Abstract
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.
Highlights
Optimal path analysis, as one of the most fundamental methods of network analysis, has been used in multiple application fields [1,2,3,4,5,6,7]
Since the constraints change according to the various schedules as the events dynamically occur in the dynamic multiple constrained optimal path (DMCOP) with type II dynamics, we can assume that the whole network search process can be split into several time frames Tc = {t1, t2, · · ·, tn}
According to the problem definition above, the solution to the DMCOP problem with type II dynamics can be split into the following three steps: (1) Because the constraints are varied and often linked with the network elements, a formal description of constraints and network elements integrated into a unified framework should be constructed to reduce the transformation complexity of different constraints; (2) Due to the dynamically added constraints, the route generation strategy, which can dynamically integrate constraints during feasible path generation and optimal path searching, should be constructed [32]; (3) As the actual network problems are often large in scale, an efficient solution strategy should be carefully designed
Summary
As one of the most fundamental methods of network analysis, has been used in multiple application fields (e.g., transportation, tourism, and evacuation) [1,2,3,4,5,6,7]. One key issue that increases the complexity of solving DMCOP with type II dynamics is that a variety of constraints exists, including numerical constraints (e.g., the weight value or range requirement of path weights), network elements constraints (e.g., must-visit nodes), and the topological structure of the path (e.g., noncyclic or cyclic visiting routes). We introduced GA to the problem of multisource multisink optimal evacuation routing that partially provides the possibility to design the DMCOP algorithm to support different constraints This method is performed from the perspective of data structure and lacks the integration of type II constraints to form a normative approach through a formal mathematical expression, and this method is more focused on the weight and topological change of networks rather than the constraint change. A case study of tourism route planning is developed to test our algorithm
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