Transit Route Design Using Scheduling and Multiobjective Programming Techniques

Abstract

This research provides a new and efficient approach to solve the Transit Route Design (lRD ) problem. This is considered the most complex and cumbersome problem across network route allocation problems. The wide range of the TRD characteristics creates difficulties to formulize the problem uniquely. At the same time, the TRD complexity type creates combinatorial problems, and its formulation cannot be solved via known mathematical programming approaches and packages. The suggested model deals with both its complexity and its practical issues. This is the first time that three transit operational components are being considered simultaneously: route design; timetabling (frequencies); and vehicle scheduling. The approach used has an impact on three components involved: the operator, the user, and the considered authority. The objectives of these three components do not always coincide. From the operator viewpoint, the system should minimize its expenses while, from the user perspective, the system should maximize its level-of-service. This trade-off situation creates this work's optimization framework. The formulation of this work contains two objective functions -each to be minimized. However, it is impossible to treat both functions simultaneously, and hence, multi-objective programming is being used. This multi-objective programming technique was not used, to our knowledge, for solving the TRD problem. In fact, due to the problem complexity, the ordinary mathematical programming methods cannot be used in this technique, and therefore, a new approach is provided. This new procedure is heuristic in nature and divided into two phases: (a) generation of finite sets of alternative efficient non-inferior solutions, and (b) evaluation and selection of the various solutions using multi-objective preference techniques for discrete variables ("compromise programming" procedure). This approach enables to solve the complex lRD problem. It combines mathematical programming with decision-making methods, using search and enumeration processes while performing the optimization. Thus, it is possible to encounter relatively large-scale problems (networks) with the possibility to interact with the solution method during intermediate steps.

A multi-objective metaheuristic approach for the Transit Network Design Problem

“…Some authors suggest that by varying the values of these weights, a set of solutions with different trade-off levels can be obtained (Baaj and Mahmassani 1991). • Calculating a set of non-dominated solutions and selecting a posteriori a single one (Israeli and Ceder 1993;Mauttone and Urquhart 2004).…”

“…No explicit method to set these coefficients is given in the literature related to the TNDP. In this work we adopt the a posteriori mode (Ehrgott and Gandibleux 2002) (formerly applied in Israeli and Ceder (1993), Mauttone and Urquhart (2004)), that we call multi-objective approach for the TNDP. We propose an algorithm to find a set of non-dominated solutions which can be used in subsequent steps by the decision maker, either to select a single non-dominated solution, to compare the solutions with an existing solution or to evaluate alternative solutions.…”

“…• High combinatorial complexity: Israeli and Ceder (1993) classified the problem as a complex variant of the generalized network design problem (Magnanti and Wong 1984), which is NP-hard. • The TNDP requires an assignment submodel: the evaluation of a given solution (from the users viewpoint) needs a behavior model of the passengers concerning the routes and frequencies of the solution.…”

“…The a posteriori mode has been adopted only in Israeli and Ceder (1993) and Mauttone and Urquhart (2004). To the best of our knowledge no interactive multi-objective optimization method has been applied to the TNDP.…”

Measurement of the Operating Parameters and Numerical Analysis of the Mechanical Subsystem

“…Following is a memory device, where it is possible to store obtained data for further processing. Measuring string does not have to contain all involved parts; it is possible to drop some of them, or expire some parts and to complete the measurements according to requirements of concrete application [1].…”