The transit network design problem is one of the most significant problems faced by transit operators and city authorities in the world. This transportation planning problem belongs to the class of difficult combinatorial optimization problem, whose optimal solution is difficult to discover. The paper develops a Swarm Intelligence (SI) based model for the transit network design problem. When designing the transit network, we try to maximize the number of satisfied passengers, to minimize the total number of transfers, and to minimize the total travel time of all served passengers. Our approach to the transit network design problem is based on the Bee Colony Optimization (BCO) metaheuristics. The BCO algorithm is a stochastic, random-search technique that belongs to the class of population-based algorithms. This technique uses a similarity among the way in which bees in nature look for food, and the way in which optimization algorithms search for an optimum of a combinatorial optimization problem. The numerical experiments are performed on known benchmark problems. We clearly show that our approach, based on the BCO algorithm, is competitive with other approaches in the literature, and it can generate high-quality solutions.

Transit network design by Bee Colony Optimization

Firefly algorithm is one of the new metaheuristic algorithms for optimization problems. The algorithm is inspired by the flashing behavior of fireflies. In the algorithm, randomly generated solutions will be considered as fireflies, and brightness is assigned depending on their performance on the objective function. One of the rules used to construct the algorithm is, a firefly will be attracted to a brighter firefly, and if there is no brighter firefly, it will move randomly. In this paper we modify this random movement of the brighter firefly by generating random directions in order to determine the best direction in which the brightness increases. If such a direction is not generated, it will remain in its current position. Furthermore the assignment of attractiveness is modified in such a way that the effect of the objective function is magnified. From the simulation result it is shown that the modified firefly algorithm performs better than the standard one in finding the best solution with smaller CPU time.

/pdf/modified-firefly-algorithm-2ebvhqa2b8.pdf

Modified Firefly Algorithm

The present paper deals with timetable optimisation from the perspective of minimising the waiting time experienced by passengers when transferring either to or from a bus. Due to its inherent complexity, this bi-level minimisation problem is extremely difficult to solve mathematically, since timetable optimisation is a non-linear non-convex mixed integer problem, with passenger flows defined by the route choice model, whereas the route choice model is a non-linear non-continuous mapping of the timetable. Therefore, a heuristic solution approach is developed in this paper, based on the idea of varying and optimising the offset of the bus lines. Varying the offset for a bus line impacts the waiting time passengers experience at any transfer stop on the bus line. In the bi-level timetable optimisation problem, the lower level is a transit assignment calculation yielding passengers’ route choice. This is used as weight when minimising waiting time by applying a Tabu Search algorithm to adapt the offset values for bus lines. The updated timetable then serves as input in the following transit assignment calculation. The process continues until convergence. The heuristic solution approach was applied on the large-scale public transport network in Denmark. The timetable optimisation approach yielded a yearly reduction in weighted waiting time equivalent to approximately 45 million Danish kroner (9 million USD).

/pdf/user-perspectives-in-public-transport-timetable-optimisation-3g0pkots0f.pdf

User perspectives in public transport timetable optimisation

Appropriate public transport systems are crucial in modern cities. Given the high costs that they represent and the impact they have on people’s lives, effective tools are required to support their design. With this in mind, the Transit Network Design problem (TNDP) and the Transit Network Design and Frequency Setting problem (TNDFSP) have been extensively studied in the domain of Operations Research. However, due to the complexity of these problems, multiple simplifications are typically made when modelling and designing solution algorithms. Therefore, still no optimization techniques are available to address these problems in practice. Moreover, different studies address different versions of the problem, with varying assumptions and constraints, complicating the comparison of results or solution approaches. This paper presents an extensive survey of studies addressing the TNDP and the TNDFSP. It discusses the different assumptions, constraints, objectives, solution approaches and testing instances that have been considered in the literature. Furthermore, a detailed analysis is done regarding the case studies considered for the TNDFSP. Moreover, the variants of the passenger assignment subproblem that have been applied within the TNDP and the TNDFSP are discussed. The analysis shows that extensive research has been done regarding these problems. However, it also identified the significant gap that still exists between theory and practice, even in the studies addressing case studies.

A survey on the transit network design and frequency setting problem

Transportation plays a vital role in the development of a country and the car is the most commonly used means. However, in third world countries long waiting time for public buses is a common problem, especially when people need to switch buses. The problem becomes critical when one considers buses joining different villages and cities. Theoretically this problem can be solved by assigning more buses on the route, which is not possible due to economical problem. Another option is to schedule the buses so that customers who want to switch buses at junction cities need not have to wait long. This paper discusses how to model single frequency routes bus timetabling as a fuzzy multiobjective optimization problem and how to solve it using preference-based genetic algorithm by assigning appropriate fuzzy preference to the need of the customers. The idea will be elaborated with an example.

/pdf/bus-timetabling-as-a-fuzzy-multiobjective-optimization-f8yljp97br.pdf

Bus Timetabling as a Fuzzy Multiobjective Optimization Problem Using Preference-based Genetic Algorithm

The mass transit route network design (MTRND) problem is a bi-level NP-hard problem and difficult to solve for a global optimum solution. This paper proposes a genetic algorithm for solving the MTRND problem. In the proposed algorithm, two smart generating methodologies are formulated to achieve a better searching space for the initial feasible solution. An efficient network model, a gene repairing strategy and a redundancy checking mechanism were applied to minimize the computation time. Improved fitness function was embedded with the passenger assignment model and utilized to improve the quality of the solution. The proper combination of crossover operators and mutation operators was found for the MTRND. The proposed algorithm was tested with the current MRT network in Taipei as a specimen. Results indicate that the proposed algorithm is effective in solving real-world problems.

https://ir.nctu.edu.tw:443/bitstream/11536/5774/1/000276343100014.pdf

Mass transit route network design using genetic algorithm

Previous research regarding customer relationship management has shown that acquiring a new customer costs much more than retaining an existing customer. Thus, from the perspective of transit agencies, maintaining existing passengers is a cost-effective strategy. This paper investigates the patronage behavior of bus passengers when real-time transit information (RTTI) is made available. Survival analysis based on survey data collected in Kaohsiung city, Taiwan, shows that the risk of RTTI users ceasing their use of transit was 32.9% that of RTTI non-users. Moreover, passengers using RTTI tended to use public transportation 0.15 years longer than those who did not use RTTI. This study found that RTTI helps to retain passengers and provides concrete suggestions regarding RTTI promotion and bus business management for administrators.

Effects of real-time transit information services on the patronage behavior of passengers

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Mass transit route network design using genetic algorithm

Effects of real-time transit information services on the patronage behavior of passengers