Showing papers on "Assignment problem published in 1991"

Dynamic traffic assignment for urban road networks

Abstract: This paper presents a nonlinear programming formulation of the dynamic user-equilibrium assignment problem (DUE) for urban road networks with multiple trip origins and destinations. DUE is a temporal generalization of the static user-equilibrium assignment problem (SUE) with additional constraints to insure temporally continuous paths of flow. In DUE, the full assignment period of several hours is discretized into shorter time intervals of 10–15 minutes each for which trip departure matrices are assumed to be known. This formulation of DUE includes SUE as a special case in which there is only one time interval for the full assignment period. The assumption of steady-state flows allows SUE to have all linear constraints, but DUE requires nonlinear flow continuity constraints. Whereas SUE is typically solved by methods of linear combinations, these methods create temporally discontinuous flows if applied to DUE. A dynamic traffic assignment heuristic (DTA) is presented that generates approximate solutions to DUE in an efficient manner for large networks. DTA is not a convergent solution algorithm for DUE, but was designed instead to produce assignments that approximate the DUE optimality conditions. An overview of alternative dynamic assignment approaches is given, including the limitations of other optimization and simulation approaches. Test results presented in this paper show that DTA generates both static and dynamic assignments that approximately satisfy the user-equilibrium conditions of these problems.

Load adjustment in adaptive real-time systems

Abstract: A framework is given for discussing how to adjust load in order to handle periodic processes whose timing parameters vary with time. The schedulability of adjustable periodic processes by a preemptive fixed priority scheduler is formulated in terms of a configuration selection problem. Specifically, two process transformations are introduced for the purpose of deriving a bound for the achievable utilization factor of processes whose periods are related by harmonics. This result is then generalized so that the bound is applicable to any process set and an efficient algorithm to calculate the bound is provided. When the list of allowable configurations is implicitly given by a set of scalable periodic processes, the corresponding period assignment problem is shown to be NP-complete. The authors present an approximation algorithm for the period assignment problem for which some encouraging experimental results are included. >

Logically rearrangeable multihop lightwave networks

Abstract: The optimization problem of rearrangeable multihop lightwave networks is considered. The authors formulate the flow and wavelength assignment problem, when minimizing the maximum flow in the network, as a mixed integer optimization problem subject to linear constraints. The problem is decomposed into two independent subproblems, the wavelength assignment (or connectivity problem) and the flow assignment (or routing problem). A simple heuristic provides a meaningful formulation to the connectivity problem, in a form similar to a transportation problem. An algorithm is then proposed which finds a heuristic initial logical connectivity diagram and the corresponding routing, and then iterates from that solution by applying branch-exchange operations to the connectivity diagram. The algorithm was tested on illustrative traffic matrices for an 8 node network with two transmitters and two receivers per node, and an improvement in achievable throughput over the Perfect Shuffle interconnection pattern was shown in all cases. >

New results on server problems

Abstract: In the k-server problem, one must choose how k mobile servers will serve each of a sequence of requests, making decisions in an online manner. An optimal deterministic online strategy is exhibited when the requests fall on the real line. For the weighted-cache problem, in which the cost of moving to x from any other point is $w( x )$, the weight of x, an optimal deterministic algorithm is also provided. The nonexistence of competitive algorithms for the asymmetric two-server problem and of memoryless algorithms for the weighted-cache problem is proved. A fast algorithm for oflline computing of an optimal schedule is given, and it is shown that finding an optimal offline schedule is at least as hard as the assignment problem.

Parallel synchronous and asynchronous implementations of the auction algorithm

Abstract: In this paper we discuss the parallel implementation of the auction algorithm for the classical assignment problem. We show that the algorithm admits a totally asynchronous implementation and we consider several implementations on a shared memory machine, with varying degrees of synchronization. We also discuss and explore computationally the tradeoffs involved in using asynchronism to reduce the synchronization penalty.

An algorithm for the three-index assignment problem

Abstract: We describe a branch-and-bound algorithm for solving the axial three-index assignment problem. The main features of the algorithm include a Lagrangian relaxation that incorporates a class of facet inequalities and is solved by a modified subgradient procedure to find good lower bounds, a primal heuristic based on the principle of minimizing maximum regret plus a variable depth interchange phase for finding good upper bounds, and a novel branching strategy that exploits problem structure to fix several variables at each node and reduce the size of the total enumeration tree. Computational experience is reported on problems with up to 78 equations and 17,576 variables. The primal heuristics were tested on problems with up to 210 equations and 343,000 variables.

A note on “level schedules for mixed-model assembly lines in just-in-time production systems”

Abstract: This note formulates an assignment problem for obtaining optimal level schedules for mixed-model assembly lines in JIT production systems. The problem was formulated as a quadratic integer programming problem in a recent paper by Miltenburg 1989 where, however, only enumerative algorithms and heuristics were proposed for its solution. Our assignment formulation can also be extended to more general objective functions than the one used by Miltenburg.

Parallel simulated annealing using speculative computation

Abstract: A parallel simulated annealing algorithm that is problem-independent, maintains the serial decision sequence, and obtains speedup which can exceed log/sub 2/P on P processors is discussed. The algorithm achieves parallelism by using the concurrency technique of speculative computation. Implementation of the parallel algorithm on a hypercube multiprocessor and application to a task assignment problem are described. The simulated annealing solutions are shown to be, on average, 28% better than the solutions produced by a random task assignment algorithm and 2% better than the solutions produced by a heuristic. >

On-line algorithms for weighted bipartite matching and stable marriages

Abstract: We give an on-line deterministic algorithm for the weighted bipartite matching problem that achieves a competitive ratio of (2n − 1) in any metric space. This algorithm is optimal — there is no on-line deterministic algorithm that achieves a competitive ratio better than (2n − 1) in all metric spaces.

Algorithms for solving fisk's stochastic traffic assignment model

Abstract: In this, the logit-based stochastic traffic assignment model is explored. Two new improved algorithms are presented for solving this type of stochastic assignment problem. The major improvement achieved in these algorithms is that the step length in each iteration of the search process is optimized instead of using fixed step lengths as in the existing method of successive averages (MSA).

Convergent algorithm for dynamic traffic assignment

Abstract: A link flow formulation and a convergent solution algorithm for the dynamic user equilibrium (DUE) traffic assignment problem for road networks with multiple trip origins and destinations are presented. The link flow formulation does not implicitly assume complete enumeration of all origin-destination paths as does the equivalent path flow formulation. DUE is a temporal generalization of the static user equilibrium (SUE) assignment problem with additional constraints to ensure temporally continuous paths of flow. Whereas SUE can be solved by methods of linear combinations, these methods can create temporally discontinuous flows if applied to DUE. This convergent dynamic algorithm (CDA) uses the Frank-Wolfe method of linear combinations to find successive solutions to DUE while holding node time intervals fixed from each origin. In DUE, the full assignment period of several hours is discretized into shorter time intervals of 10 to 15 min each, for which trip departure matrices are assumed to be known. The performance of CDA is compared with that of a heuristic solution procedure called DTA. CDA can be applied to solving DUE on large networks, and the examples presented show that CDA consistently converges to solutions that closely satisfy the DUE optimality conditions. With computational advances such as parallel computing, CDA can be run in near real-time on large-scale networks and used with in-vehicle route advisory systems for traffic management during evacuations and special events.

The Auction Algorithm for Assignment and Other Network Flow Problems

Abstract: The auction algorithm is an intuitive method for solving the classical assignment problem It outperforms substantially its main competitors for important types of problems, both in theory and in practice, and is also naturally well suited for parallel computation The algorithm represents a significant departure from the cost improvement idea that underlies primal simplex and dual ascent methods; at any one iteration, it may deteriorate both the primal and the dual cost, although in the end it does find an optimal primal solution We derive the algorithm from first principles, explain its computational properties, and discuss its extensions to transportation and transhipment problems

A parallel shortest augmenting path algorithm for the assignment problem

Abstract: : We describe a parallel version of the shortest augmenting path algorithm for the assignment problem. While generating the initial dual solution and partial assignment in parallel does not require substantive changes in the sequential algorithm, using several augmenting paths in parallel does require a new dual variable recalculation method. The parallel algorithm was tested on a 14-processor Butterfly Plus computer, on problems with up to 900 million variables. The speedup obtained increases with problem size. The algorithm was also embedded into a parallel branch and bound procedure for the traveling salesman problem on a directed graph, which was test on the Butterfly Plus on problems involving up to 7,500 cities. To our knowledge, these are the largest assignment problems and traveling salesman problems solved so far.

An infeasible (exterior point) simplex algorithm for assignment problems

Abstract: The so called Modified Hung—Rom Algorithm, based upon theoretical considerations of Hirsch-paths, seems to be one of the most efficient algorithms for assignment problems. Since any two basic feasible solutions to a linear problem can always be connected with a short simplex path passing through the infeasible region, development of algorithms based upon theoretical considerations on infeasible paths seems to be of great practical interest. This paper presents an algorithm of this kind for assignment problems.

An expert system methodology for aircraft-gate assignment

Abstract: The aircraft-gate assignment problem is a significant concern in airline operations. This paper addresses the use of knowledge based expert systems to help solve the aircraft-gate assignment problem. The problem is described and the factors that need to be considered in aircraft-gate assignment are identified and delineated. The expert system's architecture is presented and its working is described.

An Empirical Analysis of the Dense Assignment Problem: Sequential and Parallel Implementations

Abstract: The best algorithms for the dense assignment problem are acknowledged to be the auction algorithm and the shortest augmenting path algorithm. In this investigation we present an empirical analysis of two of the current best software implementations of these two methods on three different serial machines. These software implementations were developed by D. P. Bertsekas of the Massachusetts Institute of Technology and by R. Jonker and T. Volgenant of the University of Amsterdam. This report is an independent evaluation of the software implementation of these two algorithms. For the sample of problems examined and the sample of hardware used (IBM 3081D, Sequent Symmetry S81, and VAX 750), we found that the shortest augmenting path algorithm was the fastest. We also report our empirical results with a parallel version of the shortest augmenting path algorithm. On 1200×1200 dense assignment problems, speedups of approximately four were achieved using ten processors. Million arc problems were solved in less tha...

A close look at task assignment in distributed systems

Abstract: C. C. Shen and W. H. Tsai (IEEE Trans. Comput., vol.C-34, no.3, p.197-203 1985) proposed a graph matching algorithm for solving the static task assignment problem. It combines two important ideas: (1) graph homomorphism and (2) application of the A* algorithm. Task-dependent information is used as a heuristic to reduce the search effort in finding an optimal path to the goal node. An examination is made of Shen and Tsai's strategy and their complexity measure. The authors propose some simple alternatives to their algorithm that are effective in reducing the number of nodes generated (and expanded) without sacrificing the optimality criteria. >

Multitarget tracking and multidimensional assignment problems

Abstract: A fundamental problem in multi-target tracking is the data association problem of partitioning the observations into tracks and false alarms so that an accurate estimate of the true tracks can be recovered. Here, this problem is formulated as a multi-dimensional assignment problem using gating techniques to introduce sparsity into the problem, filtering techniques to generate tracks which are then used to score each assignment of a collection of observations to its corresponding filtered track. Problem complexity is further reduced by decomposing the problem into disjoint components using graph theoretic methods. A recursive Lagrangean relaxation algorithm is then developed to obtain high quality suboptimal solutions in real-time. The algorithms are, however, applicable to a large class of sparse multi-dimensional assignment problems arising in general multi-target and multi-sensor tracking. Results of extensive numerical testing are presented for a case study to demonstrate the speed, robustness, and exceptional quality of the solutions.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Geometric algorithms for a minimum cost assignment problem

Abstract: We consider the minimum cost A-assignment problem, which is equivalent to the minimum weight one-to-many matching problem in a complete bipartite graph r = (A ,B), where A and B have n and k nodes respectively. Formulating the problem as a geometric problem, we give an qkn + k“n”’)-tirne randomized algorithm, which is better than existing qkt$ + n2 log n)-time algorithm if ks nob.

On-line weighted matching

Abstract: We study on-line versions of weighted matching problems in metric spaces. We present a simple algorithm for online minimum weighted bipartite matching that is 2k – 1 competitive, where 2k is the number of nodes. We show that this bound is optimal. For on-line maximum matching, we prove that the greedy algorithm achieves an optimal competitive factor of 3. In contrast, we prove that greedy algorithm performs exponentially poorly for on-line minimum matching. We show how lower and upper bounds can be translated between this problem and the standard

The plant layout problem in automated manufacturing systems

Abstract: The plant layout problem is usually formulated as a quadratic assignment problem (QAP). In this paper, we incorporate the throughput related aspects of the automated manufacturing system into the layout problem. We modify the QAP formulation by explicitly considering the throughput requirements of automated manufacturing systems. Our formulation also incorporates the cost of keeping a certain number of pallet-fixtures in the system. The resulting modified quadratice assignment problem (MQAP) is presented. An optimal solution method for MQAP is developed and its computational performance is evaluated.

Graph theoretical considerations of channel offset systems in a cellular mobile system

Abstract: The problem of assigning channels in a channel-offset-type of cellular mobile radio communication system is formulated as a problem of assigning channels to the vertices of a network. It is shown that the assignment problem in a network is a generalized graph coloring problem. When the interchannel interference function is a rational number, the optimal channel offset scheme is obtained. and upper and lower bounds of the minimum total bandwidth in a channel-offset scheme are derived. These factors give basic and useful knowledge for designing a channel-offset system of a cellular mobile system, and they are useful not only for a fixed channel assignment but also for a dynamic channel assignment and rearrangement. >

Some facets for an assignment problem with side constraints

Abstract: This paper presents a class of facet-defining inequalities for an assignment problem with the additional constraints that specified variables are required to be equal to each other. In a special case, the complete polyhedral description is given.

Performance Characteristics of the Jacobi and the Gauss-Seidel Versions of the Auction Algorithm on the Alliant FX/8

Abstract: Recently, D. Bertsekas proposed a new method to solve the linear assignment problem that appears to be well suited for concurrent computation. The method, called the auction algorithm is a primal-dual iterative scheme that updates the dual solution by performing coordinate steps similar to those of the Jacobi and Gauss-Seidel (GS) methods for unconstrained optimization. Bertsekas noted that the GS version tends to converge a little faster on uniprocessor computers but is generally much less parallelizable. Consequently, several questions arise regarding the relative performance of these two versions: How will their performances be affected by changes in problem size, cost range, and problem data? How should one design an efficient implementation for each version that takes full advantage of novel computer hardware capabilities such as concurrency and vectorization? How does the concurrency of computations affect the sensitivity of the solution times to changes in the cost range for each version? Will Jaco...

An Approximate Dual Projective Algorithm for Solving Assignment Problems.

Abstract: This paper discusses a new algorithm for solving the assignment problem. This algorithm, called the Approximate Dual Projective algorithm for assignment (ADP/A), is a variant of the Karmarkar interior point algorithm for LPs, specialized to solve the assignment problem. Computational results are reported on various classes of assignment problems. These results indicate that this method, holds promise for solving large assignment problems.

Design of manufacturing cells: Operation assignment in printed circuit board manufacturing

Abstract: We consider an operation assignment problem that arose from a printed circuit (PC) board assembly process. Components can either be inserted on boards manually or by machine. The objective is to determine an assignment of components (operations) to a set of capacitated machines (with the remainder of the components inserted manually) to minimize the total set-up and processing cost for assembling all boards. The problem can be formulated as a mixed integer linear program, but is too large to be practically solved. For the case of one machine, we present two different solution heuristics. We show that while each can be arbitrarily bad, on average the algorithms perform quite well. For the case of multiple machines, we present four different solution heuristics. We discuss implementation of our results at Hewlett-Packard.

A reconfigurable ATM switch fabric for fault tolerance and traffic balancing

Abstract: A large-scale asynchronous transfer mode (ATM) switch fabric that can be constructed with currently feasible technology is proposed. Based on analysis of the technology, it is found that module interconnection becomes the bottleneck for a large fast packet switch. Fault tolerance for the switch is achieved by dynamic reconfiguration of the module interconnection network. The design improves system reliability with relatively low hardware overhead. An abstract model of the replacement problem for the design is presented, and the problem is transformed into a well-known assignment problem. The maximum fault tolerance is found, and a fast replacement algorithm is given. The reconfiguration capability can also be used to ameliorate imbalanced traffic flows. The authors formulate this traffic flow assignment problem for the switch fabric and show that the problem is NP-hard. A simple heuristic algorithm is proposed, and an example is given. >