Markov Chain Monte Carlo Method For Ant’s Walk

In the studies of ant foraging,researchers believe that exploring an uncertain environment and sampling from complex probability distributions like Markov Chain Monte Carlo(MCMC)method can be understood as equivalent problems.Therefore,the optimal foraging behaviour at the colony level can be achieved by mapping the trajectory left by ants in uncertain environment to the sampling process of Markov chain Monte Carlo method(MCMC)on the basis of the probabilistic matching(Kelly)strategy.However,regular MCMC models can not settle the problem that it is tough for ants to reach food resources that are multimodal distributed with distantly separated modes.The purpose of this work is to design a more applicable ant foraging model to solve problems with the current model.The main work includes:1.Based on the existing partial momentum refreshment(PMR)model,we propose a stochastic approximation partial momentum refreshment(SAPMR)model which not only performs as well as the regular MCMC models on bimodal distributions with two close modes,but also tackling the problem of leaping over the energy barriers of multimodal distributions with distantly separated modes.2.We use existing studies on ant movement behavior to evaluate the authenticity of the model.The synthetic data created by SAPMR possesses “ant-like”characteristics,such as distribution of step length,superdiffussion with long jumps,the changing trend of autocorrelation,power-law relationship between average event speed and event duration,and the universal function whose value is approximately 1.The results show that,compared with the original ant foraging model,our proposed SAPMR model has different degrees of improvement in different food resource distribution.And in the new model verification methods,the results show that the SAPMR model and real ants have similar movement characteristics.