Research And Application Of Box-Covering Optimization Algorithm And Polymer Path Planning Strategy Based On Link Cost Function

With the comprehensive development of smart city construction,the rational planning and scientific construction of the urban transportation system has developed rapidly.In scientific research,a theoretical method related to statistical mechanics is proposed,which provides new ideas and perspectives for dealing with traffic.However,due to the unstructured characteristics and complexity of complex transportation networks,the study of its global architecture and the extraction of unique properties are hindered.This paper uses the thinking of complex systems to think about traffic problems,and uses the traffic network to portray its abstract complex structure,which provides a powerful theoretical paradigm and test examples for further research.This paper first focuses on the path planning problem in transportation networks.Considering the shortage of current dynamic programming algorithms and most of the path planning algorithms focusing only on local overhead,this paper analyzes the general path planning problem of transportation networks based on the physical characteristics of interacting polymers and disordered systems,and learns based on polymer mutual The core idea of the role of the path planning algorithm.The algorithm uses message passing technology to reduce the impact of all single path decisions on global planning while reducing the huge cost caused by traffic congestion.However,the algorithm needs to optimize the small-path parameters to obtain the optimal path planning configuration.Due to the random selection of the initial nodes and the random guidance of the subsequent nodes,the “weird circle” effect may be caused(The nodes involved in message passing during the path planning process are randomly selected and directed,resulting in repeated delivery and invalid delivery of a large number of messages),which leads to the problem that the path planning results do not converge.Therefore,based on the BPR link cost function,this paper proposes a polymer path planning algorithm using the BPR link cost function.The algorithm can not only obtain the optimal cost results in the global network,but also assign a global optimal path configuration to each user.Finally,this paper combines the noise cancellation mechanism to design a convergence mechanism to terminate the iteration of invalid messages in advance,accelerate the calculation of path planning,and improve the convergence and execution efficiency of the algorithm to some extent.The topology of complex systems prompted us to use renormalization and other methods to obtain their introverted properties and external representations.In order to make the complex network show a clear fractal scale as much as possible,the scientists applied the fractal geometry to the complex network,and thus produced a lot of different box coverage methods.In the second part of this paper,we first introduce the research status of fractal characteristics in complex networks,and clarify the mathematical definition of box dimensions and the characterization of scale invariance,and the importance of fractal attributes to complex systems analysis;the practical application of the renormalization method describes in detail several classical box covering methods.By analyzing the advantages and disadvantages of these box coverage methods,we apply the renormalization method to the experimental test in real network data.In order to quickly obtain better box coverage results,this paper combines the advantages of Maximum Excluded Mass Burning method(MEMB)and Random Sequential box-covering method(RS),and fully considers the real situation.The user has designed a box-covering optimization method(MCWR)for different precision and time requirements.