Multi-agent Optimization Algorithm And Its Application In Asphalt Pavement Rutting Prediction

Artificial intelligence(AI)is an important driving force for a new round of scientific and technological revolution and industrial transformation.Optimization,as the core mathematical basis of AI,ushers in a golden opportunity for development.However,with the vigorous development of big data and information technology,the scale and complexity of optimization problems are increasing,and the design of optimization algorithms is also facing unprecedented challenges.The development of network science,especially the cooperation technology of multi-agent systems,provides a new idea for the design of optimization algorithms and breaks through the dilemma that traditional algorithms cannot solve large-scale optimization problems.Therefore,the research on the design of multi-agent optimization algorithms has important theoretical value and practical significance.In addition,asphalt highway play the role of main force,main battlefield and pacesetter in the construction of China’s transportation power.The rutting prediction is the basis for pavement maintenance,and also the basis for transportation infrastructure construction planning and resource allocation.This thesis mainly studies the continuous-time algorithm design of two kinds of resource allocation problems and privacy preservation of two kinds of online multi-agent optimization problems.In addition,the mechanical-empirical models are built for the prediction of rutting depth of asphalt pavement.The main innovations are as follows:1.The continuous-time multi-agent optimization algorithms are designed for two kinds of resource allocation problems.First of all,under the undirected switching communication topology,for the economic dispatch problem in smart grid,the relationship between the primal variables and Lagrangian dual variables is analyzed by using the particularity of box inequality constraints.And a continuous-time distributed algorithm is designed that only uses the sign information of the relative dual variables between neighbors,and the convergence of the algorithm is analyzed under the assumption that the objective function is mild.Secondly,under the undirected fixed communication topology,a differential inclusion system is proposed based on the Karush-Kuhn-Tucker(KKT)condition to solve the resource allocation problem with coupled inequality constraints and nonsmooth objective and constraint functions.And the stability of the system at the equilibrium point is established by using the set-valued La Salle invariance principle when the initial state values satisfy the equality constraint.2.The privacy-preserving multi-agent online algorithms are designed for the two kinds of online optimization problems.Firstly,under the unbalanced directed communication topology with row stochastic weight matrix,for the online optimization problem with set constraints,the distributed iterative method is used to estimate the left Perron eigenvector of the weight matrix to eliminate the imbalance of the graph.And a distributed online optimization algorithm with privacy preservation is designed based on the state decomposition method.Under the assumptions that the local objective function and the subgradient satisfy the general convexity and boundedness respectively,it is proved that the static regret bound of the algorithm grows sublinearly with the learning time.Secondly,under the undirected switching communication topology,for the online optimization problem with long-term inequality constraints,a distributed privacy-preserving online optimization algorithm is proposed based on Lagrangian regularization method,differential privacy technology and state decomposition method.And the performance of the algorithm is analyzed using dynamic regret and cumulative absolute constraint violation.It is also proved that the algorithm can guarantee (?)-differential privacy of each agent at each iteration.3.Two new mechanical-empirical models for predicting rutting depth of thick asphalt concrete base pavement structures are designed based on nonlinear optimization and multi-agent consensus.First of all,the constitutive equation of fractional-order Burgers model is derived by using the constitutive equation of basic mechanical elements.With full consideration of the influence of temperature and traffic load on rutting depth,an explicit model for predicting rutting depth is constructed.Levenberg-Marquardt(LM)algorithm is used to fit the rutting depth data of six thick asphalt concrete base pavement structures in RIOHTrack full-scale track,and the fitting results are evaluated.Secondly,a new framework for predicting rutting depth is constructed by using LM algorithm based on multi-agent consensus and back propagation(BP)neural network.The framework uses the LM algorithm based on multi-agent consensus to fit the rutting data of six thick asphalt concrete base pavement structures in the RIOHTrack full-scale track at the same time to obtain a mechanical-empirical model with a unified expression.And then BP neural network is used to predict the error between the real rutting data and the data obtained from the unified model.Finally,the two proposed mechanical-empirical models are compared with the rutting depth models in the Specifications for Design of Highway Asphalt Pavement of China(JTG D50-2017)and the American Mechanical Empirical Pavement Design Guidelines(MEPDG).The results show that the two mechanical-empirical models have a good effect for rutting prediction of thick asphalt concrete base pavement structure.