1,798 research outputs found
A Special Case of the Multiple Traveling Salesmen Problem in End-of-Aisle Picking Systems
This study focuses on the problem of sequencing requests for an end-of-aisle automated storage and retrieval system in which each retrieved load must be returned to its earlier storage location after a worker has picked some products from the load. At the picking station, a buffer is maintained to absorb any fluctuations in speed between the worker and the storage/retrieval machine. We show that, under conditions, the problem of optimally sequencing the requests in this system with a buffer size of m loads forms a special case of the multiple traveling salesmen problem in which each salesman visits the same number of cities. Several interesting structural properties for the problem are mathematically shown. In addition, a branch-and-cut method and heuristics are proposed. Experimental results show that the proposed simulated annealing-based heuristic performs well in all circumstances and significantly outperforms benchmark heuristics. For instances with negligible picking times for the worker, we show that this heuristic provides solutions that are, on average, within 1.8% from the optimal value
Learning scalable and transferable multi-robot/machine sequential assignment planning via graph embedding
Can the success of reinforcement learning methods for simple combinatorial
optimization problems be extended to multi-robot sequential assignment
planning? In addition to the challenge of achieving near-optimal performance in
large problems, transferability to an unseen number of robots and tasks is
another key challenge for real-world applications. In this paper, we suggest a
method that achieves the first success in both challenges for robot/machine
scheduling problems.
Our method comprises of three components. First, we show a robot scheduling
problem can be expressed as a random probabilistic graphical model (PGM). We
develop a mean-field inference method for random PGM and use it for Q-function
inference. Second, we show that transferability can be achieved by carefully
designing two-step sequential encoding of problem state. Third, we resolve the
computational scalability issue of fitted Q-iteration by suggesting a heuristic
auction-based Q-iteration fitting method enabled by transferability we
achieved.
We apply our method to discrete-time, discrete space problems (Multi-Robot
Reward Collection (MRRC)) and scalably achieve 97% optimality with
transferability. This optimality is maintained under stochastic contexts. By
extending our method to continuous time, continuous space formulation, we claim
to be the first learning-based method with scalable performance among
multi-machine scheduling problems; our method scalability achieves comparable
performance to popular metaheuristics in Identical parallel machine scheduling
(IPMS) problems
The Minimum Backlog Problem
We study the minimum backlog problem (MBP). This online problem arises, e.g.,
in the context of sensor networks. We focus on two main variants of MBP.
The discrete MBP is a 2-person game played on a graph . The player
is initially located at a vertex of the graph. In each time step, the adversary
pours a total of one unit of water into cups that are located on the vertices
of the graph, arbitrarily distributing the water among the cups. The player
then moves from her current vertex to an adjacent vertex and empties the cup at
that vertex. The player's objective is to minimize the backlog, i.e., the
maximum amount of water in any cup at any time.
The geometric MBP is a continuous-time version of the MBP: the cups are
points in the two-dimensional plane, the adversary pours water continuously at
a constant rate, and the player moves in the plane with unit speed. Again, the
player's objective is to minimize the backlog.
We show that the competitive ratio of any algorithm for the MBP has a lower
bound of , where is the diameter of the graph (for the discrete
MBP) or the diameter of the point set (for the geometric MBP). Therefore we
focus on determining a strategy for the player that guarantees a uniform upper
bound on the absolute value of the backlog.
For the absolute value of the backlog there is a trivial lower bound of
, and the deamortization analysis of Dietz and Sleator gives an
upper bound of for cups. Our main result is a tight upper
bound for the geometric MBP: we show that there is a strategy for the player
that guarantees a backlog of , independently of the number of cups.Comment: 1+16 pages, 3 figure
Persistent Monitoring of Events with Stochastic Arrivals at Multiple Stations
This paper introduces a new mobile sensor scheduling problem, involving a
single robot tasked with monitoring several events of interest that occur at
different locations. Of particular interest is the monitoring of transient
events that can not be easily forecast. Application areas range from natural
phenomena ({\em e.g.}, monitoring abnormal seismic activity around a volcano
using a ground robot) to urban activities ({\em e.g.}, monitoring early
formations of traffic congestion using an aerial robot). Motivated by those and
many other examples, this paper focuses on problems in which the precise
occurrence times of the events are unknown {\em a priori}, but statistics for
their inter-arrival times are available. The robot's task is to monitor the
events to optimize the following two objectives: {\em (i)} maximize the number
of events observed and {\em (ii)} minimize the delay between two consecutive
observations of events occurring at the same location. The paper considers the
case when a robot is tasked with optimizing the event observations in a
balanced manner, following a cyclic patrolling route. First, assuming the
cyclic ordering of stations is known, we prove the existence and uniqueness of
the optimal solution, and show that the optimal solution has desirable
convergence and robustness properties. Our constructive proof also produces an
efficient algorithm for computing the unique optimal solution with time
complexity, in which is the number of stations, with time
complexity for incrementally adding or removing stations. Except for the
algorithm, most of the analysis remains valid when the cyclic order is unknown.
We then provide a polynomial-time approximation scheme that gives a
-optimal solution for this more general, NP-hard problem
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