# Application of Angle Related Cost Function Optimization for Dynamic Path Planning Algorithm
## 2 Related Works  
A number of works have been published on the topic of path searching in congested systems. [PERSON] provided a comprehensive and systematic presentation of the mathematical models for the simulation of transportation systems and the methodologies for the analysis and design of these systems. Theoretical and operational aspects were presented in a rigorous and exhaustive framework, addressing a broad range of applications performed by researchers and practitioners [4]. Another study about transport modeling and its practical applications was presented by [PERSON] in 2011 [5].  
Path search and route choice are the main components for any path searching algorithm. [PERSON] et al. developed and tested innovative models of driver's route choice behavior [6]. The approach they exploited was to define choice sets of \"labelled\" paths to transform a large number of physical routes into a smaller number of routes, each representing a specific \"label\". A labelled path is defined as the optimal physical path with respect to some criterion function. The criteria that might be relevant to route choice include travel time, distance, scenery, congestion, signposting, etc. The label functions are estimated by maximizing the proportion of observed routes included in the sets of labelled paths.  
[PERSON] et al. explored route choice on road networks [7]. The route choice model is divided into three levels: the generation of alternatives, the perception of alternatives and choice set, and finally, the choice of alternatives belonging to the choice set. A deterministic, selective, multi-criteria approach is used to generate the routes. A covering measure is calculated by comparing observed and generated paths to take into account which routes are currently chosen.  
[PERSON] presented the Quantum Utility Model (QUM) [8], which is derived from quantum mechanics models. In QUM, it is possible to simulate the sequence of decisions in cases of unique or not-unique pre-trip decisions at intermediate levels.  
In addition, some researchers are starting to take into account the multi-dimensional attributes of the road network. [PERSON] et al. first put forward the concept of \"path quality\" and thought that path quality should be considered in the optimal path selection [9]. [PERSON] et al. presented the concept of \"reliable path\" which holds that the reliable path should be one that can guarantee the arrival on time [10]. [PERSON] et al. introduced the concept of \"driver orientation\" and chose the appropriate path as the optimal path [11].  
The existing research is focused on transforming different road attributes into unified dimensionless attributes, transforming the problem into an optimal path solution problem, and then using various optimal path algorithms to solve the problem. In fact, the optimal path search algorithm can be summarized as finding the path that meets the minimum target value of an attribute in a weighted road network. So, in this work, we aim to find a more efficient way to find the optimal path, and to enhance the real-time performance of the path searching process.