The New Approaches Based on Ant Colony Optimization and Greedy Search Algorithm for Solving Hierarchical Chinese Postman Problem with Stochastic Travel Times

Hierarchical Chinese postman problem (HCPP), a variant of the Chinese postman problem, aims to find the shortest tour or tours by passing through the arcs classified according to precedence relationship. HCPP, which has a wide application area in real-life problems such as shovel snow and routing patrol vehicles where precedence relations are important, belongs to the NP-hard problem class. In real-life problems, travel time between the two locations in city traffic varies due to reasons such as traffic jam, weather conditions, etc. Therefore travel times are uncertain. In this study, HCPP is handled with the chance-constrained stochastic programming approach, and a new type of problem, hierarchical Chinese postman problem with stochastic travel times, is introduced. Due to the NP-hard nature of the problem, the developed mathematical model with stochastic parameter values cannot find proper solutions in large size problems within the appropriate time interval. Therefore, two new solution approaches, a heuristic method based on the Greedy Search (GSA) algorithm and a meta-heuristic method based on ant colony optimization (ACO) are proposed in this study. These new algorithms were tested on modified benchmark instances and randomly generated problem instances with as many as 817 edges. The performance of algorithms was compared in terms of solution quality and computational time.

A Multiclass Cumulative Prospect Theory-Based Stochastic User Equilibrium Model with Path Constraints in Degradable Transport Networks

The limited driving range and the unavailability or insufficiency of battery charging/swapping stations cause the so-called range anxiety issue for traffic assignment involving battery electric vehicle (BEV) users. In addition, expected utility theory-based stochastic user equilibrium (EUT-SUE) model generates the perfectly rational issue when the travellers make route choice decisions. To tackle these two problems, this article improves the cumulative prospect theory-based stochastic user equilibrium (CPT-SUE) model in a degradable transport network through incorporating the constraints of multiple user classes and distance limit. In this degradable network, the travellers experience stochastic travel times due to network link capacity degradations. For this improved CPT-SUE model, the equivalent variational inequality (VI) model and associated method of successive averages (MSA) based solution are provided. The improved CPT-SUE model is tested and compared with the EUT-SUE model with distance limit, with results showing that the improved CPT-SUE model can handle jointly the range anxiety issue and the perfectly rational issue.