Page IV was not included in the thesis, and thus not included in the page count. / <p> Discretization is an important tool to transfer optimization problems that include differentiations and integrals into standard optimization problems with a finite number of variables and a finite number of constraints. Recently, Betts and Campbell proposed a heat-transfer optimization problem that includes the heat partial differential equation as one of its constraints, and the objective function includes integrals of the temperature function squared. Using discretization methods, this problem can be converted to a convex quadratic optimization problem, which can be solved by standard interior point method solvers in polynomial time.</p> <p> The discretized model of the one dimensional problem is further analyzed, and some of its variants are studied. Extensive numerical testing is performed to demonstrate the power of the "discretize then optimize". Then the heat transfer optimization problem is generalized to two dimensions, and the discretized model and computational comparisons for this variant are included.</p> <p> Flexibility of discretization methods allow us to apply the same "diseretize then optimize" methodology to solve optimization problems that include differential and integral functions as constraints or objectives.</p> / Thesis / Master of Science (MSc)

In multi-modal transit networks with several intersecting lines and modes, travel through the network typically requires one or more transfers among transit lines and modes, and as such transfer time is a significant component of transit travel time from the perspective of passengers. Accordingly, efficient transfers are very important to increase the attractiveness and productivity of transit service. This study presents two approaches for the provision of efficient transfers: schedule coordination and real-time CP (Connection Protection) control. The coordination of transit schedules can reduce transfer time significantly. This dissertation develops an optimization model for generating transit timetables that minimize transfer-related times. The model attempts to find an optimal timetable by shifting the existing timetable and/or adding holding time to the timetable to minimize delays associated with transfers from a feeder route to a receiving route. Analytical models are developed to estimate the waiting time of the transfer passengers, and also to determine the influence of the schedule modification on the waiting times of non-transfer passengers. The developed model is evaluated through a case study, and the results show that the model reduces effectively the total transfer and waiting times through the modification of the current schedule. However, even though timetables among intersecting lines may be properly coordinated, an operational control method is necessary to maintain coordinated transfers, which may occasionally be disrupted due to unexpected delays of transit vehicles. A promising approach is to utilize real-time CP control. It involves holding a transit unit in order to wait for another transit unit that is planned to provide a coordinated transfer but has been delayed. This study also develops a CP model to apply a holding control to a receiving run in order to protect the scheduled connection. It incorporates the probabilistic nature of transit operations in formulating a cost function, and accordingly makes more robust decisions for control. The developed model is evaluated and compared with previous models to demonstrate its ability to improve transfer efficiency and reduce the waiting times of affected passengers.

In multi-modal transit networks with several intersecting lines and modes, travel through the network typically requires one or more transfers among transit lines and modes, and as such transfer time is a significant component of transit travel time from the perspective of passengers. Accordingly, efficient transfers are very important to increase the attractiveness and productivity of transit service. This study presents two approaches for the provision of efficient transfers: schedule coordination and real-time CP (Connection Protection) control. The coordination of transit schedules can reduce transfer time significantly. This dissertation develops an optimization model for generating transit timetables that minimize transfer-related times. The model attempts to find an optimal timetable by shifting the existing timetable and/or adding holding time to the timetable to minimize delays associated with transfers from a feeder route to a receiving route. Analytical models are developed to estimate the waiting time of the transfer passengers, and also to determine the influence of the schedule modification on the waiting times of non-transfer passengers. The developed model is evaluated through a case study, and the results show that the model reduces effectively the total transfer and waiting times through the modification of the current schedule. However, even though timetables among intersecting lines may be properly coordinated, an operational control method is necessary to maintain coordinated transfers, which may occasionally be disrupted due to unexpected delays of transit vehicles. A promising approach is to utilize real-time CP control. It involves holding a transit unit in order to wait for another transit unit that is planned to provide a coordinated transfer but has been delayed. This study also develops a CP model to apply a holding control to a receiving run in order to protect the scheduled connection. It incorporates the probabilistic nature of transit operations in formulating a cost function, and accordingly makes more robust decisions for control. The developed model is evaluated and compared with previous models to demonstrate its ability to improve transfer efficiency and reduce the waiting times of affected passengers.