Showing papers on "Assignment problem published in 2006"
TL;DR: This article enhances the ILS algorithm using acceptance criteria that allow moves to worse local optima and proposes population-based ILS extensions and shows their excellent performance when compared to other state-of-the-art algorithms for the QAP.
339 citations
22 Jan 2006
TL;DR: The (1 - 1/e)-approximation algorithm is extended to a nonseparable assignment problem with applications in maximizing revenue for budget-constrained combinatorial auctions and the AdWords assignment problem and the existence of cycles of best response moves, and exponentially long best-response paths to (pure or sink) equilibria is proved.
Abstract: A separable assignment problem (SAP) is defined by a set of bins and a set of items to pack in each bin; a value, fij, for assigning item j to bin i; and a separate packing constraint for each bin - ie for bin i, a family Li of subsets of items that fit in bin i The goal is to pack items into bins to maximize the aggregate value This class of problems includes the maximum generalized assignment problem (GAP)1) and a distributed caching problem (DCP) described in this paperGiven a β-approximation algorithm for finding the highest value packing of a single bin, we give1 A polynomial-time LP-rounding based ((1 − 1/e)β)-approximation algorithm2 A simple polynomial-time local search (β/β+1 - e) - approximation algorithm, for any e > 0Therefore, for all examples of SAP that admit an approximation scheme for the single-bin problem, we obtain an LP-based algorithm with (1 - 1/e - e)-approximation and a local search algorithm with (1/2-e)-approximation guarantee Furthermore, for cases in which the subproblem admits a fully polynomial approximation scheme (such as for GAP), the LP-based algorithm analysis can be strengthened to give a guarantee of 1 - 1/e The best previously known approximation algorithm for GAP is a 1/2-approximation by Shmoys and Tardos; and Chekuri and Khanna Our LP algorithm is based on rounding a new linear programming relaxation, with a provably better integrality gapTo complement these results, we show that SAP and DCP cannot be approximated within a factor better than 1 -1/e unless NP⊆ DTIME(nO(log log n)), even if there exists a polynomial-time exact algorithm for the single-bin problemWe extend the (1 - 1/e)-approximation algorithm to a nonseparable assignment problem with applications in maximizing revenue for budget-constrained combinatorial auctions and the AdWords assignment problem We generalize the local search algorithm to yield a 1/2-e approximation algorithm for the k-median problem with hard capacities Finally, we study naturally defined game-theoretic versions of these problems, and show that they have price of anarchy of 2 We also prove the existence of cycles of best response moves, and exponentially long best-response paths to (pure or sink) equilibria
258 citations
TL;DR: This work considers the supply chain of a manufacturer who produces time-sensitive products that have a large variety, a short life cycle, and are sold in a very short selling season and proposes several fast heuristics for the intractable problems.
Abstract: We consider the supply chain of a manufacturer who produces time-sensitive products that have a large variety, a short life cycle, and are sold in a very short selling season. The supply chain consists of multiple overseas plants and a domestic distribution center (DC). Retail orders are first processed at the plants and then shipped from the plants to the DC for distribution to domestic retailers. Due to variations in productivity and labor costs at different plants, the processing time and cost of an order are dependent on the plant to which it is assigned. We study the following static and deterministic order assignment and scheduling problem faced by the manufacturer before every selling season: Given a set of orders, determine which orders are to be assigned to each plant, find a schedule for processing the assigned orders at each plant, and find a schedule for shipping the completed orders from each plant to the DC, such that a certain performance measure is optimized. We consider four different performance measures, all of which take into account both delivery lead time and the total production and distribution cost. A problem corresponding to each performance measure is studied separately. We analyze the computational complexity of various cases of the problems by either proving that a problem is intractable or providing an efficient exact algorithm for the problem. We propose several fast heuristics for the intractable problems. We analyze the worst-case and asymptotic performance of the heuristics and also computationally evaluate their performance using randomly generated test instances. Our results show that the heuristics are capable of generating near-optimal solutions quickly.
196 citations
TL;DR: A task clustering method which takes the execution times of the tasks into account; two metrics to determine the order in which tasks are assigned to the processors; a refinement heuristic which improves a given assignment, and a refinement algorithm which improves the solutions of the existing algorithms by up to 15% are used.
144 citations
TL;DR: This paper presents a hybrid particle swarm optimization algorithm for finding the near optimal task assignment with reasonable time and the experimental results manifest that the proposed method is more effective and efficient than a genetic algorithm.
136 citations
TL;DR: This work proposes a new algorithm for the generalized assignment problem that proves to be more effective than previously existing methods and is especially effective for types D and E instances, which are known to be very difficult.
117 citations
TL;DR: A way to evaluate the quality of a given semi-matching is presented and it is shown that, under this measure, an optimal semi- matching balances the load on the right-hand vertices with respect to any Lp-norm.
107 citations
TL;DR: In this article, a genetic algorithm-based approach is developed to solve the problem of flexible job shop scheduling under resource constraints, which is an extension of classical job shop problems that permit an operation of each job to be processed by more than one machine.
Abstract: A flexible job-shop-scheduling problem is an extension of classical job-shop problems that permit an operation of each job to be processed by more than one machine. The research methodology is to assign operations to machines (assignment) and determine the processing order of jobs on machines (sequencing) such that the system objectives can be optimized. This problem can explore very well the common nature of many real manufacturing environments under resource constraints. A genetic algorithm-based approach is developed to solve the problem. Using the proposed approach, a resource-constrained operations-machines assignment problem and flexible job-shop scheduling problem can be solved iteratively. In this connection, the flexibility embedded in the flexible shop floor, which is important to today's manufacturers, can be quantified under different levels of resource availability.
105 citations
TL;DR: This paper studies the performance of two stochastic local search algorithms for the biobjective Quadratic Assignment Problem with different degrees of correlation between the flow matrices to suggest that the performance with respect to solution quality and computation time depends strongly on the correlation between those matrices.
97 citations
TL;DR: A modification of the standard assignment problem is proposed whereby the correspondences are required to preserve the ordering of the points induced from the shapes' contours to solve the problem of solving for point correspondences when the shapes are each defined by a single, closed contour.
Abstract: A common approach to determining corresponding points on two shapes is to compute the cost of each possible pairing of points and solve the assignment problem (weighted bipartite matching) for the resulting cost matrix. We consider the problem of solving for point correspondences when the shapes of interest are each defined by a single, closed contour. A modification of the standard assignment problem is proposed whereby the correspondences are required to preserve the ordering of the points induced from the shapes' contours. Enforcement of this constraint leads to significantly improved correspondences. Robustness with respect to outliers and shape irregularity is obtained by required only a fraction of feature points to be matched. Furthermore, the minimum matching size may be specified in advance. We present efficient dynamic programming algorithms to solve the proposed optimization problem. Experiments on the Brown and MPEG-7 shape databases demonstrate the effectiveness of the proposed method relative to the standard assignment problem.
95 citations
TL;DR: This work reviews a number of the problem formulations, including two-dimensional asymmetric single and multi-assignment problems, the corresponding multi-dimensional versions, and the newer group assignment problems.
TL;DR: In this paper, the authors present an alternative formulation of the assignment problem, which does not include due times and is based on a rough analogy to inventory management and is solved using an exact algorithm.
Abstract: This paper deals with automated guided vehicles (AGVs) which transport containers between the quay and the stack on automated container terminals. The focus is on the assignment of transportation jobs to AGVs within a terminal control system operating in real time. First, we describe a rather common problem formulation based on due times for the jobs and solve this problem both with a greedy priority rule based heuristic and with an exact algorithm. Subsequently, we present an alternative formulation of the assignment problem, which does not include due times. This formulation is based on a rough analogy to inventory management and is solved using an exact algorithm. The idea behind this alternative formulation is to avoid estimates of driving times, completion times, due times, and tardiness because such estimates are often highly unreliable in practice and do not allow for accurate planning. By means of simulation, we then analyze the different approaches. We show that the inventory-based model leads to better productivity on the terminal than the due-time-based formulation.
TL;DR: A non-linear mathematical model is developed with the objective of minimizing the travel distance of the pallets in the center and a substantial improvement is obtained by the model compared with the current operating system.
TL;DR: A novel user equilibrium traffic assignment model based on travel time reliability is presented in view of day-to-day demand fluctuation and the existence of at least one solution for the VI problem is rigorously proved.
Abstract: A novel user equilibrium traffic assignment model based on travel time reliability is presented in view of day-to-day demand fluctuation. Because of daily demand variations, path travel times are not constants, and so they can be viewed as random variables. Assuming that travelers are able to learn the variation of path travel time from experience, a demand-driven user equilibrium principle based on travel time reliability is proposed to characterize travelers' path choice behavior under uncertainty in travel times caused by demand variation. This principle can be formulated as a variational inequality (VI) problem in terms of path flows. The existence of at least one solution for the VI problem, for which a heuristic solution algorithm is adopted, is rigorously proved. Numerical examples are used to illustrate the applications of the proposed model and the solution algorithm.
TL;DR: This paper proposes a model for the periodic fleet assignment problem with time windows in which departure times are also determined, and proposes a non-linear integer multi-commodity network flow formulation.
TL;DR: A framework for the simultaneous optimization of evacuation traffic distribution and assignment is proposed and the ODE concept can be used to obtain an optimal destination and route assignment by solving a one-destination (1D) traffic assignment problem on a modified network representation.
Abstract: In the conventional evacuation planning process, evacuees are assigned to fixed destinations mainly on the basis of geographical proximity. However, the use of such prespecified destinations (an origin-destination table) almost always results in less-than-optimal evacuation efficiency because of uncertain road conditions, including traffic congestion, road blockage, and other hazards associated with the emergency. By relaxing the constraint of assigning evacuees to prespecified destinations, a one-destination evacuation (ODE) concept has the potential to improve evacuation efficiency greatly. To this end, a framework for the simultaneous optimization of evacuation traffic distribution and assignment is proposed. The ODE concept can be used to obtain an optimal destination and route assignment by solving a one-destination (1D) traffic assignment problem on a modified network representation. When tested for a countywide special event-based evacuation case study, the proposed 1D model presents substantial im...
TL;DR: The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).
Abstract: This paper is concerned with the system optimum-dynamic traffic assignment (SO-DTA) problem when the time-dependent demands are random variables with known probability distributions. The model is a stochastic extension of a deterministic linear programming formulation for SO-DTA introduced by Ziliaskopoulos (Ziliaskopoulos, A.K., 2000. A linear programming model for the single destination system optimum dynamic traffic assignment problem, Transportation Science, 34, 1–12). The proposed formulation is chance-constrained based and we demonstrate that it provides a robust SO solution with a user specified level of reliability. The model provides numerous insights and can be a useful tool in producing robust control and management strategies that account for uncertainty in applications where SO-DTA is relevant (e.g. evacuation modeling, computing alternate routes around freeway incidents and establishing lower bounds on network performance).
01 Mar 2006
TL;DR: A suite of suboptimal, but computationally tractable (polynomial time) algorithms are given, based on a solution to the problem of finding the optimal translation and rotation given a fixed assignment.
Abstract: In this paper we study the problem of parameterized assignment. This problem arises when a team of mobile robots must decide what role to take on in a given planar formation, where the parameters are the rotation and translation of the formation. A suite of suboptimal, but computationally tractable (polynomial time) algorithms are given, based on a solution to the problem of finding the optimal translation and rotation given a fixed assignment. Numerical examples show the viability of the proposed, suboptimal solutions.
Proceedings Article•
04 Dec 2006TL;DR: This paper presents a new method, called COMPOSE, for exploiting combinatorial optimization for sub-networks within the context of a max-product belief propagation algorithm, and describes highly efficient methods for computing max-marginals for subnetworks corresponding both to bipartite matchings and to regular networks.
Abstract: In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or close-to-optimal assignment can be found very efficiently using combinatorial optimization algorithms: certain MRFs with mutual exclusion constraints can be solved using bipartite matching, and MRFs with regular potentials can be solved using minimum cut methods. However, these solutions do not apply to the many MRFs that contain such tractable components as sub-networks, but also other non-complying potentials. In this paper, we present a new method, called COMPOSE, for exploiting combinatorial optimization for sub-networks within the context of a max-product belief propagation algorithm. COMPOSE uses combinatorial optimization for computing exact max-marginals for an entire sub-network; these can then be used for inference in the context of the network as a whole. We describe highly efficient methods for computing max-marginals for subnetworks corresponding both to bipartite matchings and to regular networks. We present results on both synthetic and real networks encoding correspondence problems between images, which involve both matching constraints and pairwise geometric constraints. We compare to a range of current methods, showing that the ability of COMPOSE to transmit information globally across the network leads to improved convergence, decreased running time, and higher-scoring assignments.
TL;DR: An ant colony optimization algorithm is developed to solve the quadratic assignment problem and is compared with other metaheuristics.
TL;DR: This paper develops failure-resilient techniques for monitoring link delays and faults in a Service Provider or Enterprise IP network and proposes greedy approximation algorithms that achieve a logarithmic approximation factor for the station selection problem and a constant factors for the probe assignment problem.
Abstract: In this paper, we develop failure-resilient techniques for monitoring link delays and faults in a Service Provider or Enterprise IP network. Our two-phased approach attempts to minimize both the monitoring infrastructure costs as well as the additional traffic due to probe messages. In the first phase, we compute the locations of a minimal set of monitoring stations such that all network links are covered, even in the presence of several link failures. Subsequently, in the second phase, we compute a minimal set of probe messages that are transmitted by the stations to measure link delays and isolate network faults. We show that both the station selection problem as well as the probe assignment problem are NP-hard. We then propose greedy approximation algorithms that achieve a logarithmic approximation factor for the station selection problem and a constant factor for the probe assignment problem. These approximation ratios are provably very close to the best possible bounds for any algorithm.
TL;DR: This paper presents a new approach to the Crew Assignment Problem arising in the context of airline companies operating short and medium haul flights, and shows how this problem can be formulated as a large scale integer linear program with a general structure combining different types of constraints and not exclusively partitioning or covering constraints as usually suggested in previous papers.
TL;DR: This paper proposes two hybrid meta-heuristics approaches for solving the task assignment problem (TSAP), in which each processor is limited in the number of task it can handle, due to the so called resource constraint.
TL;DR: This talk provides a heuristic approach for the integrated solution of two decision problems, which occur consecutively while planning the charge and discharge operations of container ships in container terminals.
Abstract: This talk deals with the combination of two decision problems, which occur consecutively while planning the charge and discharge operations of container ships in container terminals. The Berth Allocation Problem (BAP) considers the allocation of ships to berths in the course of time. The Crane Assignment Problem (CAP) addresses the assignment of quay cranes to ships. We provide a heuristic approach for the integrated solution of these problems and present computational results based on real world data.
21 Feb 2006
TL;DR: Fast polynomial time Murty ranked assignment algorithms can replace Reid's original NP-hard exhaustive hypothesis identification, probability evaluation, and branch-and-prune methods and can rapidly determine the maximally likely data association hypothesis, the second most likely, etc.
Abstract: The authors reformulate Reid's multiple hypothesis tracking algorithm to exploit a K-best ranked linear assignment algorithm for data association. The reformulated algorithm is designed for real-time tracking of large numbers of closely spaced objects. A likelihood association matrix is constructed that, for each scan, for each cluster, for each cluster hypothesis, exactly and compactly encodes the complete set of Reid's data association hypotheses. The set of this matrix's feasible assignments with corresponding non-vanishing products is shown to map one-to-one respectively onto the set of Reid's data association hypotheses and their corresponding probabilities. The explicit structure of this matrix is a new result and leads to an explicit hypothesis counting formula. Replacement of the likelihood association matrix elements by their negative natural logs then transforms the data association matrix into a linear assignment problem matrix and recasts the problem of data association into efficiently finding sets of ranked assignments. Fast polynomial time Murty ranked assignment algorithms can thus replace Reid's original NP-hard exhaustive hypothesis identification, probability evaluation, and branch-and-prune methods and can rapidly determine the maximally likely data association hypothesis, the second most likely, etc. Results from two high fidelity surveillance sensor simulations show the validity of the proposed method.
TL;DR: Experimental results demonstrate that the proposed ACO algorithm is an effective and competitive approach in composing fairly satisfactory results with respect to solution quality and execution time for the cell assignment problem as compared with most existing heuristics or metaheuristics.
TL;DR: In this paper, the fuzzy quadratic assignment problem with penalty is formulated as expected value model, chance-constrained programming and dependent-chance programming according to various decision criteria, and the crisp equivalents are given.
TL;DR: A new local search heuristic is proposed which solves the three-index assignment problem by simplifying it to the classical assignment problem and is further hybridize with the genetic algorithm (GA).
Journal Article•
TL;DR: This paper proposes a Tabu Search (TS) and a Genetic algorithms (GA) that utilize the IP constraints to solve the over-constrained truck dock assignment problem with time windows and capacity constraint in transshipment network through crossdocks.
Abstract: In this paper, we consider the over-constrained truck dock assignment problem with time windows and capacity constraint in transshipment network through crossdocks where the number of trucks exceeds the number of docks available, the capacity of the crossdock is limited, and where the objective is to minimize the total shipping distances. The problem is first formulated as an Integer Programming (IP) model, and then we propose a Tabu Search (TS) and a Genetic algorithms (GA) that utilize the IP constraints. Computational results are provided, showing that the heuristics perform better than the CPLEX Solver in both small-scale and large-scale test sets. Therefore, we conclude that the heuristic search approaches are efficient for the truck dock assignment problem.
TL;DR: It is shown how this distance generalizes the Spearman footrule distance, preserving its good computational complexity: the rank-distance between two partial rankings can be computed in linear time, and the rank aggregation problem can be solved in polynomial time.