# Multicriteria Route Planning for In-Operation Mass Transit under Urban Data
## 2 Related Work
A kernel clustering algorithm based on the shuffled frog leaping algorithm (SFLA) is designed to predict the travel time based on the real-time and historical data of travel speed. On the basis of the expected traveling time and the vehicle velocity distribution, the route could be suggested by using the K-path algorithm with SFLA. Although these approaches successfully deal with the dynamic route planning considering the real-time traffic, the way their criteria is defined (traveling time and reliability) is not antagonistic compared to our targeted problem. Moreover, they differ from our targeted research problem in objectives. Nonetheless, the abovementioned research provides several insights into the formulations and possible solutions for multicriteria constrained route planning based upon inferred results. **Multicriteria Path Planning**. For multicriteria path planning, some research focuses on retrieving the Pareto-optimal set of trajectories that meets all objectives [58; 59]. However, the whole process is time-consuming; moreover, how to efficiently and effectively retain the subset of optimal trajectories given multiple origins under a large problem space remains a difficult issue [29]. Accordingly, there are lots of previous works that have used artificial intelligence for producing Pareto-Front [60; 61; 62]. Moreover, the urban features, for instance, the transference or competitive relationship between the new arbitrary route and the in-operation service, and the complexity as well as nonmonotonicity for urban functionalities, all make the PF inference a non-superimposable issue. As it turns out, several state-of-theart methods are not feasible for the targeted research problem. Accordingly, this paper adopts the concept of Gaussian mixture model (GMM) in background modelling [63], and further suggests a target-prioritized route-planning algorithm. Meanwhile, since the multicriteria path planning can be viewed as a variation of the multicriteria optimization problem, the techniques from some of the solutions towards multicriteria optimization may be adopted in solving our targeted research problem. Precisely, due to the time complexity of such NP-Complete problem, one of the most direct solutions through iterating all permutations or combinations turns out to be unrealistic and risks running out of finite computational resources, either time or space. Thereafter, several techniques are proposed and even synergized with some baseline methods towards solving certain research problem. For instance, combining the greedy selection and randomization, greedy-randomized adaptive search procedure (GRASP) [64] turns out to be a semigreedy heuristic and could be used to solve NP-Complete problems such as the traveling salesman problem [65; 66] or vehicle routing [67; 68]. Meanwhile, multiobjectives genetic algorithm (MOGA) [69] synergizes random search with the concepts in a genetic algorithm and can be applied for various multicriteria planning and scheduling problems [70; 71; 72]. Specifically, an evolutionary algorithm [73] focuses on applying the principles of evolution in nature to solve the problem. The procedure of the evolutionary algorithm can be divided into five stages: randomness, mutation, selection, crossover, and competition. To begin with, certain number of solutions is randomly sampled as the parents, based on which their children are generated. Then the child from each family with the best performance towards the fitness function is selected, with part of these best children chosen to be the parents in the next generation. A threshold is set to restrict the total number of solutions entering the next generation. Moreover, several modifications can be made in different stages of the procedure to enhance either the phenotype or genotype of the generated solutions so as to deal with certain requirements in the targeted issue [74; 75].