A new bi-objective simultaneous model for timetabling and scheduling public bus transportation

The efficient design of public transportation networks is critical in establishing optimal schedules and curtailing transport costs for both passengers and transportation organizations. This study focuses on advancing existing models for selecting timetables and optimal schedules within public transportation networks. Addressing these concerns as a bi-objective optimization problem, this paper aims to develop an effective method for simultaneous optimization, targeting the reduction of transportation costs and minimizing passengers’ waiting times. Initially, this study formulates the problem using appropriate mixed-integer linear programming. To tackle this challenging optimization problem, various algorithms, including the non-dominated sorting genetic algorithm (NSGA), bi-objective particle swarm optimization algorithm (bi-objective PSO), and bi-objective red deer algorithm (bi-objective RDA), are employed. The selection of these algorithms aims to explore different solution spaces and their abilities to produce Pareto-optimal solutions. To assess the effectiveness of these Pareto algorithms in addressing the problem, the epsilon constraint method is utilized. Additionally, a redesign method is introduced to confront optimization challenges in this specific research domain. Leveraging bi-objective problem estimator parameters and the response level method, the algorithms’ parameters are optimized, elucidating the best-case scenarios for each parameter. A comprehensive comparative analysis of algorithm performance is conducted, considering various criteria, including solution time, convergence, and diversity of solutions. Furthermore, sensitivity analyses are carried out on problem-sensitive parameters in a case study, culminating in significant managerial implications for addressing the proposed problem in real-world scenarios.