Topic
Assignment problem
About: Assignment problem is a research topic. Over the lifetime, 7588 publications have been published within this topic receiving 172820 citations. The topic is also known as: marriage problem.
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TL;DR: A unified framework to specifically treat the objective functions of the previous models is introduced and linear representations of these models are provided and conditions under which the optimal solutions can be obtained in polynomial time are identified.
Abstract: Assigning aircraft to available gates at an airport can have a major impact on the efficiency of flight schedules and on the level of passenger satisfaction with the service. Unexpected changes, due to air traffic delays, severe weather conditions, or equipment failures, may disrupt the initial assignments and compound the difficulty of maintaining smooth station operations. Recently, mathematical models and procedures (optimal and heuristic) have been proposed to provide solutions with minimum dispersion of idle time periods for static aircraft-gate assignment problems. This paper introduces a unified framework to specifically treat the objective functions of the previous models. It also provides linear representations of these models and identifies the conditions under which the optimal solutions can be obtained in polynomial time. Furthermore, a genetic algorithm utilizing problem specific knowledge is proposed to provide effective alternative solutions.
83 citations
01 Jan 1998
TL;DR: Experimental results show how the proposed method can be a viable solution for node assignment in a VLIW compiler for clustered machines and the low computational complexity of this approach is shown.
Abstract: This report proposes a new heuristic/model driven approach to assign nodes of a computational DAG to clusters for a VLIW machine with a partitioned register file. Our approach exploits a heuristically found initial clustering to speed up the convergence of a deterministic descent algorithm. The initial configuration is determined through a longest path driven strategy that collects a number of paths or sub-dags starting from the DAG's leaves. The initial node assignment problem is then simplified to the assignment of these partial components to one of the k clusters. We approach the component assignment problem in two different ways depending upon some heuristically detected DAG symmetries. The descent algorithm starts from the initial configuration and modifies the assignment for each partial component by minimizing a cost function being an estimate of the schedule length for all nodes in the DAG on a given machine. The estimate is carried out by a simplified list scheduler taking quantitatively into account things like register pressure, resources allocation, etc. We compared our approach with a common heuristic known as BUG (Bottom Up Greedy) on a set of scientific and multimedia-like computational kernels. Experimental results show a reduction from 5 to 50% in the static schedule length depending from the DAG's complexity, symmetry and intrinsic parallelism and from architectural parameters like number of clusters, registers banks size, etc. Best results were obtained for large DAGs (hundreds of nodes) where the assignment of nodes to clusters is determinant to reduce the inter-cluster copies and the resource conflicts; another important factor is sometimes the reduction in register spills to/from memory due to the load balancing between clusters. These results and the low computational complexity of this approach show how the proposed method can be a viable solution for node assignment in a VLIW compiler for clustered machines.
83 citations
TL;DR: The classical linear Assignment problem is considered with two objectives; an exact method based on the two-phase approach and the so-called MOSA (Multi-Objective Simulated Annealing), which is improved by initialization with a greedy approach.
Abstract: The classical linear Assignment problem is considered with two objectives. The aim is to generate the set of efficient solutions. An exact method is first developed based on the two-phase approach. In the second phase a new upper bound is proposed so that larger instances can be solved exactly. The so-called MOSA (Multi-Objective Simulated Annealing) is then recalleds its efficiency is improved by initialization with a greedy approach. Its results are compared to those obtained with the exact method. Extensive numerical experiments have been realized to measure the performance of the MOSA method.
83 citations
TL;DR: This paper aims to develop a theoretically sound simulation-based DUE model and its solution algorithm, with particular emphasis on obtaining solutions that satisfy the DUE conditions.
Abstract: A variety of analytical and simulation-based models and algorithms have been developed for the dynamic user equilibrium (DUE) traffic assignment problem. This paper aims to develop a theoretically sound simulation-based DUE model and its solution algorithm, with particular emphasis on obtaining solutions that satisfy the DUE conditions. The DUE problem is reformulated, via a gap function, as a nonlinear minimization problem (NMP). The NMP is then solved by a column generation-based optimization procedure which embeds (i) a simulation-based dynamic network loading model to capture traffic dynamics and determine experienced path travel costs for a given path flow pattern and (ii) a path-swapping descent direction method to solve the restricted NMP defined by a subset of feasible paths. The descent direction method circumvents the need to compute the gradient of the objective function in finding search directions, or to determine suitable step sizes, which is especially valuable for large-scale simulation-based DUE applications. Computational results for both small and large real road networks confirm that the proposed formulation and solution algorithm are effective in obtaining near-optimal solutions to the DUE problem.
83 citations