Optimal Route Searching with Multiple Dynamical Constraints—A Geometric Algebra Approach

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.Two different types of dynamics can increase the complexity of the DMCOP problem. With type I dynamics, the network condition, such as the weight or topology, changes during optimal path searching; the constraints are not altered. For example, in adaptive dynamic traffic navigation, the optimal path should be dynamically generated with the traffic conditions, where the weights are dynamically changed according to the current traffic status. With type II dynamics, the network conditions are not changed; however, the constraints used to restrict the searching of the optimal path change with time. One example is event-forced constraints, which are not determined unless a certain kind of event (e.g., emergency or user interactions) occurs. In this way, the constraints should be changed according to the specific schedule of the event dynamically occurring. Since these different constraints cannot be known in advance, these constraints should be added dynamically during route planning [15]. For instance, in a typical scenario of a long-distance self-driving tour, the navigation may first start from route planning with a start point and an end point. During the travel, users may add location constraints [16], reliability constraints [17], turn constraints [18] for intercity traffic and cycle routes [19], or satisfaction constraints [20]. Certain emergency cases may also exist that require the planned route to be dynamically adjusted in a short amount of time according to a series of constraints.Previous initial studies have addressed the solution of DMCOP with type I dynamics (i.e., network status changes) [21]. Schott and Staples ...

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