Adaptive Computational Chemotaxis in Bacterial Foraging Optimization: An Analysis

In his seminal paper published in 2002, Passino pointed out how individual and groups of bacteria forage for nutrients and how to model it as a distributed optimization process, which he called the bacterial foraging optimization algorithm (BFOA). One of the major driving forces of BFOA is the chemotactic movement of a virtual bacterium that models a trial solution of the optimization problem. This paper presents a mathematical analysis of the chemotactic step in BFOA from the viewpoint of the classical gradient descent search. The analysis points out that the chemotaxis employed by classical BFOA usually results in sustained oscillation, especially on flat fitness landscapes, when a bacterium cell is close to the optima. To accelerate the convergence speed of the group of bacteria near the global optima, two simple schemes for adapting the chemotactic step height have been proposed. Computer simulations over several numerical benchmarks indicate that BFOA with the adaptive chemotactic operators shows better convergence behavior, as compared to the classical BFOA. The paper finally investigates an interesting application of the proposed adaptive variants of BFOA to the frequency-modulated sound wave synthesis problem, appearing in the field of communication engineering.