# Multicriteria Route Planning for In-Operation Mass Transit under Urban Data
## 4 Multicriteria Route Planning for Mass Transit
### The Algorithm
Furthermore, BiasSpan can suggest a solution in the scale of at most 10\({}^{-1}\) s for cases under all tested problem spaces. Meanwhile, despite the complexity in the constraints, the evaluation result on the runtime meets our estimation that the time complexity for BiasSpan is mainly related to the size of the problem space. With evaluation in two real-world in-operation mass-transit system from Tainan (175 km\({}^{2}\) for city centre only, 2192 km\({}^{2}\) for suburbs and mountain area included) and Chicago (the area of Chicago CBD is 4.09 km\({}^{2}\), and 606 km\({}^{2}\) for the whole city of Chicago), the result makes us believe that BiasSpan is reliable for real-world scenarios. Furthermore, according to the hypervolume (HV) and various statistical analysis towards BiasSpan against other comparative methods, a significant difference for the performance of BiasSpan over its competitors is demonstrated. Indeed, BiasSpan secures the Pareto optimal among all the candidates from comparative methods, and retrieves better solutions for at least 76% of all test cases in accordance to the optimization criteria; moreover, the overall performance for BiasSpan is close to the optimal solution generated by the brute-force method in small spaces where all combinations can be enumerated under the time constraint. Additionally, BiasSpan takes less time given a larger-scale input (>100 km\({}^{2}\)), and turns out to be a suitable approach for dealing with real-world scenarios (e.g., 175 to 2192 km\({}^{2}\)). ## 6 Conclusions

The BiasSpan method is proposed to solve the problem of nonmonotonic multicriteria constrained route planning. This paper puts more emphasis on the real-world application of deploying an additional mass-transit service for an in-operation mass-transit system based on various constraints, such as must-visit stations and limits for additional stations to be recommended. The evaluation is conducted on two in-operation mass-transit systems in Chicago and Tainan, where the results indicate that the BiasSpan effectively prevents the herding effect in the station recommendation stage by quantifying and neutralizing the relationship with in-operation services as well as the complex urban functionalities. Furthermore, BiasSpan turns out to retrieve solutions in a Pareto-optimal sense over comparative methods between profit under queried constraints (the expected passenger flow to be maximized, referring to the social welfare for the public) and expenditure of the route (the cost to be minimized, referring to the sustainability for the government), and runs one logarithmic-scale time span less than baselines or route planning algorithms. The experiments show that the proposed BiasSpan method retains the Pareto optimal among comparative algorithms. Statistical analysis also demonstrates the significant difference in performance obtained by BiasSpan over its competitors. Moreover, BiasSpan takes at least one logarithmic-scale time span less in a real-world scale over other route planning methods. This characteristic allows BiasSpan to support and to provide quantitative analysis of an arbitrary route in a timely manner. Therefore, the future work for BiasSpan is three-fold: first, based on the multisource bidirectional spanning strategy, when merging trajectories, we can use the matching technique to optimize the serialization of the stations to achieve better PF performance; second, the concept of awareness could be applied in the Gaussian mixture model for modelling spatial influence; finally, synergies with other state-of-the-art nonmonotonic inference models could be taken into account while evaluating the reliability of the proposed BiasSpan method. Supervision, H.-P.H. ; methodology, F.L. and H.-P.H. ; validation, F.L. ; investigation, F.L. and H.-P.H. ; resources, H.-P.H. ; data curation, F.L. ; writing--original draft preparation, F.L. and H.-P.H. ; writing--review and editing, F.L. and H.-P.H. ; funding acquisition, H.-P.H. All authors have read and agreed to the published version of the manuscript.