Research On The Optimization Of Network Systems Under Uncertain Conditions

Nowadays,in our daily life,the network is everywhere.We live in a highly networked society.A large number of practical problems can be abstracted as network and network optimization problems.In this thesis,graph and network theory,uncertainty theory,uncertainty programming theory and network optimization theory are used to study the optimization of network system under uncertain conditions.On the basis of in-depth study of the concepts of graph and network,the concept of uncertain network system is refined and perfected,and a unified identification method of uncertain network system is proposed.According to uncertainty theory and uncertainty programming theory,the shortest path problem and minimum spanning tree problem in uncertain network system are studied from three different modeling mechanisms.The network optimization models based on conditional measure are established and the hybrid intelligent algorithm based on measure simulation technology is designed.In an application example,tunnel network planning is carried out for underground logistics system.The main work is as follows:(1)Research on general definition,classification and unified identification of uncertain network systems based on uncertainty condition measure.Firstly,through the analysis and research of certainty graph and uncertainty graph,certainty network and uncertain network,the uncertain characteristics of network system are extracted.A general definition of uncertain network system is proposed,which unifies the uncertainty of network attributes and network structure in network system.The existing uncertain network system is divided into three categories.Then,the idea of conditional measure in uncertainty theory is introduced to integrate attribute uncertainty and structural uncertainty in network system.The uncertainty of-network system is characterized by conditional measure,and the uncertainty conditional measure matrix for identifying uncertain network system is proposed by analogizing the form of adjacency matrix.(2)Research on the shortest path problem in uncertain network system based on conditional measure.Firstly,based on the idea of conditional measure and different decision criteria,three kinds of mathematical models are established to solve the shortest path problem in uncertain network systems.They are the expected shortest path model based on expectation programming,the maximum opportunity shortest path model based on correlated chance programming and the shortest path model based on chance constrained programming.Then a hybrid intelligent algorithm based measure simulation technology and Floyd algorithm is designed to solve the shortest path optimization model.The algorithm first simulates the uncertain function in the optimization model by measure simulation technology,and then transforms the uncertain programming model into its equivalent deterministic form,and finally the traditional algorithm is used to solve the dcterministic optimization problem.(3)Research on degree-constrained minimum spanning tree problem based on conditional measure in uncertain network system.Firstly,the limitation of load and current in practical application is considered,and the restriction condition of degree constraints is added.Then,according to different decision criteria,based on expectation programming,correlated chance programming and chance-constrained programming,three optimization models of degree-constrained minimum spanning tree problem based on conditional measure are established.Secondly,the models of the shortest path problem and the minimum spanning tree problem are compared and explained.Finally,a hybrid intelligent algorithm based on measure simulation technology and D-Prim algorithm is designed to solve the optimization model.(4)An example of uncertain network system(tunnel planning of underground logistics system)is studied.Firstly,the planning problem of underground logistics system is abstracted as the shortest path problem in uncertain network system.Then,an optimal tunnel planning model based on conditional measure is established.Finally,the idea of the hierarchical optimization design and hybrid intelligent algorithm are used to solve the problem.