Abstract
The main problem with the soft-computing algorithms is a determination of their parameters. The tuning rules are very general and need experiments during a trial and error method. The equations describing the bat algorithm have the form of difference equations, and the algorithm can be treated as a stochastic discrete-time system. The behaviour of this system depends on its dynamic and preservation stability conditions. The paper presents the stability analysis of the bat algorithm described as a stochastic discrete-time state-space system. The observability and controllability analyses were made in order to verify the correctness of the model describing the dynamic of BA. Sufficient conditions for stability are derived based on the Lyapunov stability theory. They indicate the recommended areas of the location of the parameters. The analysis of the position of eigenvalues of the state matrix shows how the different values of parameters affect the behaviour of the algorithm. They indicate the recommended area of the location of the parameters. Simulation results confirm the theory-based analysis.
Highlights
In recent years, the nature-inspired metaheuristic algorithms for optimization problems become very popular
The genetic algorithms [4] are based on the biological fundamentals, tabu search is based on the social behaviour [5], and ant colony optimization [6, 7] or particle swarm optimization (PSO) [8] is based on the swarm behaviour
We described the dynamic of bat algorithm (BA) by the statespace form
Summary
The nature-inspired metaheuristic algorithms for optimization problems become very popular. They can recognize the difference between food/prey and background barriers (2) The i-th bat is at position xi and flies randomly with a velocity vi It emits an audio signal with a variable frequency between f min, f max , a varying wavelength λi, and loudness Ai to search for food. We can consider BA as a balanced combination of exploration, realized by an algorithm similar to the standard particle swarm optimization and exploitation realized by an intensive local search The balance between these techniques is controlled by the loudness L and emission rate r, updated as follows: Lki +1 = αLki , rki +1 = r0i 1 – exp –γk , where the coefficients α and γ are constants.
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