient-free optimizer based on the BAS algorithm, inspired by mimicking the food foraging behavior of beetles. BAS-swarm takes advantage of the fact that the antennae of insects are not single sensory organs. The antennae contain an array of tiny fiber. Antennae fiber enables the insects to have a microscopic insight into the environment when moving toward the source of food smell. BAS-swarm uses this insight to improve the performance of BAS by approximating the gradient direction at each iteration with the help of a swarm of antenna fiber. Since the proposed algorithm approximates gradient by mimicking the behavior of beetle antenna fiber located at random locations, it does not require the numerical computation of the actual gradient, making it very efficient for optimization of nonlinear non-convex systems. We verified the accuracy and efficiency of the proposed algorithm by training single-layer neural networks with nonlinear activation function and compared its performance with Particle Swarm Optimizer (PSO), a well-studied extremum seeking algorithm, and the original BAS algorithm. The experiment shows that the proposed algorithm provides several-fold improvement and faster convergence as compared to other metaheuristic algorithms.