Online Bin Packing Algorithm Research Articles

Optimal Online Bin Packing Algorithms for Some Cases with Two Item Sizes

Optimal Online Bin Packing Algorithms for Some Cases with Two Item Sizes

Developing a Maximum Inscribed Rectangle Heuristic to Satisfy Rush Orders for Heavy Plate Steel

Steel service centers receive rush orders that must be fulfilled on very short notice. Each order only consumes a portion of one steel plate, so plate selection and job placement are the critical factors that affect the service center’s primary performance metric: plate yield. In conjunction with a steel service center, Artco Steel, we model this problem as a two-dimensional online bin-packing algorithm. Unique in the online bin-packing literature, we calculate the maximum inscribed rectangle (MIR) before and after job placement as the basis for heuristics that assign each job to a plate and position the job on the plate. Our work is the first paper to extend the online two-dimensional bin-packing problem to incorporate scrap, rectangular bin sizes, and a finite number of bins. The MIR procedure significantly outperformed Artco’s existing practice of giving priority to the most recently used plate, and the heuristic’s straightforward nature allowed easy adoption in 2010.

Asymptotic Approximation Ratios for Certain Classes of Online Bin Packing Algorithms

Asymptotic Approximation Ratios for Certain Classes of Online Bin Packing Algorithms

Online Offloading Scheduling and Resource Allocation Algorithms for Vehicular Edge Computing System

To accommodate the exponentially increasing computation demands of vehicle-based applications, vehicular edge computing (VEC) system was introduced. This paper considers a three-layer VEC architecture and proposes an online offloading scheduling and resource allocation (OOSRA) algorithm to improve the system performance. Specifically, this study designs a game-theoretic online algorithm to solve the problem of computation task offloading scheduling, and employs an online bin-packing algorithm to compute the resource allocation modified from the First Fit algorithm, which can be adapted to various traffic flow and service attributes. Extensive simulations are conducted, and a numerical analysis of simulation results verifies the effectiveness of the OOSRA-VEC system. The algorithms proposed in this paper are online, adaptive, and distributed, which can provide useful references for future development in VEC system protocols.

On Online Algorithms for Bin, Strip, and Box Packing, and Their Worst-Case and Average-Case Analysis

In this survey, we consider online algorithms for bin packing and strip packing problems, as well as their generalizations (multidimensional bin packing, multiple strip packing, and packing into strips of different widths). For the latter problem, only the worst-case analysis is described; for the other problems, both the worst-case and average-case (probabilistic) asymptotic ratios are presented. The best lower and upper bounds are considered. Basic algorithms and methods for their analysis are discussed.

The optimal absolute ratio for online bin packing

We present an online bin packing algorithm with absolute competitive ratio 5/3, which is optimal.

Bin packing problem with scenarios

Scheduling over scenarios is one of the latest approaches in modelling scheduling problems including uncertainty. However, to the best of our knowledge, scenarios have never been applied to the bin packing problem, so here we introduce the bin packing problem with scenarios. In this model, we have a list of items with sizes between 0 and 1, and each item is assigned to one or more scenarios. In reality, the items of only one scenario will occur, but this chosen scenario is unknown at the time of packing, so the algorithms have to examine all scenarios. This means that the items have to be packed into bins such that for any scenario, the total size of the items in this scenario is at most 1 in each bin. The objective of the standard bin packing problem is to minimize the number of bins. Here, we introduce some extensions of the objective function to the scenario based model, and we present our competitive analysis of some online bin packing algorithms adapted to scenarios.

Online Bin Packing with Advice of Small Size

In this paper, we study the advice complexity of the online bin packing problem. In this well-studied setting, the online algorithm is supplemented with some additional information concerning the input. We improve upon both known upper and lower bounds of online algorithms for this problem. On the positive side, we first provide a relatively simple algorithm that achieves a competitive ratio arbitrarily close to 1.5, using constant-size advice. Our result implies that 16 bits of advice suffice to obtain a competitive ratio better than any online algorithm without advice, thus improving the previously known bound of O(log(n)) bits required to attain this performance. In addition, we introduce a more complex algorithm that still requires only constant-size advice, and has a competitive ratio arbitrarily close to 1.47012. This is the currently best performance of any online bin packing algorithm with sublinear advice. On the negative side, we extend a construction due to Boyar et al. (Algorithmica 74(1), 507–527 2016) so as to show that no online algorithm with sub-linear advice can be 7/6-competitive, improving on the lower bound of 9/8 from Boyar et al.

Об онлайновых алгоритмах для задач упаковки в контейнеры и полосы, их анализе в худшем случае и в среднем

Об онлайновых алгоритмах для задач упаковки в контейнеры и полосы, их анализе в худшем случае и в среднем

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 $$13/9 = 1.44\ldots $$ for any given buffer size not less than 1. They also gave a lower bound of $$4/3=1.33\ldots $$ 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 $$h_\infty (r)$$ for the r-parametric problem when the buffer capacity is 3. Since $$h_\infty (2) = 1.42312\ldots $$ , 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.

Semi-on-line bin packing: a short overview and a new lower bound

Here we review the main results in the area of semi-on-line bin packing. Then we present a new lower bound for the asymptotic competitive ratio of any on-line bin packing algorithm which knows the optimum value in advance.

New lower bounds for certain classes of bin packing algorithms

On-line algorithms have been extensively studied for the one-dimensional bin packing problem. In this paper, we investigate two classes of one-dimensional bin packing algorithms, and we give better lower bounds for their asymptotic worst-case behavior. For on-line algorithms so far the best lower bound was given by van Vliet in (1992) [12]. He proved that there is no on-line bin packing algorithm with better asymptotic performance ratio than 1.54014…. In this paper, we give an improvement on this bound to 248161=1.54037… and we investigate the parametric case as well. For those lists where the elements are preprocessed according to their sizes in non-increasing order, Csirik et al. (1983) [1] proved that no on-line algorithm can have an asymptotic performance ratio smaller than 87. We improve this result to 5447.

A Novel Scheduling Algorithm Based on Game Theory and Reinforcement Learning

In this paper we proposed a new dynamic scheduling algorithm for power scheduling problem. The algorithm is based on game theory and reinforcement learning approach. We compared the performance of our algorithm with that of online bin packing and MAB algorithm. We observed that our algorithm performs better than online bin packing when there is a variation in the deadlines. This is because our algorithm schedules the requests on the basis of their actions and the probability of missing the deadline and online bin packing algorithm schedules requests based on the sequence of requests as they arrive. We observed that our approach is more useful, when scheduling requests repeat themselves for long duration.

On Bin Packing with Conflicts

We consider the offline and online versions of a bin packing problem called bin packing with conflicts. Given a set of items $V=\{ 1,2,\dots,n\}$ with sizes $s_1,s_2,\dots,s_n\in[0,1]$ and a conflict graph $G=(V,E)$, the goal is to find a partition of the items into independent sets of $G$, where the total size of items in each independent set is at most 1 so that the number of independent sets in the partition is minimized. This problem is clearly a generalization of both the classical (one-dimensional) bin packing problem where $E=\emptyset$ and of the graph coloring problem where $s_i=0$ for all $i=1,2,\dots,n$. Since coloring problems on general graphs are hard to approximate, following previous work, we study the problem on specific graph classes. For the offline version, we design improved approximation algorithms for perfect graphs and other special classes of graphs: These are a $\frac52=2.5$-approximation algorithm for perfect graphs; a $\frac73\approx2.33333$-approximation algorithm for a subclass of perfect graphs, which contains interval graphs and chordal graphs; and a $\frac74=1.75$-approximation for algorithm bipartite graphs. For the online problem on interval graphs, we design a 4.7-competitive algorithm and show a lower bound of $\frac{155}{36}\approx4.30556$ on the competitive ratio of any algorithm. To derive the last lower bound, we introduce the first lower bound on the asymptotic competitive ratio of any online bin packing algorithm with known optimal value, which is $\frac{47}{36}\approx1.30556$.

Online bin packing with resource augmentation

In competitive analysis, we usually do not put any restrictions on the computational complexity of online algorithms, although efficient algorithms are preferred. Thus, if such an algorithm were given the entire input in advance, it could give an optimal solution (in exponential time). Instead of giving the algorithm more knowledge about the input, in this paper we consider the effects of giving an online bin packing algorithm larger bins than the offline algorithm it is compared to. We give new algorithms for this problem that combine items in bins in an unusual way, and give bounds on their performance which improve upon the best possible bounded space algorithm. We also give general lower bounds for this problem which are nearly matching for bin sizes b ≥ 2 .

On the online bin packing problem

A new framework for analyzing online bin packing algorithms is presented. This framework presents a unified way of explaining the performance of algorithms based on the Harmonic approach. Within this framework, it is shown that a new algorithm, Harmonic++, has asymptotic performance ratio at most 1.58889. It is also shown that the analysis of Harmonic+1 presented in Richey [1991] is incorrect; this is a fundamental logical flaw, not an error in calculation or an omitted case. The asymptotic performance ratio of Harmonic+1 is at least 1.59217. Thus, Harmonic++ provides the best upper bound for the online bin packing problem to date.

Deep performance analysis of Refined Harmonic bin packing algorithm

Refined Harmonic (RH) is one of the best on-line bin packing algorithms. The algorithm was first proposed by Lee&Lee in 1985 and the upper bound of the worst-case performance ratio has been proved to be 1.63596..., In this paper, it is proved that 1.63596... is also the lower bound. The average performance of RH is also studied for the first time. It is shown that the average-case performance ratio of RH is 1.28243... under the uniform distribution.

Performance analysis and improvement for some linear on-line bin-packing algorithms

The study on one-dimensional bin packing problem may bring about many important applications such as multiprocessor scheduling, resource allocating, real-world planning and packing. Harmonic algorithms (including H K, RH, etc.) for bin packing have been famous for their linear-time and on-line properties for a long time. This paper profoundly analyzes the average-case performance of harmonic algorithms for pieces of i.i.d. sizes, provides the average-case performance ratio of H K under (0,d] (d ≤ 1) uniform distribution and the average-case performance ratio of RH under (0,1] uniform distribution. We also finished the discussion of the worst-case performance ratio of RH. Moreover, we propose a new improved version of RH that obtains better worst- and average-case performance ratios.

Bounded Space On-Line Bin Packing: Best Is Better than First

We present a sequence of new linear-time, bounded-space, on-line bin packing algorithms, the K -Bounded Best Fit algorithms (BBF K ). They are based on the Θ(n log n) Best Fit algorithm in much the same way as the Next-K Fit algorithms are based on the Θ(n log n) First Fit algorithm. Unlike the Next-K Fit algorithms, whose asymptotic worst-case ratios approach the limiting value of \frac 17 10 from above as K \rightarrow ∈fty but never reach it, these new algorithms have worst-case ratio \frac 17 10 for all K \geq 2 . They also have substantially better average performance than their bounded-space competition, as we have determined based on extensive experimental results summarized here for instances with item sizes drawn independently and uniformly from intervals of the form (0, u] , 0 < u ≤ 1 . Indeed, for each u < 1 , it appears that there exists a fixed memory bound K(u) such that BBF K(u) obtains significantly better packings on average than does the First Fit algorithm, even though the latter requires unbounded storage and has a significantly greater running time. For u = 1 , BBF K can still outperform First Fit (and essentially equal Best Fit) if K is allowed to grow slowly. We provide both theoretical and experimental results concerning the growth rates required.

An Operating Room Scheduling Strategy to Maximize the Use of Operating Room Block Time

Determining the appropriate amount of block time to allocate to surgeons and selecting the days on which to schedule elective cases can maximize operating room (OR) use.We used computer simulation to model OR scheduling. Inputs in the computer model included different methods to determine when a patient will have surgery (on-line bin-packing algorithms), case durations, lengths of time patients wait for surgery (2 wk is the median longest length of time that the outpatients [n = 367] surveyed considered acceptable), hours of block time each day, and number of blocks each week. For block time to be allocated to maximize OR utilization, two parameters must be specified: the method used to decide on what day a patient will have surgery and the average length of time patients wait to have surgery. OR utilization depends greatly on, and increases as, the average length of time patients wait for surgery increases. Implications: Operating room utilization can be maximized by allocating block time for the elective cases based on expected total hours of elective cases, scheduling patients into the first available date provided open block time is available within 4 wk, and otherwise scheduling patients in "overflow" time outside of the block time. (Anesth Analg 1999;89:7-20)