From theory to practice: maximizing revenues for on-line dial-a-ride

We consider the on-line dial-a-ride problem, where a server fulfills requests that arrive over time. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that the server earns for fulfilling the request. The goal is to serve requests within a time limit while maximizing the total revenue. We first prove that no deterministic online algorithm can be competitive unless the input graph is complete and edge weights are unit. We therefore focus on these graphs and present a 2-competitive algorithm for this problem. We also consider two variations of this problem: (1) the input graph is complete bipartite and (2) there is a single node that is the source for every request, and present a 1-competitive algorithm for the former and an optimal algorithm for the latter. We also provide experimental results for the complete and complete bipartite graphs. Our simulations support our theoretical findings and demonstrate that our algorithms perform well under settings that reflect realistic dial-a-ride systems.     

Online MapReduce processing on two identical parallel machines

In this work we investigate the online over-list MapReduce processing problem on two identical parallel machines, aiming at minimizing the makespan. Jobs are revealed one by one, and each job consists of one map task and one reduce task. The map task can be arbitrarily split and processed on both machines simultaneously, while the reduce task has to be processed on a single machine and it cannot be started unless the map task has been completed. We first show that the general case of the problem reduces to the classical two machine online scheduling model with an optimal competitive ratio of 3/2. For a special case where the map task is at least as long as the reduce task, we prove that no online algorithm can be less than 4/3-competitive. An optimal Greedy algorithm with a matching competitive ratio is proposed as well.     

Tabu search for the real-world carpooling problem

Carpooling is a flexible shared transportation system which can effectively reduce the vehicle numbers and fuel consumption. Although many carpooling systems have been proposed, most of them lack practicality, veracity, and efficiency. In this paper, we propose a new useful variant model of the long-term carpooling problem which involves multiple origins and one destination. Such problems commonly occur in a wide number of carpooling situations in real-world scenarios. Our work is motivated by the practical needs to solve environmental pollution, parking problems, traffic jams and low utilization of resources. A Tabu search algorithm is proposed in this paper to solve the carpooling problem. The proposed algorithm aims at a wide range of passenger distribution and routing problems. The computational results based on real world user data show the effectiveness of the proposed algorithm. Moreover, we developed a mobile application based on our carpooling model.     

Single machine batch scheduling with release times

Motivated by a high-throughput logging system, we investigate the single machine scheduling problem with batching, where jobs have release times and processing times, and batches require a setup time. Our objective is to minimize the total flow time, in the online setting. For the online problem where all jobs have identical processing times, we propose a 2-competitive algorithm and we prove a corresponding lower bound. Moreover, we show that if jobs with arbitrary processing times can be processed in any order, any online algorithm has a linear competitive ratio in the worst case. A preliminary version of a part of this paper was presented at the 31st International Symposium on Mathematical Foundations of Computer Science (MFCS 2006). We gratefully acknowledge reviewers’ comments that helped to improve the presentation of this work. Supported by the Swiss SBF under contract no. C05.0047 within COST-295 (DYNAMO) of the European Union. Research carried out while B. Weber was affiliated with the Institute of Theoretical Computer Science, ETH Zurich.     

考虑订单类型的两台平行批处理机在线调度模型研究

探讨了两台平行批处理机的调度决策问题,着重考虑了订单具有不同加工类型、同一批次只能加工相同类型的订单以及机器批容量有限的调度情形。针对订单实时到达且需要立即决策是否接受的实际情景,运用在线理论构建了平行机批调度在线模型。证明了该问题的竞争比下界为2Bw/（1+√Bw）,其中B和w分别表示批容量和单个订单的最大完工收益。进而设计给出了收益阈值算法PT并证明其对于订单具有紧交货期限的情形竞争比为2（1+Bw）/（1+√Bw）;对于非紧交货期限的情形,证明了修正的PT算法具有竞争比为1+2（1+Bw）/（1+√Bw）。     

An online algorithm for continuous slab caster scheduling

Lee et al. (Lee, K., Chang, S.Y., and Hong, Y., 2004. Continuous slab caster scheduling and interval graphs. Production Planning & Control, 13 (5), 495–501) have introduced a slab caster scheduling problem and developed an optimal algorithm. Their algorithm is efficient but an offline algorithm that we need the information on all the customer orders a priori to implement. In this article, we propose an online algorithm that we can implement without knowledge of the orders yet to arrive. We show that the offline version of our new algorithm also provides an optimal solution and the online version has the worst case performance ratio of 3. We also give a short proof on the correctness of Lee et al.'s algorithm.     

局内租赁问题的风险补偿模型及其竞争分析

将风险的概念引入局内租赁问题中,建立了该问题的风险补偿模型,并对存在和不存在 利率情况下的局内租赁问题作了分析. 和局内问题中传统的竞争比分析不同的是,竞争比分析 只反映局内策略与基准算法(局外最优算法) 的相对绩效,但这往往忽略了很多的有用信息,且 分析模型很不灵活. 然而在风险补偿模型中,投资者可以控制风险,根据自己不同的风险容忍 度和未来预期选择最优的租赁策略     

A new effective branch-and-bound algorithm to the high order MIMO detection problem

This paper develops a branch-and-bound method based on a new convex reformulation to solve the high order MIMO detection problem. First, we transform the original problem into a \(\{-1,1\}\) constrained quadratic programming problem with the smallest size. The size of the reformulated problem is smaller than those problems derived by some traditional transformation methods. Then, we propose a new convex reformulation which gets the maximized average objective value as the lower bound estimator in the branch-and-bound scheme. This estimator balances very well between effectiveness and computational cost. Thus, the branch-and-bound algorithm achieves a high total efficiency. Several simulations are used to compare the performances of our method and other benchmark methods. The results show that this proposed algorithm is very competitive for high accuracy and relatively good efficiency.     

New algorithms for online rectangle filling with <Emphasis Type="BoldItalic">k</Emphasis>-lookahead

We study the online rectangle filling problem which arises in channel aware scheduling of wireless networks, and present deterministic and randomized results for algorithms that are allowed a k-lookahead for k≥2. Our main result is a deterministic min {1.848,1+2/(k−1)}-competitive online algorithm. This is the first algorithm for this problem with a competitive ratio approaching 1 as k approaches +∞. The previous best-known solution for this problem has a competitive ratio of 2 for any k≥2. We also present a randomized online algorithm with a competitive ratio of 1+1/(k+1). Our final result is a closely matching lower bound (also proved in this paper) of $1+1/(\sqrt{k+2}+\sqrt{k+1})^{2}>1+1/(4(k+2))$1+1/(\sqrt{k+2}+\sqrt{k+1})^{2}>1+1/(4(k+2)) on the competitive ratio of any randomized online algorithm against an oblivious adversary. These are the first known results for randomized algorithms for this problem.     

Solving the Multidimensional Assignment Problem by a Cross-Entropy method

The Multidimensional Assignment Problem (MAP) is a higher dimensional version of the linear assignment problem, where we find tuples of elements from given sets, such that the total cost of the tuples is minimal. The MAP has many recognized applications such as data association, target tracking, and resource planning. While the linear assignment problem is solvable in polynomial time, the MAP is NP-hard. In this work, we develop a new approach based on the Cross-Entropy (CE) methods for solving the MAP. Exploiting the special structure of the MAP, we propose an appropriate family of discrete distributions on the feasible set of the MAP that allow us to design an efficient and scalable CE algorithm. The efficiency and scalability of our method are proved via several tests on large-scale problems with up to 5 dimensions and 20 elements in each dimension, which is equivalent to a 0–1 linear program with 3.2 millions binary variables and 100 constraints.     

Traffic regulation with single- and dual-homed ISPs under a percentile-based pricing policy

We investigate how a customer (an enterprise or a large organization), when facing a percentile-based pricing policy, can optimally balance the Internet access cost and the traffic buffering delay penalty by traffic regulation. The problem is referred to as the Optimal Traffic Regulation (OTR) problem. Solutions to various cases of the OTR problem are provided. For a customer with a single-homed ISP, we present optimal solutions to the OTR problem based on dynamic programming for the offline case with a known traffic demand pattern. A real-time traffic scheduling algorithm is proposed to deal with the online case where the traffic demands are different from a given demand pattern. We further extend the dynamic programming model to the case of dual-homed ISPs. Experimental results on the data from an Internet trace confirm the effectiveness of our solutions. Part of the results has been presented in the First International Conference on Scalable Information Systems.     

Greedy algorithms for the profit-aware social team formation problem

Motivated by applications in online labor markets, we study the problem of forming multiple teams of experts in a social network to accomplish multiple tasks that require different combinations of skills. Our goal is to maximize the total profit of tasks that are completed by these teams subject to the capacity constraints of the experts. We study both the offline and online settings of the problem. For the offline problem, we present a simple and practical algorithm that improves upon previous results in many situations. For the online problem, we design competitive deterministic and randomized online algorithms. These are complemented by some hardness results in both settings.

     

Online scheduling of equal length jobs on unbounded parallel batch processing machines with limited restart

We consider the online scheduling of equal length jobs on unbounded parallel batch processing machines to minimize makespan with limited restart. In the problem \(m\) identical unbounded parallel batch processing machines are available to process the equal length jobs arriving over time. The processing batches are allowed limited restart. Here, “restart” means that a running task may be interrupted, losing all the work done on it, and the jobs in the interrupted task are then released and become independently unscheduled jobs, called restarted jobs. “Limited restart” means that only a running batch that contains no restarted jobs can be restarted. For this problem, we present a best possible online algorithm.     

Almost optimal solutions for bin coloring problems

In this paper we study two interesting bin coloring problems: Minimum Bin Coloring Problem (MinBC) and Online Maximum Bin Coloring Problem (OMaxBC), motivated from several applications in networking. For the MinBC problem, we present two near linear time approximation algorithms to achieve almost optimal solutions, i.e., no more than OPT+2 and OPT+1 respectively, where OPT is the optimal solution. For the OMaxBC problem, we first introduce a deterministic 2-competitive greedy algorithm, and then give lower bounds for any deterministic and randomized (against adaptive offline adversary) online algorithms. The lower bounds show that our deterministic algorithm achieves the best possible competitive ratio. The research of this paper was partially supported by an NSF CAREER award CCF-0546509.     

An Appellate Court Case Assignment Algorithm

This paper describes a case assignment (calendaring) algorithm for a multi-judge appellate court system. In the algorithm, cases of unequal work content are selected for assignment to one of m panels (or clusters) from a set of N available cases. Each panel of cases is heard by a team of three judges. Each appellate case has an estimated work load and a priority ranking based on the type of appeal and filing date with the court. The algorithm balances both the total work load and the number of cases assigned to each panel while insuring that the highest priority cases are assigned to those available. The assignment problem is normally capacity constrained in that not all of the N cases can be assigned to one of the m panels on the monthly calendar. The algorithm is based on a neighborhood search and bounding principle that continually improves upon an initial feasible solution. Empirical results are presented to demonstrate the effectiveness and efficiency of the algorithm.     

一类占线融资租赁问题的最优竞争策略与风险补偿模型

运用占线算法与竞争分析方法,研究了资产所有权在一定的租赁时间后转移给承租人的融资租赁问题的最优竞争策略与风险补偿模型。首先给出了该问题的最优离线解;然后,根据约定的租赁时限与购买价格及租赁费用的大小关系,分别给出了3种情形的占线策略及相应的竞争比分析;最后,在AL-BINALI提出的占线风险补偿分析框架下,给出了2种预期形式及相应最优占线收益策略。     

Competitive analysis of online machine rental and online parallel machine scheduling problems with workload fence

In this paper, we introduce the concept of “workload fence" into online machine rental and machine scheduling problems. With the knowledge of workload fence, online algorithms acquire the information of a finite number of first released jobs in advance. The concept originates from the frozen time fence in the domain of master scheduling in materials management. The total processing time of the jobs foreseen, corresponding to a finite number of jobs, is called workload fence, which is irrelevant to the job sequence. The remaining jobs in the sequence, however, can only become known on their arrival. This work aims to reveal whether the knowledge of workload fence helps to boost the competitive performance of deterministic online algorithms. For the online machine rental problem, we prove that the competitiveness of online algorithms can be improved with a sufficiently large workload fence. We further propose a best online algorithm for the corresponding scenario. For online parallel machine scheduling with workload fence, we give a positive answer to the above question for the case where the workload fence is equal to the length of the longest job. We also show that the competitiveness of online algorithms may not be improved even with a workload fence strictly larger than the largest length of a job. The results help one manager to make a better decision regarding the tradeoff between the performance improvement of online algorithms and the cost caused to acquire the knowledge of workload fence.

     

Improved approximation algorithms for non-preemptive multiprocessor scheduling with testing

Multiprocessor scheduling, also called scheduling on parallel identical machines to minimize the makespan, is a classic optimization problem which has been extensively studied. Scheduling with testing is an online variant, where the processing time of a job is revealed by an extra test operation, otherwise the job has to be executed for a given upper bound on the processing time. Albers and Eckl recently studied the multiprocessor scheduling with testing; among others, for the non-preemptive setting they presented an approximation algorithm with competitive ratio approaching 3.1016 when the number of machines tends to infinity and an improved approximation algorithm with competitive ratio approaching 3 when all test operations take one unit of time each. We propose to first sort the jobs into non-increasing order of the minimum value between the upper bound and the testing time, then partition the jobs into three groups and process them group by group according to the sorted job order. We show that our algorithm achieves better competitive ratios, which approach 2.9513 when the number of machines tends to infinity in the general case; when all test operations each takes one time unit, our algorithm achieves even better competitive ratios approaching 2.8081.

     

基于遗传算法的装备采购决策优化研究

在装备采购中，由于需求单位地域分布和担负的任务各不相同，对装备的品种、数量、时限要求也就不一样，如何使装备采购科学化、合理化，是一个涉及多变量、多目标的复杂系统问题。在综合考虑装备采购各项因素的基础上，构建多约束条件下的多目标模糊指派模型，提出了基于遗传算法的解决方案，最后通过案例进行仿真实验，验证该算法的可行性和有效性，解决了采用传统优化方法难以解决的装备采购优化决策问题。     

Online scheduling with chain precedence constraints of equal-length jobs on parallel machines to minimize makespan

We study the online scheduling problem on m identical parallel machines to minimize makespan, i.e., the maximum completion time of the jobs, where m is given in advance and the jobs arrive online over time. We assume that the jobs, which arrive at some nonnegative real times, are of equal-length and are restricted by chain precedence constraints. Moreover, the jobs arriving at distinct times are independent, and so, only the jobs arriving at a common time are restricted by the chain precedence constraints. In the literature, a best possible online algorithm of a competitive ratio 1.3028 is given for the case \(m=2\). But the problem is unaddressed for \(m\ge 3\). In this paper, we present a best possible online algorithm for the problem with \(m\ge 3\), where the algorithm has a competitive ratio of 1.3028 for \(3\le m\le 5\) and 1.3146 for \(m\ge 6\).