Showing papers on "Assignment problem published in 2008"

Assignment problems

Abstract: This book provides a comprehensive treatment of assignment problems from their conceptual beginnings in the 1920s through present-day theoretical, algorithmic, and practical developments. The authors have organized the book into 10 self-contained chapters to make it easy for readers to use the specific chapters of interest to them without having to read the book linearly. The topics covered include bipartite matching algorithms, linear assignment problems, quadratic assignment problems, multi-index assignment problems, and many variations of these problems. Exercises in the form of numerical examples provide readers with a method of self-study or students with homework problems, and an associated webpage offers applets that readers can use to execute some of the basic algorithms as well as links to computer codes that are available online. Audience: Assignment Problems is a useful tool for researchers, practitioners, and graduate students. Researchers will benefit from the detailed exposition of theory and algorithms related to assignment problems, including the basic linear sum assignment problem and its many variations. Practitioners will learn about practical applications of the methods, the performance of exact and heuristic algorithms, and software options. This book also can serve as a text for advanced courses in discrete mathematics, integer programming, combinatorial optimization, and algorithmic computer science. Contents: Preface; Chapter 1: Introduction; Chapter 2: Theoretical Foundations; Chapter 3: Bipartite Matching Algorithms; Chapter 4: Linear Sum Assignment Problem; Chapter 5: Further Results on the Linear Sum Assignment Problem; Chapter 6: Other Types of Linear Assignment Problems; Chapter 7: Quadratic Assignment Problems: Formulations and Bounds; Chapter 8: Quadratic Assignment Problems: Algorithms; Chapter 9: Other Types of Quadratic Assignment Problems; Chapter 10: Multi-index Assignment Problems; Bibliography; Author Index; Subject Index

Optimal approximation for the submodular welfare problem in the value oracle model

Abstract: In the Submodular Welfare Problem, m items are to be distributed among n players with utility functions wi: 2[m] → R+. The utility functions are assumed to be monotone and submodular. Assuming that player i receives a set of items Si, we wish to maximize the total utility ∑i=1n wi(Si). In this paper, we work in the value oracle model where the only access to the utility functions is through a black box returning wi(S) for a given set S. Submodular Welfare is in fact a special case of the more general problem of submodular maximization subject to a matroid constraint: max{f(S): S ∈ I}, where f is monotone submodular and I is the collection of independent sets in some matroid. For both problems, a greedy algorithm is known to yield a 1/2-approximation [21, 16]. In special cases where the matroid is uniform (I = S: |S| ≤ k) [20] or the submodular function is of a special type [4, 2], a (1-1/e)-approximation has been achieved and this is optimal for these problems in the value oracle model [22, 6, 15]. A (1-1/e)-approximation for the general Submodular Welfare Problem has been known only in a stronger demand oracle model [4], where in fact 1-1/e can be improved [9]. In this paper, we develop a randomized continuous greedy algorithm which achieves a (1-1/e)-approximation for the Submodular Welfare Problem in the value oracle model. We also show that the special case of n equal players is approximation resistant, in the sense that the optimal (1-1/e)-approximation is achieved by a uniformly random solution. Using the pipage rounding technique [1, 2], we obtain a (1-1/e)-approximation for submodular maximization subject to any matroid constraint. The continuous greedy algorithm has a potential of wider applicability, which we demonstrate on the examples of the Generalized Assignment Problem and the AdWords Assignment Problem.

Online budgeted matching in random input models with applications to Adwords

Abstract: We study an online assignment problem, motivated by Adwords Allocation, in which queries are to be assigned to bidders with budget constraints. We analyze the performance of the Greedy algorithm (which assigns each query to the highest bidder) in a randomized input model with queries arriving in a random permutation. Our main result is a tight analysis of Greedy in this model showing that it has a competitive ratio of 1 - 1/e for maximizing the value of the assignment. We also consider the more standard i.i.d. model of input, and show that our analysis holds there as well. This is to be contrasted with the worst case analysis of [MSVV05] which shows that Greedy has a ratio of 1/2, and that the optimal algorithm presented there has a ratio of 1 - 1/e. The analysis of Greedy is important in the Adwords setting because it is the natural allocation algorithm for an auction-style process. From a theoretical perspective, our result simplifies and generalizes the classic algorithm of Karp, Vazirani and Vazirani for online bipartite matching. Our results include a new proof to show that the Ranking alforithm of [KVV90] has a ratio of 1 - 1/e in the worst case. It has been recently discovered [KV07] (independent of our results) that one of the crucial lemmas in [KVV90], related to a certain reduction, is incorrect. Our proof is direct, in that it does not go via such a reduction, which also enables us to generalize the analysis to our online assignment problem.

OPSO: Orthogonal Particle Swarm Optimization and Its Application to Task Assignment Problems

Abstract: This paper proposes a novel variant of particle swarm optimization (PSO), named orthogonal PSO (OPSO), for solving intractable large parameter optimization problems. The standard version of PSO is associated with the lack of a mechanism responsible for the process of high-dimensional vector spaces. The high performance of OPSO arises mainly from a novel move behavior using an intelligent move mechanism (IMM) which applies orthogonal experimental design to adjust a velocity for each particle by using a systematic reasoning method instead of the conventional generate-and-go method. The IMM uses a divide-and- conquer approach to cope with the curse of dimensionality in determining the next move of particles. It is shown empirically that the OPSO performs well in solving parametric benchmark functions and a task assignment problem which is NP-complete compared with the standard PSO with the conventional move behavior. The OPSO with IMM is more specialized than the PSO and performs well on large-scale parameter optimization problems with few interactions between variables.

A distributed auction algorithm for the assignment problem

Abstract: The assignment problem constitutes one of the fundamental problems in the context of linear programming. Besides its theoretical significance, its frequent appearance in the areas of distributed control and facility allocation, where the problems? size and the cost for global computation and information can be highly prohibitive, gives rise to the need for local solutions that dynamically assign distinct agents to distinct tasks, while maximizing the total assignment benefit. In this paper, we consider the linear assignment problem in the context of networked systems, where the main challenge is dealing with the lack of global information due to the limited communication capabilities of the agents. We address this challenge by means of a distributed auction algorithm, where the agents are able to bid for the task to which they wish to be assigned. The desired assignment relies on an appropriate selection of bids that determine the prices of the tasks and render them more or less attractive for the agents to bid for. Up to date pricing information, necessary for accurate bidding, can be obtained in a multi-hop fashion by means of local communication between adjacent agents. Our algorithm is an extension to the parallel auction algorithm proposed by Bertsekas et al to the case where only local information is available and it is shown to always converge to an assignment that maximizes the total assignment benefit within a linear approximation of the optimal one.

Optimal relay assignment for cooperative communications

Abstract: Recently, cooperative communications, in the form of keeping each node with a single antenna and having a node exploit a relay node's antenna, is shown to be a promising approach to achieve spatial diversity. Under this communication paradigm, the choice of relay node plays a significant role in the overall system performance. In this paper, we study the relay node assignment problem in a network environment, where multiple source-destination pairs compete for the same pool of relay nodes in the network. The main contribution of this paper is the development of a polynomial time algorithm to solve this problem. A key idea in this algorithm is a "linear marking" mechanism, which is able to offer a linear complexity for each iteration. We give a formal proof of optimality for this algorithm. We also show several attractive properties associated with this algorithm.

On-line bipartite matching made simple

Abstract: We examine the classic on-line bipartite matching problem studied by Karp, Vazirani, and Vazirani [8] and provide a simple proof of their result that the Ranking algorithm for this problem achieves a competitive ratio of 1 -- 1/e.

Distributed uplink power control for optimal sir assignment in cellular data networks

Abstract: This paper solves the joint power control and SIR assignment problem through distributed algorithms in the uplink of multi-cellular wireless networks. The 1993 Foschini-Miljanic distributed power control can attain a given fixed and feasible SIR target. In data networks, however, SIR needs to be jointly optimized with transmit powers in wireless data networks. In the vast research literature since the mid-1990s, solutions to this joint optimization problem are either distributed but suboptimal, or optimal but centralized. For convex formulations of this problem, we report a distributed and optimal algorithm. The main issue that has been the research bottleneck is the complicated, coupled constraint set, and we resolve it through a re-parametrization via the left Perron Frobenius eigenvectors, followed by development of a locally computable ascent direction. A key step is a new characterization of the feasible SIR region in terms of the loads on the base stations, and an indication of the potential interference from mobile stations, which we term spillage. Based on this load-spillage characterization, we first develop a distributed algorithm that can achieve any Pareto-optimal SIR assignment, then a distributed algorithm that picks out a particular Pareto-optimal SIR assignment and the associated powers through utility maximization. Extensions to power-constrained and interference-constrained cases are carried out. The algorithms are theoretically sound and practically implementable: we present convergence and optimality proofs as well as simulations using 3GPP network and path loss models.

Delay-Aware Period Assignment in Control Systems

Abstract: We consider the problem of optimal static period assignment for multiple independent control tasks executing on the same CPU. Previous works have assumed that the control performance can be expressed as a function of the sampling rate only. Arguing that the control delay has a large impact on the control performance, in this work we include the control delay in the cost function. The delay is estimated using an approximate response-time analysis. Assuming linear cost functions for the controllers then allows us to solve the optimal period assignment problem analytically. The performance improvements over previous methods are verified in evaluations on synthetic task sets as well as detailed co- simulations of the controllers, the plants, and the scheduler.

Multicriteria airport gate assignment and Pareto simulated annealing

Abstract: This paper addresses an airport gate assignment problem with multiple objectives. The objectives are to minimize the number of ungated flights and the total passenger walking distances or connection times as well as to maximize the total gate assignment preferences. The problem examined is an integer program with multiple objectives (one of them being quadratic) and quadratic constraints. Of course, such a problem is inherently difficult to solve. We tackle the problem by Pareto simulated annealing in order to get a representative approximation for the Pareto front. Results of computational experiments are presented. To the best of our knowledge, this is the first attempt to consider the airport gate assignment problem with multiple objectives.

A robust approach to the UAV task assignment problem

Abstract: This paper presents a new robust approach to the task assignment of unmanned aerial vehicles (UAVs) operating in uncertain dynamic environments for which the optimization data, such as target cost and target–UAV distances, are time varying and uncertain. The impact of this uncertainty in the data is mitigated by tightly integrating two approaches for improving the robustness of the assignment algorithm. One approach is to design task assignment plans that are robust to the uncertainty in the data, which reduces the sensitivity to errors in the situational awareness (SA), but can be overly conservative for long duration plans. A second approach is to replan as the SA is updated, which results in the best plan given the current information, but can lead to a churning type of instability if the updates are performed too rapidly. The strategy proposed in this paper combines robust planning with the techniques developed to eliminate churning. This combination results in the robust filter-embedded task assignment algorithm that uses both proactive techniques that hedge against the uncertainty, and reactive approaches that limit churning behavior by the vehicles. Numerous simulations are shown to demonstrate the performance benefits of this new algorithm. Copyright © 2007 John Wiley & Sons, Ltd.

Swarm Intelligence Based Dynamic Control Channel Assignment in Cogmesh

Abstract: In this paper we address the control channel assignment problem in a cognitive radio based wireless network, namely the CogMesh. Such a network is featured by the dynamic spectrum sharing of the secondary users coexisting with the primary users. The opportunistic nature of the spectrum utilization among the secondary users makes a global control channel infeasible. The self-coordination of the network, hence, becomes a challenge task. Considering the fact that common channels may temporarily exist among a local group of secondary users, we propose an adaptive approach that selects local common control channels independently by each secondary user according to the qualities of the detected spectrum holes and the choices of its neighbors. To achieve this, a swarm intelligence-based algorithm is used to facilitate the common control channel selection. The idea is to use HELLO messages periodically broadcasted by neighbors as the pheromone to rank the common channels so as to expedite the channel selection process. The algorithm is completely distributed and therefore scalable. Moreover, it is simple, flexible, adaptive, and well balanced on the exploitation and exploration of the radio resources. The behaviors and performance of the proposed algorithm are verified by simulation.

New approaches for solving the block-to-train assignment problem

Abstract: Railroad planning involves solving two optimization problems: (i) the blocking problem, which determines what blocks to make and how to route traffic over these blocks; and (ii) the train schedule design problem, which determines train origins, destinations, and routes. Once the blocking plan and train schedule have been obtained, the next step is to determine which trains should carry which blocks. This problem, known as the block-to-train assignment problem, is considered in this paper. We provide two formulations for this problem: an arc-based formulation and a path-based formulation. The latter is generally smaller than the former, and it can better handle practical constraints. We also propose exact and heuristic algorithms based on the path-based formulation. Our exact algorithm solves an integer programming formulation with CPLEX using both a priori generation and dynamic generation of paths. Our heuristic algorithms include a Lagrangian relaxation-based method as well as a greedy construction method. We present computational results of our algorithms using the data provided by a major US railroad. We show that we can obtain an optimal solution of the block-to-train assignment problem within a few minutes of computational time, and can obtain heuristic solutions with 1–2p deviations from the optimal solutions within a few seconds. © 2007 Wiley Periodicals, Inc. NETWORKS, 2008

Competitive Weighted Matching in Transversal Matroids

Abstract: Consider a bipartite graph with a set of left-vertices and a set of right-vertices. All the edges adjacent to the same left-vertex have the same weight. We present an algorithm that, given the set of right-vertices and the number of left-vertices, processes a uniformly random permutation of the left-vertices, one left-vertex at a time. In processing a particular left-vertex, the algorithm either permanently matches the left-vertex to a thus-far unmatched right-vertex, or decides never to match the left-vertex. The weight of the matching returned by our algorithm is within a constant factor of that of a maximum weight matching.

An Evolutionary Algorithm to a Multi-Objective Deployment and Power Assignment Problem in Wireless Sensor Networks

Abstract: Wireless sensor networks design requires high quality location assignment and energy efficient power assignment for maximizing the network coverage and lifetime. Classical deployment and power assignment approaches optimize these two objectives individually or by combining them together in a single objective or by constraining one and optimizing the other. In this article a multi-objective deployment and power assignment problem (DPAP) is formulated and a multi-objective evolutionary algorithm based on decomposition (MOEA/D) is specialized. Following the MOEA/D's framework the above multiobjective optimization problem (MOP) is decomposed into many scalar single objective problems. The sub-problems are solved simultaneously by using neighborhood information. Additionally, unique problem-specific, parameter-rising, genetic operators and local search heuristics were designed specifically for the DPAP. In addition, a new encoding scheme is designed to represent a WSN based on the DPAP's design variables. Simulation results show that MOEA/D provides a high quality set of alternative solutions without any prior knowledge on the objectives preference.

Optimal Just-in-Time Schedules for Flexible Transfer Lines

Abstract: Flexible transfer lines or mixed-model assembly lines are capable of diversified small-lot production due to negligible switch-over costs. With these lines, it is possible to implement just-in-time (JIT) production, which involves producing only the necessary parts in the necessary quantities at the necessary times. The problem of sequencing flexible transfer lines according to the JIT philosophy can be formulated as a nonlinear integer programming problem. Heuristic algorithms to solve the problem have appeared in the literature. In this paper, we show that the problem can be explicitly reduced to an assignment problem. Thus, we provide an efficient algorithm for an optimal solution to the JIT sequencing problem.

A due-window assignment problem with position-dependent processing times

Abstract: We extend a classical single-machine due-window assignment problem to the case of position-dependent processing times. In addition to the standard job scheduling decisions, one has to assign a time interval (due-window), such that jobs completed within this interval are assumed to be on time and not penalized. The cost components are: total earliness, total tardiness and due-window location and size. We introduce an O(n 3) solution algorithm, where n is the number of jobs. We also investigate several special cases, and examine numerically the sensitivity of the solution (schedule and due-window) to the different cost parameters.

On earliest deadline first scheduling for temporal consistency maintenance

Abstract: A real-time object is one whose state may become invalid with the passage of time. A temporal validity interval is associated with the object state, and the real-time object is temporally consistent if its temporal validity interval has not expired. Clearly, the problem of maintaining temporal consistency of data is motivated by the need for a real-time system to track its environment correctly. Hence, sensor transactions must be able to execute periodically and also each instance of a transaction should perform the relevant data update before its deadline. Unfortunately, the period and deadline assignment problem for periodic sensor transactions has not received the attention that it deserves. An exception is the More-Less scheme, which uses the Deadline Monotonic (DM) algorithm for scheduling periodic sensor transactions. However, there is no work addressing this problem from the perspective of dynamic priority scheduling. In this paper, we examine the problem of temporal consistency maintenance using the Earliest Deadline First (EDF) algorithm in three steps: First, the problem is transformed to another problem with a sufficient (but not necessary) condition for feasibly assigning periods and deadlines. An optimal solution for the problem can be found in linear time, and the resulting processor utilization is characterized and compared to a traditional approach. Second, an algorithm to search for the optimal periods and deadlines is proposed. The problem can be solved for sensor transactions that require any arbitrary deadlines. However, the optimal algorithm does not scale well when the problem size increases. Hence, thirdly, we propose a heuristic search-based algorithm that is more efficient than the optimal algorithm and is capable of finding a solution if one exists.

Optimal Sampling Rate Assignment with Dynamic Route Selection for Real-Time Wireless Sensor Networks

Abstract: The allocation of computation and communication resources in a manner that optimizes aggregate system performance is a crucial aspect of system management. Wireless sensor network poses new challenges due to the resource constraints and real-time requirements. Existing work has dealt with the real-time sampling rate assignment problem, under single processor case and network case with static routing environment. For wireless sensor networks, in order to achieve better overall network performance, routing should be considered together with the rate assignments of individual flows. In this paper, we address the problem of optimizing sampling rates with dynamic route selection for wireless sensor networks. We model the problem as a constrained optimization problem and solve it under the network utility maximization framework. Based on the primal-dual method and dual decomposition technique, we design a distributed algorithm that achieves the optimal global network utility considering both dynamic route decision and rate assignment. Extensive simulations have been conducted to demonstrate the efficiency and efficacy of our proposed solutions.

A Survey on Reviewer Assignment Problem

Abstract: Research into Reviewer Assignment Problem (RAP) is still in its early stage but there is great world-wide interest, as the foregoing process of peer-review which is the brickwork of science authentication. The RAP approach can be divided into three phases: identifying assignment procedure, computing the matching degree between manuscripts and reviewers, and optimizing the assignment so as to achieve the given objectives. Methodologies for addressing the above three phases have been developed from a variety of research disciplines, including information retrieval, artificial intelligent, operations research, etc. This survey is not only to cover variations of RAP that have appeared in the literature, but also to identify the practical challenge and current progress for developing intelligent RAP systems.

Utility-based dynamic camera assignment and hand-off in a video network

Abstract: In this paper we propose an approach for multi-camera multi-person seamless tracking that allows camera assignment and hand-off based on a set of user-supplied criteria. The approach is based on the application of game theory to camera assignment problem. Bargaining mechanisms are considered for collaborations as well as for resolving conflicts among the available cameras. Camera utilities and person utilities are computed based on a set of criteria. They are used in the process of developing the bargaining mechanisms. Experiments for multi-camera multi-person tracking are provided. Several different criteria and their combination of them are carried out and compared with each other to corroborate the proposed approach.

General stochastic user equilibrium traffic assignment problem with link capacity constraints

Abstract: This paper addresses a general stochastic user equilibrium (SUE) traffic assignment problem with link capacity constraints. It first proposes a novel linearly constrained minimization model in terms of path flows and then shows that any of its local minimums satisfies the generalized SUE conditions. As the objective function of the proposed model involves path-specific delay functions without explicit mathematical expressions, its Lagrangian dual formulation is analyzed. On the basis of the Lagrangian dual model, a convergent Lagrangian dual method with a predetermined step size sequence is developed. This solution method merely invokes a subroutine at each iteration to perform a conventional SUE traffic assignment excluding link capacity constraints. Finally, two numerical examples are used to illustrate the proposed model and solution method.

Optimal switch location in mobile communication networks using hybrid genetic algorithms

Abstract: The optimal positioning of switches in a mobile communication network is an important task, which can save costs and improve the performance of the network. In this paper we propose a model for establishing which are the best nodes of the network for allocating the available switches, and several hybrid genetic algorithms to solve the problem. The proposed model is based on the so-called capacitated p-median problem, which have been previously tackled in the literature. This problem can be split in two subproblems: the selection of the best set of switches, and a terminal assignment problem to evaluate each selection of switches. The hybrid genetic algorithms for solving the problem are formed by a conventional genetic algorithm, with a restricted search, and several local search heuristics. In this work we also develop novel heuristics for solving the terminal assignment problem in a fast and accurate way. Finally, we show that our novel approaches, hybridized with the genetic algorithm, outperform existing algorithms in the literature for the p-median problem.