Efficient transit network design and frequencies setting multi-objective optimization by alternating objective genetic algorithm

• We address the TNDFSP a relevant problem to improve public transport and mobility.
• We propose a novel Alternating Objective Genetic Algorithm (AOGA) heuristic.
• Our algorithm applies an alternating population sorting strategy.
• Computational experiments were conducted to find Pareto frontier optimal solutions.
• The results on a benchmark instance show that our method is effective.

The multi-objective transit network design and frequency setting problem (TNDFSP) involves finding a set of routes and their associated frequencies to operate in an urban area public transport system. The TNDFSP is a difficult combinatorial optimization problem, with a large search space and multiple constraints, leading to numerous infeasible solutions. We propose an Alternating Objective Genetic Algorithm (AOGA) to efficiently solve it, in which the objective to be searched is cyclically alternated along the generations. The two objectives are to minimize both passengers’ and operators’ costs. Transit users’ costs are related to the total number of transfers, waiting and in-vehicle travel times, while operator’s costs are related to the total required fleet to operate the set of routes. Our proposed GA also employs local search procedures to properly deal with infeasibility of newly generated individuals, as well as of those mutated. Extensive computational experiments results are reported using both Mandl’s original benchmark set and instances with different demands and travel times as well, in order to determine Pareto Frontiers of optimal solutions, given that users’ and operators’ costs are conflicting objectives. The results evidence that the AOGA is very efficient, leading to improved solutions when compared to previously published results.