Mixed-integer Programming for a New Bus-lane Reservation Problem

Abstract

In this paper, we investigate a new bus-lane reservation problem in transportation network, which aims to optimally decide which lanes to be reserved for the exclusive use of buses and design bus transit paths for bus lines to achieve time-efficient bus transit with stop time window constraints. However, an exclusive bus-lane may cause negative impact on non-bus vehicles running on its adjacent non-reserved lanes as it reduces their available lanes. The objective of the problem is to minimize the total negative impact caused by reserved lanes. To address this problem, we first formulate a mixed-integer non-linear program and its complexity is proved to be NP-hard. Then, the nonlinear model is equivalently transformed into an linear one. Furthermore, properties of the problem are analyzed to reduce the search space for optimal solutions and tighten the proposed linear model. Finally, it is solved using commercial optimization software CPLEX. Computational results on randomly generated instances show the effectiveness of the proposed approach.

Identification of Optimal Left-Turn Restriction Locations using Heuristic Methods

“…Both BOA and PBIL are capable algorithms to solve complicated problems but have several limitations. PBIL samples configurations from different parts of the solution space because of its exploration focus, but this makes the PBIL algorithm slow to converge to a particular solution ( 29 ). BOA is faster to converge to a solution because it focuses on learning dependencies between decision variables but requires a large population to accurately learn these dependencies for problems with a high number of dependent decision variables.…”

“…This type of problem is most closely related to general facility location problems in the transportation research literature, which are classified as NP-hard optimization problems because of the large solution space and lack of analytical solution ( 29 ). Within urban networks, many studies have proposed methods to determine optimal location of specific treatments along individual links—for example, optimal bus lane locations ( 30 – 33 )—or at individual intersections—for example, optimal transit signal priority locations ( 34 , 35 ).…”