arXiv subjects

Samitha Samaranayake

Publications and source records attributed to Samitha Samaranayake.

At least 37 records · Page 2Linked to original sources

arXiv2022

Permutatorial Optimization via the Permutahedron

A water company decides to expand its network with a set of water lines, but it cannot build them all at once. However, it starts reaping benefits from a partial expansion. In what order should the company build the lines? We formalize a class of permutatorial problems with combinatorial/continuous subproblems capturing applications of incremental deployment. We show that, for additive/linear objective functions, efficient polyhedral methods for the subproblems extend to the permutatorial problem. Our main technical ingredient is the permutahedron.

math.OC↗

arXiv2022

Offline Vehicle Routing Problem with Online Bookings: A Novel Problem Formulation with Applications to Paratransit

Vehicle routing problems (VRPs) can be divided into two major categories: offline VRPs, which consider a given set of trip requests to be served, and online VRPs, which consider requests as they arrive in real-time. Based on discussions with public transit agencies, we identify a real-world problem that is not addressed by existing formulations: booking trips with flexible pickup windows (e.g., 3 hours) in advance (e.g., the day before) and confirming tight pickup windows (e.g., 30 minutes) at the time of booking. Such a service model is often required in paratransit service settings, where passengers typically book trips for the next day over the phone. To address this gap between offline and online problems, we introduce a novel formulation, the offline vehicle routing problem with online bookings. This problem is very challenging computationally since it faces the complexity of considering large sets of requests -- similar to offline VRPs -- but must abide by strict constraints on running time -- similar to online VRPs. To solve this problem, we propose a novel computational approach, which combines an anytime algorithm with a learning-based policy for real-time decisions. Based on a paratransit dataset obtained from the public transit agency of Chattanooga, TN, we demonstrate that our novel formulation and computational approach lead to significantly better outcomes in this setting than existing algorithms.

cs.AI↗

arXiv2022

Shareability Network Based Decomposition Approach for Solving Large-scale Single School Routing Problems

We consider the Single School Routing Problem (SSRP) where students from a single school are picked up by a fleet of school buses, subject to a set of constraints. The constraints that are typically imposed for school buses are bus capacity, a maximum student walking distance to a pickup point, and a maximum commute time for each student. This is a special case of the Vehicle Routing Problem (VRP) with a common destination. We propose a decomposition approach for solving this problem based on the existing notion of a shareability network, which has been used recently in the context of dynamic ridepooling problems. Moreover, we come up with a simplified formulation for solving the SSRP by introducing the connection between the SSRP and the weighted set covering problem (WSCP). To scale this method to large-scale problem instances, we propose i) a node compression method for the shareability network based decomposition approach, and ii) heuristic-based edge pruning techniques that perform well in practice. We show that the compressed problem leads to an Integer Linear Program (ILP) of reduced dimensionality that can be solved efficiently using off-the-shelf ILP solvers. Numerical experiments on the synthetic Boston Public School (BPS) instances are conducted to evaluate the performance of our approach. Meanwhile, our proposed SSRP formulation allows a natural extension for introducing alternate transportation modes to students, which effectively reduces the number of buses needed for each school and leads to a 15\% cost reduction on average. Moreover, two state-of-art large-scale SSRP solving techniques are compared with our proposed approaches on benchmark networks and our methods outperform both techniques under a single school setting.

math.OC↗

arXiv2022

An Online Approach to Solve the Dynamic Vehicle Routing Problem with Stochastic Trip Requests for Paratransit Services

Many transit agencies operating paratransit and microtransit services have to respond to trip requests that arrive in real-time, which entails solving hard combinatorial and sequential decision-making problems under uncertainty. To avoid decisions that lead to significant inefficiency in the long term, vehicles should be allocated to requests by optimizing a non-myopic utility function or by batching requests together and optimizing a myopic utility function. While the former approach is typically offline, the latter can be performed online. We point out two major issues with such approaches when applied to paratransit services in practice. First, it is difficult to batch paratransit requests together as they are temporally sparse. Second, the environment in which transit agencies operate changes dynamically (e.g., traffic conditions), causing estimates that are learned offline to become stale. To address these challenges, we propose a fully online approach to solve the dynamic vehicle routing problem (DVRP) with time windows and stochastic trip requests that is robust to changing environmental dynamics by construction. We focus on scenarios where requests are relatively sparse - our problem is motivated by applications to paratransit services. We formulate DVRP as a Markov decision process and use Monte Carlo tree search to evaluate actions for any given state. Accounting for stochastic requests while optimizing a non-myopic utility function is computationally challenging; indeed, the action space for such a problem is intractably large in practice. To tackle the large action space, we leverage the structure of the problem to design heuristics that can sample promising actions for the tree search. Our experiments using real-world data from our partner agency show that the proposed approach outperforms existing state-of-the-art approaches both in terms of performance and robustness.

cs.AI↗

arXiv2022

Optimization of vaccination for COVID-19 in the midst of a pandemic

During the Covid-19 pandemic a key role is played by vaccination to combat the virus. There are many possible policies for prioritizing vaccines, and different criteria for optimization: minimize death, time to herd immunity, functioning of the health system. Using an age-structured population compartmental finite-dimensional optimal control model, our results suggest that the eldest to youngest vaccination policy is optimal to minimize deaths. Our model includes the possible infection of vaccinated populations. We apply our model to real-life data from the US Census for New Jersey and Florida, which have a significantly different population structure. We also provide various estimates of the number of lives saved by optimizing the vaccine schedule and compared to no vaccination.

q-bio.PE↗

arXiv2021

A Framework for the Joint Optimization of Assignment and Pricing in Mobility-on-Demand Systems with Shared Rides

Mobility-on-Demand (MoD) systems have become a fixture in urban transportation networks, with the rapid growth of ride-hailing services such as Uber and Lyft. Ride-hailing is typically complemented with ridepooling options, which can reduce the negative externalities associated with ride-hailing services and increase the utilization of vehicles. Determining optimal policies for vehicle dispatching and pricing, two key components that enable MoD services, are challenging due to their massive scale and online nature. The challenge is amplified when the MoD platform offers exclusive (conventional ride-hailing) and shared services, and customers have the option to select between them. The pricing and dispatching problems are coupled because the realized demand depends on the quality of service (i.e., whom to share rides with) and the prices for each service type. We propose an integrated and computationally efficient method for solving the joint pricing and dispatching problem -- both when the problem is solved one request at a time or in batches (a common strategy in the industry). The main results of this research include showing that: (i) the sequential pricing problem has a closed-form solution under a multinomial logit (MNL) choice model, and (ii) the batched pricing problem is jointly concave in the expected demand distributions. To account for the spatial evolution of supply and demand, we introduce so-called retrospective costs to retain a tractable framework. Our numerical experiments demonstrate how this framework yields significant profit increases using taxicab data in Manhattan, New York City, compared to dynamic dispatching with static pricing policies.

eess.SY↗

arXiv2021

On the Request-Trip-Vehicle Assignment Problem

The request-trip-vehicle assignment problem is at the heart of a popular decomposition strategy for online vehicle routing. In this framework, assignments are done in batches in order to exploit any shareability among vehicles and incoming travel requests. We study a natural ILP formulation and its LP relaxation. Our main result is an LP-based randomized rounding algorithm that, whenever the instance is feasible, leverages mild assumptions to return an assignment whose: i) expected cost is at most that of an optimal solution, and ii) expected fraction of unassigned requests is at most $1/e$. If trip-vehicle assignment costs are $α$-approximate, we pay an additional factor of $α$ in the expected cost. We can relax the feasibility requirement by considering the penalty version of the problem, in which a penalty is paid for each unassigned request. We find that, whenever a request is repeatedly unassigned after a number of rounds, with high probability it is so in accordance with the sequence of LP solutions and not because of a rounding error. We additionally introduce a deterministic rounding heuristic inspired by our randomized technique. Our computational experiments show that our rounding algorithms achieve a performance similar to that of the ILP at a reduced computation time, far improving on our theoretical guarantee. The reason for this is that, although the assignment problem is hard in theory, the natural LP relaxation tends to be very tight in practice.

cs.DS↗

arXiv2021

Safe reopening of university campuses is possible with COVID-19 vaccination

We construct an agent-based SEIR model to simulate COVID-19 spread at a 16000-student mostly non-residential urban university during the Fall 2021 Semester. We find that mRNA vaccine coverage above 80% makes it possible to safely reopen to in-person instruction. If vaccine coverage is 100%, then our model indicates that facemask use is not necessary. Our simulations with vaccine coverage below 70% exhibit a right-skew for total infections over the semester, which suggests that high levels of infection are not exceedingly rare with campus social connections the main transmission route. Less effective vaccines or incidence of new variants may require additional intervention such as screening testing to reopen safely.

q-bio.PE↗

arXiv2021

Multimodal Mobility Systems: Joint Optimization of Transit Network Design and Pricing

The performance of multimodal mobility systems relies on the seamless integration of conventional mass transit services and the advent of Mobility-on-Demand (MoD) services. Prior work is limited to individually improving various transport networks' operations or linking a new mode to an existing system. In this work, we attempt to solve transit network design and pricing problems of multimodal mobility systems en masse. An operator (public transit agency or private transit operator) determines the frequency settings of the mass transit system, flows of the MoD service, and prices for each trip to optimize the overall welfare. A primal-dual approach, inspired by the market design literature, yields a compact mixed integer linear programming (MILP) formulation. However, a key computational challenge remains in allocating an exponential number of hybrid modes accessible to travelers. We provide a tractable solution approach through a decomposition scheme and approximation algorithm that accelerates the computation and enables optimization of large-scale problem instances. Using a case study in Nashville, Tennessee, we demonstrate the value of the proposed model. We also show that our algorithm reduces the average runtime by 60\% compared to advanced MILP solvers. This result seeks to establish a generic and simple-to-implement way of revamping and redesigning regional mobility systems in order to meet the increase in travel demand and integrate traditional fixed-line mass transit systems with new demand-responsive services.

cs.CE↗

arXiv2021

Fleet management for ride-pooling with meeting points at scale: a case study in the five boroughs of New York City

Introducing meeting points to ride-pooling (RP) services has been shown to increase the satisfaction level of both riders and service providers. Passengers may choose to walk to a meeting point for a cost reduction. Drivers may also get matched with more riders without making additional stops. There are economic benefits of using ride-pooling with meeting points (RPMP) compared to the traditional RP services. Many RPMP models have been proposed to better understand their benefits. However, most prior works study RPMP either with a restricted set of parameters or at a small scale due to the expensive computation involved. In this paper, we propose STaRS+, a scalable RPMP framework that is based on a comprehensive integer linear programming model. The high scalability of STaRS+ is achieved by utilizing a heuristic optimization strategy along with a novel shortest-path caching scheme. We applied our model to the NYC metro area to evaluate the scalability of the framework and demonstrate the importance of city-scale simulations. Our results show that city-scale simulations can reveal valuable insights for city planners that are not always visible at smaller scales. To the best of our knowledge, STaRS+ is the first study on the RPMP that can solve large-scale instances on the order of the entire NYC metro area.

eess.SY↗

arXiv2021

Real-Time Approximate Routing for Smart Transit Systems

We study real-time routing policies in smart transit systems, where the platform has a combination of cars and high-capacity vehicles (e.g., buses or shuttles) and seeks to serve a set of incoming trip requests. The platform can use its fleet of cars as a feeder to connect passengers to its high-capacity fleet, which operates on fixed routes. Our goal is to find the optimal set of (bus) routes and corresponding frequencies to maximize the social welfare of the system in a given time window. This generalizes the Line Planning Problem, a widely studied topic in the transportation literature, for which existing solutions are either heuristic (with no performance guarantees), or require extensive computation time (and hence are impractical for real-time use). To this end, we develop a $1-\frac{1}{e}-\varepsilon$ approximation algorithm for the Real-Time Line Planning Problem, using ideas from randomized rounding and the Generalized Assignment Problem. Our guarantee holds under two assumptions: $(i)$ no inter-bus transfers and $(ii)$ access to a pre-specified set of feasible bus lines. We moreover show that these two assumptions are crucial by proving that, if either assumption is relaxed, the Real-Time Line Planning Problem does not admit any constant-factor approximation. Finally, we demonstrate the practicality of our algorithm via numerical experiments on real-world and synthetic datasets, in which we show that, given a fixed time budget, our algorithm outperforms Integer Linear Programming-based exact methods.

math.OC↗

arXiv2021

Real Time Operation of High-Capacity Electric Vehicle Ridesharing Fleets

We study the feasibility of using electric vehicles in online, high-capacity ridepooling systems. Prior work has shown that online algorithms perform well for centrally-controlled, high-capacity ridepool systems. First, we propose a mixed integer linear program to expand past algorithms on ridepooling to electric vehicles fleets with the objective of scheduling vehicle charging to maintain sufficient fleet sizes at various times of day. Then we show a faster, scalable algorithm with similar performance that is practical for full-scale systems. Our contributions show the importance of having knowledge and estimates of future demand even when operating in the online setting.

eess.SY↗

arXiv2020

SEIR-Campus: Modeling Infectious Diseases on University Campuses

We introduce a Python package for modeling and studying the spread of infectious diseases using an agent-based SEIR style epidemiological model with a focus on university campuses. This document explains the epidemiological model used in the package and gives examples highlighting the ways that the package can be used.

q-bio.PE↗

arXiv2019

Can Mobility-on-Demand services do better after discerning reliability preferences of riders?

We formalize one aspect of reliability in the context of Mobility-on-Demand (MoD) systems by acknowledging the uncertainty in the pick-up time of these services. This study answers two key questions: i) how the difference between the stated and actual pick-up times affect the propensity of a passenger to choose an MoD service? ii) how an MoD service provider can leverage this information to increase its ridership? We conduct a discrete choice experiment in New York to answer the former question and adopt a micro-simulation-based optimization method to answer the latter question. In our experiments, the ridership of an MoD service could be increased by up to 10\% via displaying the predicted wait time strategically.

econ.GN↗

arXiv2019

Proactive rebalancing and speed-up techniques for on-demand high capacity ridesourcing services

We present a probabilistic proactive rebalancing method and speed-up techniques for improving the performance of a state-of-the-art real-time high-capacity fleet management framework [1]. We improve on both computational efficiency and system performance. The speed-up techniques include search-space pruning and I/O cost reduction for parallelization, reducing the computation time by up to 97.67%, in experiments on taxi trips in New York City. The proactive rebalancing routes idle vehicles to future demands based on probabilistic estimates from historical demand, increasing the service rate by 4.8% on average, and decreasing the waiting time and total delay by 5.0% and 10.7% on average, respectively.

eess.SY↗

arXiv2018

The Batched Set Cover Problem

We introduce the batched set cover problem, which is a generalization of the online set cover problem. In this problem, the elements of the ground set that need to be covered arrive in batches. Our main technical contribution is a tight $Ω(H_{m - 2^z + 1})$ lower bound on the competitive ratio of any fractional batched algorithm given an adversary that is required to produce batches of VC-dimension at least $z$, for some $z \in \mathbb{N}^0$. This restriction on the adversary is motivated by the fact that, in some real world applications, decisions are made after collecting batches of data of non-trivial VC-dimension. In particular, ridesharing systems rely on the batch assignment of trip requests to vehicles, and some related problems such as that of optimal congregation points for passenger pickups and dropoffs can be modeled as a batched set cover problem with VC-dimension greater than or equal to two. Furthermore, we note that while any online algorithm may be used to solve the batched set cover problem by artificially sequencing the elements in a batch, this procedure may neglect the rich information encoded in the complex interactions between the elements of a batch and the sets that contain them. Therefore, we propose a minor modification to an online algorithm found in [8] to obtain an algorithm that attempts to exploit such information. Unfortunately, we are unable to improve its analysis in a way that reflects this intuition. However, we present computational experiments that provide empirical evidence of a constant factor improvement in the competitive ratio. To the best of our knowledge, we are the first to use the VC-dimension in the context of online (batched) covering problems.

cs.DS↗

arXiv2018

Stochastic on-time arrival problem in transit networks

This article considers the stochastic on-time arrival problem in transit networks where both the travel time and the waiting time for transit services are stochastic. A specific challenge of this problem is the combinatorial solution space due to the unknown ordering of transit line arrivals. We propose a network structure appropriate to the online decision-making of a passenger, including boarding, waiting and transferring. In this framework, we design a dynamic programming algorithm that is pseudo-polynomial in the number of transit stations and travel time budget, and exponential in the number of transit lines at a station, which is a small number in practice. To reduce the search space, we propose a definition of transit line dominance, and techniques to identify dominance, which decrease the computation time by up to 90% in numerical experiments. Extensive numerical experiments are conducted on both a synthetic network and the Chicago transit network.

cs.DS↗

arXiv2018

A Framework to Integrate Mode Choice in the Design of Mobility-on-Demand Systems

Mobility-on-Demand (MoD) systems are generally designed and analyzed for a fixed and exogenous demand, but such frameworks fail to answer questions about the impact of these services on the urban transportation system, such as the effect of induced demand and the implications for transit ridership. In this study, we propose a unified framework to design, optimize and analyze MoD operations within a multimodal transportation system where the demand for a travel mode is a function of its level of service. An application of Bayesian optimization (BO) to derive the optimal supply-side MoD parameters (e.g., fleet size and fare) is also illustrated. The proposed framework is calibrated using the taxi demand data in Manhattan, New York. Travel demand is served by public transit and MoD services of varying passenger capacities (1, 4 and 10), and passengers are predicted to choose travel modes according to a mode choice model. This choice model is estimated using stated preference data collected in New York City. The convergence of the multimodal supply-demand system and the superiority of the BO-based optimization method over earlier approaches are established through numerical experiments. We finally consider a policy intervention where the government imposes a tax on the ride-hailing service and illustrate how the proposed framework can quantify the pros and cons of such policies for different stakeholders.

eess.SY↗