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Register a new userCompetitive Ratios for Online Multi-capacity Ridesharing
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Added by
Meghna Lowalekar
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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In multi-capacity ridesharing, multiple requests (e.g., customers, food items, parcels) with different origin and destination pairs travel in one resource. In recent years, online multi-capacity ridesharing services (i.e., where assignments are made online) like Uber-pool, foodpanda, and on-demand shuttles have become hugely popular in transportation, food delivery, logistics and other domains. This is because multi-capacity ridesharing services benefit all parties involved { the customers (due to lower costs), the drivers (due to higher revenues) and the matching platforms (due to higher revenues per vehicle/resource). Most importantly these services can also help reduce carbon emissions (due to fewer vehicles on roads). Online multi-capacity ridesharing is extremely challenging as the underlying matching graph is no longer bipartite (as in the unit-capacity case) but a tripartite graph with resources (e.g., taxis, cars), requests and request groups (combinations of requests that can travel together). The desired matching between resources and request groups is constrained by the edges between requests and request groups in this tripartite graph (i.e., a request can be part of at most one request group in the final assignment). While there have been myopic heuristic approaches employed for solving the online multi-capacity ridesharing problem, they do not provide any guarantees on the solution quality. To that end, this paper presents the first approach with bounds on the competitive ratio for online multi-capacity ridesharing (when resources rejoin the system at their initial location/depot after serving a group of requests).
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This paper studies online optimization under inventory (budget) constraints. While online optimization is a well-studied topi
We consider a new and general online resource allocation problem, where the goal is to maximize a function of a positive semidefinite (PSD) matrix with a scalar budget constraint. The problem data arrives online, and the algorithm needs to make an irrevocable decision at each step. Of particular interest are classic experiment design problems in the online setting, with the algorithm deciding whether to allocate budget to each experiment as new experiments become available sequentially. We analyze two greedy primal-dual algorithms and provide bounds on their competitive ratios. Our analysis relies on a smooth surrogate of the objective function that needs to satisfy a new diminishing returns (PSD-DR) property (that its gradient is order-reversing with respect to the PSD cone). Using the representation for monotone maps on the PSD cone given by Lowners theorem, we obtain a convex parametrization of the family of functions satisfying PSD-DR. We then formulate a convex optimization problem to directly optimize our competitive ratio bound over this set. This design problem can be solved offline before the data start arriving. The online algorithm that uses the designed smoothing is tailored to the given cost function, and enjoys a competitive ratio at least as good as our optimized bound. We provide examples of computing the smooth surrogate for D-optimal and A-optimal experiment design, and demonstrate the performance of the custom-designed algorithm.
With the popularity of the Internet, traditional offline resource allocation has evolved into a new form, called online resource allocation. It features the online arrivals of agents in the system and the real-time decision-making requirement upon the arrival of each online agent. Both offline and online resource allocation have wide applications in various real-world matching markets ranging from ridesharing to crowdsourcing. There are some emerging applications such as rebalancing in bike sharing and trip-vehicle dispatching in ridesharing, which involve a two-stage resource allocation process. The process consists of an offline phase and another sequential online phase, and both phases compete for the same set of resources. In this paper, we propose a unified model which incorporates both offline and online resource allocation into a single framework. Our model assumes non-uniform and known arrival distributions for online agents in the second online phase, which can be learned from historical data. We propose a parameterized linear programming (LP)-based algorithm, which is shown to be at most a constant factor of $1/4$ from the optimal. Experimental results on the real dataset show that our LP-based approaches outperform the LP-agnostic heuristics in terms of robustness and effectiveness.
Huang et al.~(STOC 2018) introduced the fully online matching problem, a generalization of the classic online bipartite matching problem in that it allows all vertices to arrive online and considers general graphs. They showed that the ranking algorithm by Karp et al.~(STOC 1990) is strictly better than $0.5$-competitive and the problem is strictly harder than the online bipartite matching problem in that no algorithms can be $(1-1/e)$-competitive. This paper pins down two tight competitive ratios of classic algorithms for the fully online matching problem. For the fractional version of the problem, we show that a natural instantiation of the water-filling algorithm is $2-sqrt{2} approx 0.585$-competitive, together with a matching hardness result. Interestingly, our hardness result applies to arbitrary algorithms in the edge-arrival models of the online matching problem, improving the state-of-art $frac{1}{1+ln 2} approx 0.5906$ upper bound. For integral algorithms, we show a tight competitive ratio of $approx 0.567$ for the ranking algorithm on bipartite graphs, matching a hardness result by Huang et al. (STOC 2018).
Real-time ridesharing systems such as UberPool, Lyft Line, GrabShare have become hugely popular as they reduce the costs for customers, improve per trip revenue for drivers and reduce traffic on the roads by grouping customers with similar itineraries. The key challenge in these systems is to group the right requests to travel together in the right available vehicles in real-time, so that the objective (e.g., requests served, revenue or delay) is optimized. This challenge has been addressed in existing work by: (i) generating as many relevant feasible (with respect to the available delay for customers) combinations of requests as possible in real-time; and then (ii) optimizing assignment of the feasible request combinations to vehicles. Since the number of request combinations increases exponentially with the increase in vehicle capacity and number of requests, unfortunately, such approaches have to employ ad hoc heuristics to identify a subset of request combinations for assignment. Our key contribution is in developing approaches that employ zone (abstraction of individual locations) paths instead of request combinations. Zone paths allow for generation of significantly more relevant combinations (in comparison to ad hoc heuristics) in real-time than competing approaches due to two reasons: (i) Each zone path can typically represent multiple request combinations; (ii) Zone paths are generated using a combination of offline and online methods. Specifically, we contribute both myopic (ridesharing assignment focussed on current requests only) and non-myopic (ridesharing assignment considers impact on expected future requests) approaches that employ zone paths. In our experimental results, we demonstrate that our myopic approach outperforms (with respect to both objective and runtime) the current best myopic approach for ridesharing on both real-world and synthetic datasets.
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