Transit Frequency Optimization Using Firefly Algorithm and Evaluation of the Parameters Ateş Böceği Algoritması Kullanılarak Toplu Taşıma Frekans Optimizasyonu ve Parametrelerinin Değerlendirilmesi

AKSOY, İlyas Cihan; MUTLU, Mehmet Metin; ALVER, Yalçın · 2021 · Crossref

DOI: 10.47933/ijeir.897839

archive: archived pipeline: cataloged verified

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Summary

This study addresses the Transit Network Frequency Setting Problem (TNFSP), a tactical decision-making challenge aimed at optimizing public transportation efficiency without requiring infrastructure investment. The research is motivated by the need to mitigate urban transportation issues such as congestion and pollution by increasing transit modal share, particularly in resource-constrained environments. The specific objective is to minimize total user cost—comprising in-vehicle time, waiting time, and transfer penalties—subject to a strict fleet size constraint. The authors propose using the Firefly Algorithm (FA), a relatively new metaheuristic inspired by firefly behavior, to solve this bi-level optimization problem, noting a lack of prior literature applying FA to TNFSP. The methodology employs a bi-level model where the upper level determines optimal frequencies for transit lines, and the lower level performs transit assignment based on user path choices. The transit assignment assumes users seek direct, one-transfer, or two-transfer paths, selecting among options using a logit model based on generalized cost. The FA is configured with specific parameters: population size ($nPop$) of 50, maximum generations ($z$) of 20, and light intensity ($\beta_0$) of 1. The study focuses on evaluating the impact of the randomization parameter ($\alpha$) and light absorption coefficient ($\gamma$). The model is tested on the 10-route Mandl’s Test Network, a standard benchmark consisting of 15 nodes and 21 links. The authors conducted 75 optimization runs across 25 parameter combinations to identify optimal settings, followed by 30 independent runs using the calibrated parameters. All algorithms were implemented in MATLAB. The results indicate that FA performance is highly sensitive to parameter values. Initial tests with varied parameters showed that only 20 of 75 solutions satisfied the fleet size constraint of 76 buses. The optimal parameter combination was identified as $\alpha = 1$ and $\gamma = 1$. Using these calibrated values, 30 independent runs were performed, all of which successfully adhered to the fleet constraint. The best solution achieved a total user cost of 265,505, representing a 4% reduction compared to the existing frequency set (cost of 276,433) while utilizing the same fleet size. Significant adjustments were observed in the frequencies of lines 1, 4, 5, and 8, with line 4 requiring only one bus in the optimized solution compared to nine in the existing set. The optimized solution maintained peak occupancy rates below capacity limits across all lines. The study concludes that the Firefly Algorithm is a viable tool for transit frequency optimization, provided that parameters are carefully calibrated to ensure constraint satisfaction. The 4% reduction in user cost demonstrates that FA can improve upon existing frequency sets without increasing operational costs. The authors suggest future research should compare FA’s efficiency against other established metaheuristics like Genetic Algorithms and Particle Swarm Optimization, and test the model on real-sized networks to assess broader applicability.

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