Abstract
This paper considers an urban transit network design problem (UTNDP) that deals with construction of an efficient set of transit routes and associated service frequencies on an existing road network. The UTNDP is an NP-hard problem, characterized by a huge search space, multiobjective nature, and multiple constraints in which the evaluation of candidate route sets can be both time consuming and challenging. This paper proposes a hybrid differential evolution with particle swarm optimization (DE-PSO) algorithm to solve the UTNDP, aiming to simultaneously optimize route configuration and service frequency with specific objectives in minimizing both the passengers’ and operators’ costs. Computational experiments are conducted based on the well-known benchmark data of Mandl’s Swiss network and a large dataset of the public transport system of Rivera City, Northern Uruguay. The computational results of the proposed hybrid algorithm improve over the benchmark obtained in most of the previous studies. From the perspective of multiobjective optimization, the proposed hybrid algorithm is able to produce a diverse set of nondominated solutions, given the passengers’ and operators’ costs are conflicting objectives.
Highlights
Academic Editor: Alexander Paz is paper considers an urban transit network design problem (UTNDP) that deals with construction of an efficient set of transit routes and associated service frequencies on an existing road network. e UTNDP is an NP-hard problem, characterized by a huge search space, multiobjective nature, and multiple constraints in which the evaluation of candidate route sets can be both time consuming and challenging. is paper proposes a hybrid differential evolution with particle swarm optimization (DE-PSO) algorithm to solve the UTNDP, aiming to simultaneously optimize route configuration and service frequency with specific objectives in minimizing both the passengers’ and operators’ costs
For hybrid DE-PSO, the DE algorithm is initially run for a finite number of generations, I (e.g., 20) to initialize the swarm population for the PSO. e PSO is the main algorithm to search for the optimal solution in hybrid DE-PSO
10 independent runs are performed for 200 generations, each with a population size of 30. e computational results obtained by both hybrid algorithms are given in Table 3. e entries for Avg. represents the average result after the 10 runs. e transit route network configuration constructed by the proposed hybrid DE-PSO and hybrid PSO-DE is provided in Tables 4 and 5, respectively
Summary
Each vector (in DE) or particle (in PSO) is a candidate route set from the given transit network configuration. E route construction heuristic proposed by Mumford [38] is utilized to generate the initial population of vectors/particles. E identical point mutation is utilized in the DE to create a noisy random vector, Vi,G, as follows: a random node that has at least two identical nodes from the random vector (route set) is selected. E second mutation operator is utilized in the PSO to update the personal and global best of the swarm (see Figure 3). (iii) If the common node is found, copy substring (route parts) from the personal or global best between the selected nodes to modify the current particle. At the end of each DE-PSO iteration, the nondominated solution is accumulated and isolated by discarding all the dominated solutions. e detailed framework of the proposed DE-PSO is provided in Algorithm 2
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