A quadratic assignment problem without column constraints

We convert a quadratic assignment problem [1] with a nonconvex objective function into an integer linear program. We then solve the equivalent integer program by a simple enumeration that produces global minima.     

Aggregating courier deliveries

We consider the problem of efficiently scheduling deliveries by an uncapacitated courier from a central location under online arrivals. We consider both adversary‐controlled and Poisson arrival processes. In the adversarial setting we provide a randomized (3βΔ/2δ ? 1) ‐competitive algorithm, where β is the approximation ratio of the traveling salesman problem, δ is the minimum distance between the central location and any customer, and Δ is the length of the optimal traveling salesman tour overall customer locations and the central location. We provide instances showing that this analysis is tight. We also prove a 1 + 0.271Δ/δ lower‐bound on the competitive ratio of any algorithm in this setting. In the Poisson setting, we relax our assumption of deterministic travel times by assuming that travel times are distributed with a mean equal to the excursion length. We prove that optimal policies in this setting follow a threshold structure and describe this structure. For the half‐line metric space we bound the performance of the randomized algorithm in the Poisson setting, and show through numerical experiments that the performance of the algorithm is often much better than this bound.     

UAVs cooperative task assignment and trajectory optimization with safety and time constraints

This paper proposes new methods and strategies for Multi-UAVs cooperative attacks with safety and time constraints in a complex environment. Delaunay triangle is designed to construct a map of the complex flight environment for aerial vehicles. Delaunay-Map, Safe Flight Corridor(SFC), and Relative Safe Flight Corridor(RSFC) are applied to ensure each UAV flight trajectory’s safety. By using such techniques, it is possible to avoid the collision with obstacles and collision between UAVs. Bezier-c...     

面向SPR的异构路由器聚合交换技术

互联网的快速发展使得传统的POP组网方式面临巨大的挑战,部署SPR(Single POP Router)路由器被认为是解决问题的有效手段。提出了异构路由器的聚合交换技术,可以将POP中的多个异构路由器以集群的方式实现一个规模更大的SPR路由器,具有降低组网成本、保护现有投资、简化网络管理、提高交换效率等优点。给出了聚合交换技术中需要重点研究的几个关键问题以及研究思路。     

The truck assignment problem

Let us consider the following problem: A group of cement factories produces several types of cement, but each factory produces only one type. There is also a group of purchasers and each purchaser may need several types of cement. The amounts supplied and the demands are assumed to be known for each cement factory and each purchaser. Each cement factory has several trucks, but there is only one dispatcher for ail of the trucks from all of the factories. It is assumed that the entire lcad of each truck is for one purchaser only. A truck begins its workday by leaving its base depot loaded and ends its day by returning to it empty. During the day it may be required to transport cement from any of the cement factories. The distances from various factories to individual purchasers are known. The problem to be solved is that of finding a truck schedule such that cement in the needed quantities is delivered daily to the individual purchasers and in such a manner that the total truck-kilometers traveled will be as small as possible. This paper presents the method of solution, though the assumption of an 8-hour workday may not be met. On the other hand, there are methods developed for effecting a variety of cyclic routings which can be used to lend considerable flexibility to the schedules.     

A stochastic assignment problem

There are n boxes with box i having a quota value Balls arrive sequentially, with each ball having a binary vector attached to it, with the interpretation being that if X_i = 1 then that ball is eligible to be put in box i. A ball's vector is revealed when it arrives and the ball can be put in any alive box for which it is eligible, where a box is said to be alive if it has not yet met its quota. Assuming that the components of a vector are independent, we are interested in the policy that minimizes, either stochastically or in expectation, the number of balls that need arrive until all boxes have met their quotas. © 2014 Wiley Periodicals, Inc. 62:23–31, 2015     

Bicriteria multiresource generalized assignment problem

In this study, we consider a bicriteria multiresource generalized assignment problem. Our criteria are the total assignment load and maximum assignment load over all agents. We aim to generate all nondominated objective vectors and the corresponding efficient solutions. We propose several lower and upper bounds and use them in our optimization and heuristic algorithms. The computational results have shown the satisfactory behaviors of our approaches. © 2014 Wiley Periodicals, Inc. Naval Research Logistics, 61: 621–636, 2014     

The bounded interval generalized assignment model

The bounded interval generalized assignment model is a “many-for-one” assignment model. Each task must be assigned to exactly one agent; however, each agent can be assigned multiple tasks as long as the agent resource consumed by performing the assigned tasks falls within a specified interval. The bounded interval generalized assignment model is formulated, and an algorithm for its solution is developed. Algorithms for the bounded interval versions of the semiassignment model and sources-to-uses transportation model are also discussed.     

Determining adjacent vertices on assignment polytopes

To rank the solutions to the assignment problem using an extreme point method, it is necessary to be able to find all extreme points which are adjacent to a given extreme solution. Recent work has shown a procedure for determining adjacent vertices on transportation polytopes using a modification of the Chernikova Algorithm. We present here a procedure for assignment polytopes which is a simplification of the more general procedure for transportation polytopes and which also allows for implicit enumeration of adjacent vertices.     

Tree-search algorithms for quadratic assignment problems

Problems having the mathematical structure of a quadratic assignment problem are found in a diversity of contexts: by the economist in assigning a number of plants or indivisible operations to a number of different geographical locations; by the architect or indusatrial engineer in laying out activities, offices, or departments in a building; by the human engineer in arranging the indicators and controls in an operators control room; by the electronics engineer in laying out components on a backboard; by the computer systems engineer in arranging information in drum and disc storage; by the production scheduler in sequencing work through a production facility; and so on. In this paper we discuss several types of algorithms for solving such problems, presenting a unifying framework for some of the existing algorithms, and dcscribing some new algorithms. All of the algorithms discussed proceed first to a feasible solution and then to better and better feasible solutions, until ultimately one is discovered which is shown to be optimal.     

The Hungarian method for the assignment problem

This paper has been presented with the Best Paper Award. It will appear in print in Volume 52, No. 1, February 2005.     

任务分配问题的对称群方法

探讨了无人飞行器(UAV)编队的任务分配问题。任务分配是UAV协同控制的基础,其解是任务区域内各任务的一个排列。求解UAV任务分配问题的有效方法是能在合理的计算时间内找到近似最优解的启发式算法。用对称群描述UAV任务分配的搜索空间,基于右乘运算构造搜索邻域。仿真结果验证了群论禁忌搜索算法的有效性。     

Parallel machine scheduling with job assignment restrictions

In the classical multiprocessor scheduling problem independent jobs must be assigned to parallel, identical machines with the objective of minimizing the makespan. This article explores the effect of assignment restrictions on the jobs for multiprocessor scheduling problems. This means that each job can only be processed on a specific subset of the machines. Particular attention is given to the case of processing times restricted to one of two values, 1 and λ, differing by at most 2. A matching based polynomial time ε‐approximation algorithm is developed that has a performance ratio tending to . This algorithm is shown to have the best possible performance, tending to 3/2, for processing times 1 and 2. For the special case of nested processing sets, i.e., when the sets of machines upon which individual jobs may be assigned are non‐overlapping, the behavior of list scheduling algorithms is explored. Finally, for assignment restrictions determined by just one characteristic of the machines, such as disc storage or memory constraint in the case of high performance computing, we contribute an algorithm that provides a 3/2 worst case bound and runs in time linear in the number of jobs. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Suboptimal algorithms for the quadratic assignment problem

The idea of combining relatively simple continuous methods with discrete procedures is used for the construction of suboptimal algorithms for quadratic assignment problems. Depending on the nature of the special problem these steps may vary in complexity. The simplest procedures require minimum storage space and result in tolerable computation times. Different choices of parameters and random variations may be used in order to obtain statistical distributions of suboptimal solutions. Computational results for sample problems indicate improvements on results of Steinberg, Gilmore, and Hillier and Connors.     

Quadratic programming with quadratic constraints

A program with a quadratic objective function and quadratic constraints is considered. Two duals to such programs are provided, and an algorithm is presented based upon approximations to the duals. The algorithm consists of a sequence of linear programs and programs involving the optimization of a quadratic function either unconstrained or constrained to the nonnegative orthant. An example involving production planning is presented.     

Crane scheduling with spatial constraints

In this work, we examine port crane scheduling with spatial and separation constraints. Although common to most port operations, these constraints have not been previously studied. We assume that cranes cannot cross, there is a minimum distance between cranes and jobs cannot be done simultaneously. The objective is to find a crane‐to‐job matching which maximizes throughput under these constraints. We provide dynamic programming algorithms, a probabilistic tabu search, and a squeaky wheel optimization heuristic for solution. Experiments show the heuristics perform well compared with optimal solutions obtained by CPLEX for small scale instances where a squeaky wheel optimization with local search approach gives good results within short times. © 2004 Wiley Periodicals, Inc. Naval Research Logistics, 2004.     

Limiting behavior of the stochastic sequential assignment problem

The stochastic sequential assignment problem (SSAP) considers how to allocate available distinct workers to sequentially arriving tasks with stochastic parameters such that the expected total reward obtained from the sequential assignments is maximized. Implementing the optimal assignment policy for the SSAP involves calculating a new set of breakpoints upon the arrival of each task (i.e., for every time period), which is impractical for large‐scale problems. This article studies two problems that are concerned with obtaining stationary policies, which achieve the optimal expected reward per task as the number of tasks approaches infinity. The first problem considers independent and identically distributed (IID) tasks with a known distribution function, whereas in the second problem tasks are derived from r different unobservable distributions governed by an ergodic Markov chain. The convergence rate of the expected reward per task to the optimal value is also obtained for both problems. © 2013 Wiley Periodicals, Inc. Naval Research Logistics, 2013     

在轨服务航天器任务指派问题

一个在轨服务可有多种服务选择,必须进行合理的任务指派。首先求解服务航天器满足燃耗约束下的可达区域,筛选出满足可达范围要求的目标航天器。然后,以任务执行时间、燃料消耗和航天器服务优先级为优化目标,研究多目标的任务指派问题。通过设计决策变量,考虑时间、燃耗等约束,建立了基于0-1整数规划的任务模型,采用NSGA-Ⅱ算法,求得问题的Pareto最优集,得到多组可供任务设计者选择自己偏好的折中方案。文章给出了两个多目标优化的仿真算例,算例一给出了任务指派的一般研究结论,算例二对比了另外一种算法：分层-加权法。仿真结果表明利用文章给出的方法可以较好地解决多目标下在轨服务任务指派问题。     

Multiple subset sum with inclusive assignment set restrictions

In a traditional multiple subset sum problem (MSSP), there is a given set of items and a given set of bins (or knapsacks) with identical capacities. The objective is to select a subset of the items and pack them into the bins such that the total weight of the selected items is maximized. However, in many applications of the MSSP, the bins have assignment restrictions. In this article, we study the subset sum problem with inclusive assignment set restrictions, in which the assignment set of one item (i.e., the set of bins that the item may be assigned to) must be either a subset or a superset of the assignment set of another item. We develop an efficient 0.6492‐approximation algorithm and test its effectiveness via computational experiments. We also develop a polynomial time approximation scheme for this problem. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011