The basic construction of the objective functions of the transit network design problem is described, and a new approach taking account of both passenger and operator interests is proposed. The approach presented combines the philosophy of the mathematical programming approaches with decision-making techniques in order to allow the user to select from a number of alternatives. The nature of the overall formulation is nonlinear and mixed-integer programming.

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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.

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