A Chaotic Levy Flight Bat Algorithm for Parameter Estimation in Nonlinear Dynamic Biological Systems

We propose a synergistic approach to meta-heuristic search optimization algorithm. The fine balance between intensification (exploitation) and diversification (exploration) is very important to the overall efficiency and performance of a meta-heuristic search algorithm. Too little exploration and too much exploitation could cause the system to be trapped in local optima, which makes it very difficult or even impossible to find the global optimum. The diversification via randomization provides a good way to move away from local search to the search on the global scale and avoids the solutions being trapped at local optima, while increases the diversity of the solutions. The good combination of these two major components will usually ensure that the global optimality is achievable. It is worth pointing that the use of a uniform distribution is not the only way to achieve randomization. In fact, random walks such as Levy flights on a global scale are more efficient. The track of chaotic variable can travel ergodically over the whole search space. In general, the chaotic variable has special characters, i.e., ergodicity, pseudo-randomness and irregularity. To enrich the searching behavior and to avoid being trapped into local optimum, chaotic sequence and a chaotic Levy flight are incorporated in the metaheuristic search for efficiently generating new solutions. We presented synergistic strategies for meta-heuristic optimization learning, with an emphasis on the balance between intensification and diversification. In this paper, we apply the proposed search optimization algorithm and describe a general methodology to adaptively select the values of the model parameters for the reconstruction of biological system dynamics. We illustrate the application of the method by jointly estimating the parameter vector of the dynamics of endocytosis.