The process of searching for a dynamic constrained optimal path has received increasing attention in traffic planning, evacuation, and personalized or collaborative traffic service. As most existing multiple constrained optimal path (MCOP) methods cannot search for a path given various types of constraints that dynamically change during the search, few approaches for dynamic multiple constrained optimal path (DMCOP) with type II dynamics are available for practical use. In this study, we develop a method to solve the DMCOP problem with type II dynamics based on the unification of various types of constraints under a geometric algebra (GA) framework. In our method, the network topology and three different types of constraints are represented by using algebraic base coding. With a parameterized optimization of the MCOP algorithm based on a greedy search strategy under the generation-refinement paradigm, this algorithm is found to accurately support the discovery of optimal paths as the constraints of numerical values, nodes, and route structure types are dynamically added to the network. The algorithm was tested with simulated cases of optimal tourism route searches in China’s road networks with various combinations of constraints. The case study indicates that our algorithm can not only solve the DMCOP with different types of constraints but also use constraints to speed up the route filtering.

In this paper, a tensor-based interpolation method for spatio-temporal field data is proposed. The observed data are organized as a sparse tensor, which is then represented as the decomposition of a canonical polyadic (CP) model. The latent factors, abstracting the underlying structure of sparse data, are exploited by introducing a weighted optimization solution. With the reconstruction of these factors, the values of missing data can progressively be recovered. The simulation experiments suggest that our method can interpolate spatio-temporal data with various levels of sparseness. The data can even be interpolated accurately and stably when 90% of the data are missing.