266 research outputs found
Stochastic Model Predictive Control for Autonomous Mobility on Demand
This paper presents a stochastic, model predictive control (MPC) algorithm
that leverages short-term probabilistic forecasts for dispatching and
rebalancing Autonomous Mobility-on-Demand systems (AMoD, i.e. fleets of
self-driving vehicles). We first present the core stochastic optimization
problem in terms of a time-expanded network flow model. Then, to ameliorate its
tractability, we present two key relaxations. First, we replace the original
stochastic problem with a Sample Average Approximation (SAA), and characterize
the performance guarantees. Second, we separate the controller into two
separate parts to address the task of assigning vehicles to the outstanding
customers separate from that of rebalancing. This enables the problem to be
solved as two totally unimodular linear programs, and thus easily scalable to
large problem sizes. Finally, we test the proposed algorithm in two scenarios
based on real data and show that it outperforms prior state-of-the-art
algorithms. In particular, in a simulation using customer data from DiDi
Chuxing, the algorithm presented here exhibits a 62.3 percent reduction in
customer waiting time compared to state of the art non-stochastic algorithms.Comment: Submitting to the IEEE International Conference on Intelligent
Transportation Systems 201
A polynomial-time algorithm for optimizing over N-fold 4-block decomposable integer programs
In this paper we generalize N-fold integer programs and two-stage integer
programs with N scenarios to N-fold 4-block decomposable integer programs. We
show that for fixed blocks but variable N, these integer programs are
polynomial-time solvable for any linear objective. Moreover, we present a
polynomial-time computable optimality certificate for the case of fixed blocks,
variable N and any convex separable objective function. We conclude with two
sample applications, stochastic integer programs with second-order dominance
constraints and stochastic integer multi-commodity flows, which (for fixed
blocks) can be solved in polynomial time in the number of scenarios and
commodities and in the binary encoding length of the input data. In the proof
of our main theorem we combine several non-trivial constructions from the
theory of Graver bases. We are confident that our approach paves the way for
further extensions
Option Pricing by Mathematical Programming
Financial options typically incorporate times of exercise. Alternatively, they embody setup costs or indivisibilities. Such features lead to planning problems with integer decision variables. Provided the sample space be finite, it is shown here that integrality constraints can often be relaxed. In fact, simple mathematical programming, aimed at arbitrage or replication, may find optimal exercise, and bound or identify option prices. When the asset market is incomplete, the bounds system from nonlinear pricing functionals
Fixed-Support Wasserstein Barycenters: Computational Hardness and Fast Algorithm
We study the fixed-support Wasserstein barycenter problem (FS-WBP), which
consists in computing the Wasserstein barycenter of discrete probability
measures supported on a finite metric space of size . We show first that the
constraint matrix arising from the standard linear programming (LP)
representation of the FS-WBP is \textit{not totally unimodular} when
and . This result resolves an open question pertaining to the
relationship between the FS-WBP and the minimum-cost flow (MCF) problem since
it proves that the FS-WBP in the standard LP form is not an MCF problem when and . We also develop a provably fast \textit{deterministic}
variant of the celebrated iterative Bregman projection (IBP) algorithm, named
\textsc{FastIBP}, with a complexity bound of
, where is the
desired tolerance. This complexity bound is better than the best known
complexity bound of for the IBP algorithm in
terms of , and that of from
accelerated alternating minimization algorithm or accelerated primal-dual
adaptive gradient algorithm in terms of . Finally, we conduct extensive
experiments with both synthetic data and real images and demonstrate the
favorable performance of the \textsc{FastIBP} algorithm in practice.Comment: Accepted by NeurIPS 2020; fix some confusing parts in the proof and
improve the empirical evaluatio
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