Author's Personal Copy Theoretical Computer Science Stability Analysis of the Reproduction Operator in Bacterial Foraging Optimization
Author's Personal Copy Theoretical Computer Science Stability Analysis of the Reproduction Operator in Bacterial Foraging Optimization
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通讯作者：
Arijit Biswas;Swagatam Das;S. Dasgupta;A. Abraham
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作者：
Arijit Biswas;Swagatam Das;S. Dasgupta;A. Abraham
在2002年发表的开创性论文中，帕西诺指出了个体和细菌群体如何觅食营养，以及如何将其建模为分布式优化过程，他将其命名为细菌觅食优化算法(BFOA)。BFOA的主要算子之一是虚拟细菌的繁殖现象，每个算子都模拟了优化问题的一个试解。在繁殖过程中，最不健康的细菌(在一个趋化生命周期中，目标函数的累积值较低)会死亡，而其他较健康的细菌会分裂成两个，然后从相同的位置开始探索搜索地点。这一现象与经典进化算法的选择机制有直接的相似之处。本文试图将生殖建模为一个动态模型，然后分析生殖系统在平衡点附近的稳定性，在这种情况下，平衡点是孤立最优的。它还找到了能够发生稳定繁殖事件的条件，将更差的细菌引导到更好的细菌。我们的分析表明，稳定的繁殖事件有助于细菌种群在最优附近快速收敛。
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 named the Bacterial Foraging Optimization Algorithm (BFOA). One of the major operators of BFOA is the reproduction phenomenon of virtual bacteria, each of which models one trial solution of the optimization problem. During reproduction, the least healthy bacteria (with a lower accumulated value of the objective function in one chemotactic lifetime) die and the other healthier bacteria each split into two, which then starts exploring the search place from the same location. The phenomenon has a direct analogy with the selection mechanism of classical evolutionary algorithms. This paper attempts to model reproduction as a dynamics and then analyses the stability of the reproductive system very near to an equilibrium point, which in this case is an isolated optimum. It also finds conditions under which a stable reproduction event can take place, to direct a worse bacterium towards a better one. Our analysis reveals that a stable reproduction event contributes to the quick convergence of the bacterial population near optima.