256 research outputs found
Exact distributional analysis of online algorithms with lookahead
In online optimization, input data is revealed sequentially. Optimization problems in practice often exhibit this type of information disclosure as opposed to standard offline optimization where all information is known in advance. We analyze the performance of algorithms for online optimization with lookahead using a holistic distributional approach. To this end, we first introduce the performance measurement method of counting distribution functions. Then, we derive analytical expressions for the counting distribution functions of the objective value and the performance ratio in elementary cases of the online bin packing and the online traveling salesman problem. For bin packing, we also establish a relation between algorithm processing and the Catalan numbers. The paper shows that an exact analysis is strongly interconnected to the combinatorial structure of the problem and algorithm under consideration. Results further indicate that the value of lookahead heavily relies on the problem itself. The analysis also shows that exact distributional analysis could be used in order to discover key effects and identify related root causes in relatively simple problem settings. These insights can then be transferred to the analysis of more complex settings where the introduced performance measurement approach has to be used on an approximative basis (e.g., in a simulation-based optimization)
Online Bin Packing with Advice
We consider the online bin packing problem under the advice complexity model
where the 'online constraint' is relaxed and an algorithm receives partial
information about the future requests. We provide tight upper and lower bounds
for the amount of advice an algorithm needs to achieve an optimal packing. We
also introduce an algorithm that, when provided with log n + o(log n) bits of
advice, achieves a competitive ratio of 3/2 for the general problem. This
algorithm is simple and is expected to find real-world applications. We
introduce another algorithm that receives 2n + o(n) bits of advice and achieves
a competitive ratio of 4/3 + {\epsilon}. Finally, we provide a lower bound
argument that implies that advice of linear size is required for an algorithm
to achieve a competitive ratio better than 9/8.Comment: 19 pages, 1 figure (2 subfigures
Online 3D Bin Packing with Constrained Deep Reinforcement Learning
We solve a challenging yet practically useful variant of 3D Bin Packing
Problem (3D-BPP). In our problem, the agent has limited information about the
items to be packed into the bin, and an item must be packed immediately after
its arrival without buffering or readjusting. The item's placement also
subjects to the constraints of collision avoidance and physical stability. We
formulate this online 3D-BPP as a constrained Markov decision process. To solve
the problem, we propose an effective and easy-to-implement constrained deep
reinforcement learning (DRL) method under the actor-critic framework. In
particular, we introduce a feasibility predictor to predict the feasibility
mask for the placement actions and use it to modulate the action probabilities
output by the actor during training. Such supervisions and transformations to
DRL facilitate the agent to learn feasible policies efficiently. Our method can
also be generalized e.g., with the ability to handle lookahead or items with
different orientations. We have conducted extensive evaluation showing that the
learned policy significantly outperforms the state-of-the-art methods. A user
study suggests that our method attains a human-level performance
Learning Practically Feasible Policies for Online 3D Bin Packing
We tackle the Online 3D Bin Packing Problem, a challenging yet practically
useful variant of the classical Bin Packing Problem. In this problem, the items
are delivered to the agent without informing the full sequence information.
Agent must directly pack these items into the target bin stably without
changing their arrival order, and no further adjustment is permitted. Online
3D-BPP can be naturally formulated as Markov Decision Process (MDP). We adopt
deep reinforcement learning, in particular, the on-policy actor-critic
framework, to solve this MDP with constrained action space. To learn a
practically feasible packing policy, we propose three critical designs. First,
we propose an online analysis of packing stability based on a novel stacking
tree. It attains a high analysis accuracy while reducing the computational
complexity from to , making it especially suited for RL
training. Second, we propose a decoupled packing policy learning for different
dimensions of placement which enables high-resolution spatial discretization
and hence high packing precision. Third, we introduce a reward function that
dictates the robot to place items in a far-to-near order and therefore
simplifies the collision avoidance in movement planning of the robotic arm.
Furthermore, we provide a comprehensive discussion on several key implemental
issues. The extensive evaluation demonstrates that our learned policy
outperforms the state-of-the-art methods significantly and is practically
usable for real-world applications.Comment: Science China Information Science
Tight bounds for NF-based bounded-space online bin packing algorithms
In Zheng et al. (J Comb Optim 30(2):360–369, 2015) modelled a surgery problem by the one-dimensional bin packing, and developed a semi-online algorithm to give an efficient feasible solution. In their algorithm they used a buffer to temporarily store items, having a possibility to lookahead in the list. Because of the considered practical problem they investigated the 2-parametric case, when the size of the items is at most 1/2. Using an NF-based online algorithm the authors proved an ACR of 13/9 = 1.44 … for any given buffer size not less than 1. They also gave a lower bound of 4/3 = 1.33 … for the bounded-space algorithms that use NF-based rules. Later, in Zhang et al. (J Comb Optim 33(2):530–542, 2017) an algorithm was given with an ACR of 1.4243, and the authors improved the lower bound to 1.4230. In this paper we present a tight lower bound of h∞ (r) for the r-parametric problem when the buffer capacity is 3. Since h∞ (2) = 1.42312 …, our result—as a special case—gives a tight bound for the algorithm-class given in 2017. To prove that the lower bound is tight, we present an NF-based online algorithm that considers the r-parametric problem, and uses a buffer with capacity of 3. We prove that this algorithm has an ACR that is equal to the lower bounds for arbitrary r. © Springer Science+Business Media, LLC 2017
Scheduling of data-intensive workloads in a brokered virtualized environment
Providing performance predictability guarantees is increasingly important in cloud platforms, especially for data-intensive applications, for which performance depends greatly on the available rates of data transfer between the various computing/storage hosts underlying the virtualized resources assigned to the application. With the increased prevalence of brokerage services in cloud platforms, there is a need for resource management solutions that consider the brokered nature of these workloads, as well as the special demands of their intra-dependent components. In this paper, we present an offline mechanism for scheduling batches of brokered data-intensive workloads, which can be extended to an online setting. The objective of the mechanism is to decide on a packing of the workloads in a batch that minimizes the broker's incurred costs, Moreover, considering the brokered nature of such workloads, we define a payment model that provides incentives to these workloads to be scheduled as part of a batch, which we analyze theoretically. Finally, we evaluate the proposed scheduling algorithm, and exemplify the fairness of the payment model in practical settings via trace-based experiments
Semi-online Scheduling with Lookahead
The knowledge of future partial information in the form of a lookahead to
design efficient online algorithms is a theoretically-efficient and realistic
approach to solving computational problems. Design and analysis of semi-online
algorithms with extra-piece-of-information (EPI) as a new input parameter has
gained the attention of the theoretical computer science community in the last
couple of decades. Though competitive analysis is a pessimistic worst-case
performance measure to analyze online algorithms, it has immense theoretical
value in developing the foundation and advancing the state-of-the-art
contributions in online and semi-online scheduling. In this paper, we study and
explore the impact of lookahead as an EPI in the context of online scheduling
in identical machine frameworks. We introduce a -lookahead model and design
improved competitive semi-online algorithms. For a -identical machine
setting, we prove a lower bound of and design an optimal
algorithm with a matching upper bound of on the competitive
ratio. For a -identical machine setting, we show a lower bound of
and design a -competitive improved semi-online
algorithm.Comment: 14 pages, 1 figur
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