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We study the problem of the optimal design of routes and frequencies in urban public transit systems, the Transit Network Design Problem (TNDP), which is modeled as a multi-objective combinatorial optimization problem. A new heuristic based on the GRASP metaheuristic is proposed to solve the TNDP. As a multiobjective metaheuristic, it produces in a single run a set of non-dominated solutions representing different trade-off levels between the conflicting objectives of users and operators. Previous approaches have dealt with the multi-objective nature of the problem by weighting the different objectives into a single objective function. The case proposed by Mandl is used to show that the multi-objective metaheuristic is capable of producing a diverse set of solutions, which are compared with solutions obtained by other authors. We show that the proposed algorithm produces more non-dominated solutions than the Weighted Sum Method with the same computational effort, using the case of Mandl and another real test case.

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Frequency setting takes place at the strategic and tactical planning stages of public transportation systems. The problem consists in determining the time interval between subsequent vehicles for a given set of lines, taking into account interests of users and operators. The result of this stage is considered as input at the operational level. In general, the problem faced by planners is how to distribute a given fleet of buses among a set of given lines. The corresponding decisions determine the frequency of each line, which impacts directly on the waiting time of the users and operator costs. In this work, we consider frequency setting as the problem of minimizing simultaneously users' total travel time and fleet size, which represents the interest of operators. There is a trade-off between these two measures; therefore, we face a multiobjective problem. We extend an existing single-objective formulation to account explicitly for this tradeoff, and propose a Tabu Search solving method to handle efficiently this multi-objective variant of the problem. The proposed methodology is then applied to a real medium-sized problem instance, using data of Puerto Montt, Chile. We consider two data sets corresponding to morning-peak and off-peak periods. The results obtained show that the proposed methodology is able to improve the current solution in terms of total travel time and fleet size. In addition, the proposed method is able to efficiently suggest (in computational terms) different trade-off solutions regarding the conflicting objectives of users and operators.to the users and minimize the level of required resources delivered by the operators. Problem data is given by the itinerary of each line and origin-destination (OD) demand within a specific time horizon. An important component of the model is the assignment sub-model, which represents the behavior of the users with respect to a set of lines and frequencies. This sub-model is needed to measure the performance of the system with respect to the users, that is, the level of service.The literature concerning transit frequency optimization can be classified into (i) analytical models that admit closed-form solutions and (ii) mathematical programming formulations either explicit or not, with associated solution algorithms. In the first group, there are formulations that characterize the system in terms of few variables and allow getting a full description of the optimal solution. Although these models make considerable simplifications of the real system, they allow obtaining practical guidelines that are theoretically well founded [3,4], for example, the well-known rule of the square root [5,6]. The other important stream of work is based on a detailed characterization of the transit system, in terms of the route network and the demand that should be transported over it. These studies formulate the optimization problem in terms of a graph model, where decision variables are the capacities of the arcs (represented by the frequencies) and the flows that represent the...

ABSTRACT. We propose a model and solution method to a simultaneous route design and frequency setting problem on a main corridor from one of the Bus Rapid Transit (BRT) Systems of Colombia. The proposed model considers objectives of users and operators in a combinatorial multi-objective optimization framework and takes into account real constraints on the operation of some Colombian BRT systems not found in previous models. The problem is solved heuristically by a Genetic Algorithm which is tailored from an existing work, to consider specific characteristics of the real scenario. The methodology is validated with current data from one of the most important bus corridors in a Colombian BRT system. The results obtained improve the current solutions for this corridor.

The problem addressed in this paper attempts to efficiently solve a network design with redundant connections, often used by telephone operators and internet services. This network connects customers with one master node and sets some rules that shape its construction, such as number of customers, number of components and types of links, in order to meet operational needs and technical constraints. We propose a combinatorial optimization problem called CmTNSSP (Capacitated m Two-Node-Survivable Star Problem), a relaxation of CmRSP (Capacitated m Ring Star Problem). In this variant of CmRSP the rings are not constrained to be cycles; instead, they can be two node connected components. The contributions of this paper are (a) introduction and definition of a new problem (b) the specification of a mathematical programming model of the problem to be treated, and (c) the approximate resolution thereof through a GRASP metaheuristic, which alternates local searches that obtain incrementally better solutions, and exact resolution local searches based on mathematical programming models, particularly Integer Linear Programming ones. Computational results obtained by developed algorithms show robustness and competitiveness when compared to results of the literature relative to benchmark instances. Likewise, the experiments show the relevance of considering the specific variant of the problem studied in this work.