Considering inter-task resource constraints in task allocation

This paper focuses on task allocation with single-task robots, multi-robot tasks and instantaneous assignment, which has been shown to be strongly NP-hard. Although this problem has been studied extensively, few efficient approximation algorithms have been provided due to its inherent complexity. In this paper, we first provide discussions and analyses for two natural greedy heuristics for solving this problem. Then, a new greedy heuristic is introduced, which considers inter-task resource constraints to approximate the influence between different assignments in task allocation. Instead of only looking at the utility of the assignment, our approach computes the expected loss of utility (due to the assigned robots and task) as an offset and uses the offset utility for making the greedy choice. A formal analysis is provided for the new heuristic, which reveals that the solution quality is bounded by two different factors. A new algorithm is then provided to approximate the new heuristic for performance improvement. Finally, for more complicated applications, we extend this problem to include general task dependencies and provide a result on the hardness of approximating this new formulation. Comparison results with the two natural heuristics in simulation are provided for both formulations, which show that the new approach achieves improved performance.     

Using genetic algorithms to design mesh networks

Designs for mesh communication networks must meet conflicting, interdependent requirements. This sets the stage for a complex problem with a solution that targets optimal topological connections, routing, and link capacity assignments. These assignments must minimize cost while satisfying traffic requirements and keeping network delays within permissible values. Since such a problem is NP-complete, developers must use heuristic techniques to handle the complexity and solve practical problems with a modest number of nodes. One heuristic technique, genetic algorithms, appears to be ideal to handle the design of mesh networks with capability of handling discrete values, multiobjective functions, and multiconstraint problems. Existing applications of genetic algorithms to this problem, however, have only optimized the network topology. They ignore the difficult subproblems of routing and capacity assignment, a crucial determiner of network quality and cost. This article presents a total solution to mesh network design using a genetic algorithm approach. The application is a 10-city network that links Hong Kong and nine other cities in China. The development demonstrates that this method can be used for networks of reasonable size with realistic topology and traffic requirements     

On the variable-depth-search heuristic for the linear-cost generalized assignment problem

The classical assignment problem seeks to determine a mapping between a set of assignees and a set of assignments. The linear cost assignment problem (LCGAP), as a generalized model, incorporates the relative workloads between assignees and assignments. Although LCGAP is computationally intractable, it has been extensively studied because of its practical implications in many real world situations. Variable-depth-search heuristic (VDSH) method is one of the solution methods that have been developed to produce quality near-optimal solutions to LCGAP. The main structure of VDSH consists of two basic operations: reassign and swap. In this paper, we make further observations on this effective heuristic method through a series of computational experiments. The numerical results statistically evince that different combina-tions of these two operations will result in solutions of different quality levels. These findings are expected to have similar implications to search heuristics for other optimization problems.     

Branch-and-bound task allocation with task clustering-based pruning

We propose a task allocation algorithm that aims at finding an optimal task assignment for any parallel programs on a given machine configuration. The theme of the approach is to traverse a state–space tree that enumerates all possible task assignments. The efficiency of the task allocation algorithm comes from that we apply a pruning rule on each traversed state to check whether traversal of a given sub-tree is required by taking advantage of dominance relation and task clustering heuristics. The pruning rules try to eliminate partial assignments that violate the clustering of tasks, but still keeping some optimal assignments in the future search space. In contrast to previous state–space searching methods for task allocation, the proposed pruning rules significantly reduce the time and space required to obtain an optimal assignment and lead the traversal to a near optimal assignment in a small number of states. Experimental evaluation shows that the pruning rules make the state–space searching approach feasible for practical use.     

A genetic algorithm for the project assignment problem

In this paper we present a genetic algorithm as an aid for project assignment. The assignment problem illustrated concerns the allocation of projects to students. Students have to choose from a list of possible projects, indicating their preferred choices in advance. Inevitably, some of the more popular projects become ‘over-subscribed’ and assignment becomes a complex problem. The developed algorithm has compared well to an optimal integer programming approach. One clear advantage of the genetic algorithm is that, by its very nature, we are able to produce a number of feasible project assignments, thus facilitating discussion on the merits of various allocations and supporting multi-objective decision making.     

基于禁忌搜索算法求解随机约束满足问题

为了求解具有增长取值域的随机约束满足问题（CSP）,提出了一种基于禁忌搜索并与模拟退火相结合的算法。首先,利用禁忌搜索得到一组启发式的初始赋值,即由一个随机初始化的可行解通过邻域构造一组候选解,再利用禁忌表使候选解向最小化目标函数值的方向移动;如果得到的最优赋值不是问题的解,就把它作为启发式的初始赋值,再执行模拟退火对这组赋值进行修正直到得到全局最优解。数值实验结果表明,所提算法在接近问题的理论相变阈值时仍然能有效地找到问题的解,与其他局部搜索算法相比,表现出了显著的优越性,可用于随机CSP的算法设计。     

Distributed database design—Optimization vs feasibility

This paper is concerned with the problem of optimal assignment of data to sites in a distributed relational database. It is shown that in general the optimal allocation will require exponential time in terms of the input. Several heuristic algorithms that can be applied to various constraints and which provide feasible, near optimal results, as well as a model that determines the “best” assignment for a given input out of several optimal and near optimal assignments have been developed. The model is shown to be efficient, to require polynomial time, to be practical in terms of feasible inputs and to achieve assignments with near minimal global and local costs.     

A Riccati-type algorithm for solving generalized Hermitian eigenvalue problems

The paper describes a heuristic algorithm for solving a generalized Hermitian eigenvalue problem fast. The algorithm searches a subspace for an approximate solution of the problem. If the approximate solution is unacceptable, the subspace is expanded to a larger one, and then, in the expanded subspace a possibly better approximated solution is computed. The algorithm iterates these two steps alternately. Thus, the speed of the convergence of the algorithm depends on how to generate a subspace. In this paper, we derive a Riccati equation whose solution can correct the approximate solution of a generalized Hermitian eigenvalue problem to the exact one. In other words, the solution of the eigenvalue problem can be found if a subspace is expanded by the solution of the Riccati equation. This is a feature the existing algorithms such as the Krylov subspace algorithm implemented in the MATLAB and the Jacobi–Davidson algorithm do not have. However, similar to solving the eigenvalue problem, solving the Riccati equation is time-consuming. We consider solving the Riccati equation with low accuracy and use its approximate solution to expand a subspace. The implementation of this heuristic algorithm is discussed so that the computational cost of the algorithm can be saved. Some experimental results show that the heuristic algorithm converges within fewer iterations and thus requires lesser computational time comparing with the existing algorithms.

     

Assignment of Movies to Heterogeneous Video Servers

A video-on-demand (VOD) system provides an electronic video rental service to geographically distributed users. It can adopt multiple servers to serve many users concurrently. As a VOD system is being used and evolved, its servers probably become heterogeneous. For example, if a new server is added to expand the VOD system or replace a failed server, the new server may be faster with a larger storage size. This paper investigates how to assign movies to heterogeneous servers in order to minimize the blocking probability. It is proven that this assignment problem is NP-hard, and a lower bound is derived on the minimal blocking probability. The following approach is proposed for assignment: 1) problem relaxation—a relaxed assignment problem is formulated and solved to determine the ideal load that each server should handle, and 2) goal programming—an assignment and reassignment are performed iteratively while fulfilling all the constraints so that the load handled by each server is close to the ideal one. This approach is generic and applicable to many assignment problems. This approach is adopted to design two specific algorithms for movie assignment with and without replication. It is demonstrated that these algorithms can find optimal or close-to-optimal assignments.     

Performance Analysis of Resource Selection Schemes for a Large Scale Video-on-Demand System

The designers of a large scale video-on-demand system face an optimization problem of deciding how to assign movies to multiple disks (servers) such that the request blocking probability is minimized subject to capacity constraints. To solve this problem, it is essential to develop scalable and accurate analytical means to evaluate the blocking performance of the system for a given file assignment. The performance analysis is made more complicated by the fact that the request blocking probability depends also on how disks are selected to serve user requests for multicopy movies. In this paper, we analyze several efficient resource selection schemes. Numerical results demonstrate that our analysis is scalable and sufficiently accurate to support the task of file assignment optimization in such a system.     

A stochastic neighborhood search approach for airport gate assignment problem

An appropriate and efficient gate assignment is of great importance in airports since it plays a major role in the revenue obtained from the airport operations. In this study, we have focused mainly on maximum gate employment, or in other words minimize the total duration of un-gated flights. Here, we propose a method that combines the benefits of heuristic approaches with some stochastic approach instead of using a purely probabilistic approach to top-down solution of the problem. The heuristic approaches are usually used in order to provide a fast solution of the problem and later stochastic searches are used in order to ameliorate the previous results of the heuristic approach whenever possible. The proposed method generates an assignment order for the whole planes that corresponds to assignment priority. The ordering process is followed by the allocation step. Since, in practice, each airport has its own physical architecture, there have been arisen many constraints mainly concerning airplane types and parking lots in this step. Sequentially handling the plane ordering and allocation phases provides us great modularity in handling the constraints. The effectiveness of the proposed methodology has been tried to be illustrated firstly on fictively generated flight schedule data and secondly on the real world data obtained from a real world application developed for ?stanbul Atatürk Airport.     

Coordinated scheduling of production and delivery from multiple plants

This paper deals with the scheduling of orders and vehicle assignment for production and distribution planning in a scenario of no-wait, immediate delivery to the customer site. We first describe the problem and then present an integer programming model that maximizes the weighted value of the orders served. We consider a special case of the problem which can be solved in polinomial time by a minimum cost flow algorithm. Based on this approach we develop a heuristic procedure for the general case. Comparisons with an exact graph-based method attest that our heuristic produces good-quality solutions in short running times.     

Techniques for increasing the stream capacity of a high-performancemultimedia server

High-performance servers and high-speed networks will form the backbone of the infrastructure required for distributed multimedia information systems. A server for an interactive distributed multimedia system may require thousands of gigabytes of storage space and a high I/O bandwidth. In order to maximize the system utilization, and thus minimize the cost, it is essential that the load be balanced among each of the server's components, viz. the disks, the interconnection network and the scheduler. Many algorithms for maximizing retrieval capacity from the storage system have been proposed in the literature. This paper presents techniques for improving the server capacity by assigning media requests to the nodes of a server so as to balance the load on the interconnection network and the scheduling nodes. Five policies for request assignment-round-robin (RR), minimum link allocation (MLA), minimum contention allocation (MCA), weighted minimum link allocation (WMLA) and weighted minimum contention allocation (WMCA)-are developed. The performance of these policies on a server model developed by the authors (1995) is presented. We also consider the issue of file replication, and develop two schemes for storing the replicas: the parent group-based round-robin placement (PGBRRP) scheme, and the group-wide round-robin placement (GWRRP) scheme. The performance of the request assignment policies in the presence of file replication is presented     

A Dantzig-Wolfe Decomposition Based Heuristic Scheme for Bi-level Dynamic Network Design Problem

We present a heuristic to solve the NP-hard bi-level network design problem (NDP). The heuristic is developed based on the Dantzig-Wolfe decomposition principle such that it iteratively solves a master problem and a pricing problem. The master problem is the budget allocation linear program solved by CPLEX to determine the budget allocation and construct a modified cell transmission network for the pricing problem. The pricing problem is the user-optimal dynamic traffic assignment (UODTA) solved by an existing combinatorial algorithm. To facilitate the decomposition principle, we propose a backward connectivity algorithm and complementary slackness procedures to efficiently approximate the required dual variables from the UODTA solution. The dual variables are then employed to augment a new column in the master program in each iteration. The iterative process repeats until a stopping criterion is met. Numerical experiments are conducted on two test networks. Encouraging results demonstrate the applicability of the heuristic scheme on solving large-scale NDP. Though a single destination problem is considered in this paper, the proposed scheme can be extended to solve multi-destination problems as well.     

Integrated task assignment and path optimization for cooperating uninhabited aerial vehicles using genetic algorithms

The problem of integrating task assignment and planning paths for a group of cooperating uninhabited aerial vehicles, servicing multiple targets, is addressed. In the problem of interest the uninhabited aerial vehicles need to perform multiple consecutive tasks cooperatively on each ground target. A Dubins car model is used for motion planning, taking into account each vehicle's specific constraint of minimum turn radius. By using a finite set to define the visitation angle of a vehicle over a target we pose the integrated problem of task assignment and path optimization in the form of a graph. This new approach results in suboptimal trajectory assignments. Refining the visitation angle discretization allows for an improved solution. Due to the computational complexity of the resulting combinatorial optimization problem, we propose genetic algorithms for the stochastic search of the space of solutions. We distinguish between two cases of vehicle group composition: homogeneous, where all vehicles are identical; and heterogeneous, where the vehicles may have different operational capabilities and kinematic constraints. The performance of the genetic algorithms is demonstrated through sample runs and a Monte Carlo simulation study. Results show that the algorithms quickly provide good feasible solutions, and find the optimal solution for small sized problems.     

Heuristic manipulation,tabu search and frequency assignment

Heuristic manipulation attempts to modify the search space of an optimization problem, using information provided by an underlying heuristic method. In this paper it is applied in combination with tabu search to the fixed spectrum frequency assignment problem.The frequency assignment problem involves the assignment of discrete channels (or frequencies) to the transmitters of a radio network, such as a mobile telephone network. Frequency separation is necessary to avoid interference by other transmitters to the signal received from the wanted transmitter at the reception points. Unnecessary separation causes an excess requirement for spectrum. Good assignments minimize interference and the spectrum required. In fixed spectrum frequency assignment the frequency spectrum available is given and the target is to minimize the interference in the network.Computational experiments confirm that the manipulation technique is able to drive the underlying tabu search algorithm towards improved solutions.     

Quality assurance laboratory planning system to maximize worker preference subject to certification and preference balance constraints

This research addresses the assignment of technicians to quality control tests in a pharmaceutical manufacturing environment. The problem is complex as it includes constraints related to the capabilities of the quality assurance technicians, as well as various criteria related to efficiency, customer service, and worker satisfaction. We consider several factors that are particular to labor scheduling in the pharmaceutical industry: preference to certain types of work and certification related to training in specific tests. We propose and utilize a technician satisfaction metric and develop a heuristic to maximize this measure. Experiments are performed in order to evaluate the performance of the proposed heuristic, and gain insights regarding the relationship among key experimental factors. The results demonstrate that, in general, the proposed heuristic quickly generates scheduling assignments that provide a very good approximation of the optimal solution.     

A genetic algorithm based heuristic for scheduling of virtual manufacturing cells (VMCs)

We present a genetic algorithm (GA) based heuristic approach for job scheduling in virtual manufacturing cells (VMCs). In a VMC, machines are dedicated to a part as in a regular cell, but machines are not physically relocated in a contiguous area. Cell configurations are therefore temporary, and assignments are made to optimize the scheduling objective under changing demand conditions. We consider the case where there are multiple jobs with different processing routes. There are multiple machine types with several identical machines in each type and are located in different locations in the shop floor. Scheduling objective is weighted makespan and total traveling distance minimization. The scheduling decisions are the (i) assignment of jobs to the machines, and (ii) the job start time at each machine. To evaluate the effectiveness of the GA heuristic we compare it with a mixed integer programming (MIP) solution. This is done on a wide range of benchmark problem. Computational results show that GA is promising in finding good solutions in very shorter times and can be substituted in the place of MIP model.     

Methodology for an orderly quadratic assignment problem

An assignment arrangement problem (AAP), in which an arrangement represents a geometric straight line joining two pre-defined points (for facility and location), is introduced. This problem is a special class of QAP, and is different from all existing QAP's, as it requires a pre-established order between all assignments included in addition to a multi-objective function involved. It is shown that this un-conventional problem cannot be solved using current conventional exchange heuristic procedures. A new pairwise exchange is developed and programmed for solution and evaluation. The AAP and the solution procedure introduced are flexible and may be applicable to other problems which fit the general QAP formulation.     

Replica placement algorithms for mobile transaction systems

In distributed mobile systems, communication cost and disconnections are major concerns. In this paper, we address replica placement issues to achieve improved performance for systems supporting mobile transactions. We focus on handling correlated data objects and disconnections. Frequently, requests and/or transactions issued by mobile clients may access multiple data objects and should be considered together in terms of replica allocation. We discuss the replication cost model for correlated data objects and show that the problem of finding an optimal solution is NP. We further adjust the replication cost model for disconnections. A heuristic "expansion-shrinking" algorithm is developed to efficiently make replica placement decisions. The algorithm obtains near optimal solutions for the correlated data model and yields significant performance gains when disconnection is considered. Experimental studies show that the heuristic expansion-shrinking algorithm significantly outperforms the general frequency-based replication schemes.