Solving demand-responsive feeder transit service design with fuzzy travel demand: A collaborative ant colony algorithm approach

This paper presents a fuzzy optimization model for demand-responsive feeder transit services (DRT) that can transport an uncertain number of passengers from demand points to the rail station. The proposed model features fuzzy triangular number variables used to describe the changes in travel deman d. Moreover, some practical factors such as boarding time windows and expected ride time are comprehensively considered in the model. The problem is formulated as a mixed-integer fuzzy expectation model to minimize the total travel distance for all routes, and its deterministic linear programming model is then obtained based on the credibility theory. Because the proposed model is an extension of the NP-hard problem, this study involves the design of a collaborative ant colony optimization (ACO), which redefines the construct rules, pheromones, heuristic information, and selection strategies of solutions to address the limitations of traditional ACO such as the premature convergence. When ACO applied to a case study in Nanjing City, China, sensitivity analyses are performed to investigate the impact of the number of vehicles on results of the scheduling, compared with the traditional model. Finally, the proposed ACO is compared with ACO, standard ACO, particle swarm optimization (PSO), and genetic algorithm (GA) to prove its validity.