Bacterial Foraging Algorithm

The Bacterial Foraging Algorithm mimics the foraging behavior of Escherichia coli bacteria in the human intestinal tract, representing a bio-inspired optimization approach. In the BFA model, solutions to optimization problems correspond to bacterial states within the search space, equivalent to fitness values of the objective function. The BFA algorithm comprises three fundamental operations: chemotaxis, reproduction, and elimination-dispersal.

During the chemotaxis process, bacteria exhibit aggregation behavior toward nutrient-rich regions. The bacterial movement pattern consists of two modes: tumbling and swimming (run). A tumble is defined as a unit step movement in any random direction. Following a tumble, if the fitness value improves, the bacterium continues moving in the same direction for several steps until either the fitness ceases to improve or a predetermined step limit is reached. This directed movement is termed swimming. From an implementation perspective, chemotaxis involves generating random direction vectors and evaluating fitness improvements through objective function calculations, enabling local region exploration through iterative position updates.

Once the life cycle completes (reaching the critical chemotaxis count), bacteria undergo reproduction. The reproduction process follows the natural selection principle of "survival of the fittest." Based on the accumulated fitness sum during chemotaxis, the poorer half of bacteria perish while the fitter half split into two identical offspring. The child bacteria inherit their parent's biological characteristics, maintaining identical positions and step lengths. To maintain search diversity, the total bacterial population typically remains constant during reproduction. Algorithmically, this involves sorting bacteria by fitness and performing population replacement operations while preserving elite solutions.

Although chemotaxis and reproduction enhance bacterial search capability, complex optimization problems may still lead to local minima convergence. To address this limitation, BFA incorporates an elimination-dispersal phase to strengthen global optimization performance. After completing a certain number of reproduction cycles, bacteria are dispersed to random positions within the search space with a predefined probability. This mechanism facilitates escape from local optima by reinitializing particle positions, thereby promoting comprehensive search space exploration and improved solution quality. The dispersal operation is typically implemented through random number generation and boundary checking to ensure valid position assignments.