Solving the Dynamic Dial-a-Ride Problem Using a Rolling-Horizon Event-Based Graph

In many ridepooling applications transportation requests arrive throughout the day and have to be answered and integrated into the existing (and operated) vehicle routing. To solve this dynamic dial-a-ride problem we present a rolling-horizon algorithm that dynamically updates the current solution by solving an MILP formulation. The MILP model is based on an event-based graph with nodes representing pick-up and drop-off events associated with feasible user allocations in the vehicles. The proposed solution approach is validated on a set of real-word instances with more than 500 requests. In 99.5% of all iterations the rolling-horizon algorithm returned optimal insertion positions w.r.t. the current schedule in a time-limit of 30 seconds. On average, incoming requests are answered within 2.8 seconds

A Tight Formulation for the Dial-a-Ride Problem

Ridepooling services play an increasingly important role in modern transportation systems. With soaring demand and growing fleet sizes, the underlying route planning problems become increasingly challenging. In this context, we consider the dial-a-ride problem (DARP): Given a set of transportation requests with pick-up and delivery locations, passenger numbers, time windows, and maximum ride times, an optimal routing for a fleet of vehicles, including an optimized passenger assignment, needs to be determined. We present tight mixed-integer linear programming (MILP) formulations for the DARP by combining two state-of-the-art models into novel location-augmented-event-based formulations. Strong valid inequalities and lower and upper bounding techniques are derived to further improve the formulations. We then demonstrate the theoretical and computational superiority of the new model: First, the formulation is tight in the sense that, if time windows shrink to a single point in time, the linear programming relaxation yields integer (and hence optimal) solutions. Second, extensive numerical experiments on benchmark instances show that computational times are on average reduced by 49.7% compared to state-of-the-art event-based approaches

No influence of 5-HTTLPR gene polymorphism on migraine symptomatology, comorbid depression, and chronification

Background. - The serotonergic system is thought to play an important role for mediating susceptibility to migraine and depression, which is frequently found comorbid in migraine. The functional polymorphism in the serotonin transporter gene linked polymorphic region (5-HTTLPR/SLC6A4) was previously associated with attack frequency and, thus, possibly with chronification. Objective. - We hypothesized that patients with the "s" allele have higher attack frequency and, paralleling results in depression research, higher scores of depression. Methods. - Genetic analysis of the SLC6A4 44 bp insertion/deletion polymorphism (5-HTTLPR) was performed in 293 patients with migraine with and without aura. Self-rating questionnaires were used for assessment of depression. Results. - Multinomial logistic regression analysis found no evidence for association of the 5-HTTLPR polymorphism with either depression or migraine attack frequency. Conclusion. - We were not able to demonstrate any influence of the serotonin transporter 5-HTTLPR polymorphism on migraine phenomenology (attack frequency or comorbid depression), thereby excluding this variant to be a common genetic denominator for chronic migraine and depression