This study proposes an efficient exact algorithm for the precedence-constrained single-machine scheduling problem to minimize total job completion cost where machine idle time is forbidden. The proposed algorithm is b...
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This study proposes an efficient exact algorithm for the precedence-constrained single-machine scheduling problem to minimize total job completion cost where machine idle time is forbidden. The proposed algorithm is based on the SSDP (Successive Sublimation Dynamic Programming) method and is an extension of the authors' previous algorithms for the problem without precedence constraints. In this method, a lower bound is computed by solving a Lagrangian relaxation of the original problem via dynamic programming and then it is improved successively by adding constraints to the relaxation until the gap between the lower and upper bounds vanishes. Numerical experiments will show that the algorithm can solve all instances with up to 50 jobs of the precedence-constrained total weighted tardiness and total weighted earliness-tardiness problems, and most instances with 100 jobs of the former problem. (C) 2013 Elsevier B.V. All rights reserved.
Let G be an unweighted connected graph on n vertices. We show that an embedding of the shortest path metric of G into the line with minimum distortion can be found in time 5(n+0(n)). This is the first algorithm breaki...
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Let G be an unweighted connected graph on n vertices. We show that an embedding of the shortest path metric of G into the line with minimum distortion can be found in time 5(n+0(n)). This is the first algorithm breaking the trivial n!-barrier. (C) 2011 Elsevier B.V. All rights reserved.
In wireless sensor networks, maximizing the lifetime of a data gathering tree without aggregation has been proved to be NP-complete. In this paper, we prove that, unless P = NP, no polynomial-time algorithm can approx...
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In wireless sensor networks, maximizing the lifetime of a data gathering tree without aggregation has been proved to be NP-complete. In this paper, we prove that, unless P = NP, no polynomial-time algorithm can approximate the problem with a factor strictly greater than 2/3. The result even holds in the special case where all sensors have the same initial energy. Existing works for the problem focus on approximation algorithms, but these algorithms only find sub-optimal spanning trees and none of them can guarantee to find an optimal tree. We propose the first non-trivial exact algorithm to find an optimal spanning tree. Due to the NP-hardness nature of the problem, this proposed algorithm runs in exponential time in the worst case, but the consumed time is much less than enumerating all spanning trees. This is done by several techniques for speeding up the search. Featured techniques include how to grow the initial spanning tree and how to divide the problem into subproblems. The algorithm can handle small networks and be used as a benchmark for evaluating approximation algorithms.
L(2, 1)-labeling is a graph coloring model inspired by a frequency assignment in telecommunication. It asks for such a labeling of vertices with nonnegative integers that adjacent vertices get labels that differ by at...
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L(2, 1)-labeling is a graph coloring model inspired by a frequency assignment in telecommunication. It asks for such a labeling of vertices with nonnegative integers that adjacent vertices get labels that differ by at least 2 and vertices in distance 2 get different labels. It is known that for any k >= 4 it is NP-complete to determine if a graph has a L(2, 1)-labeling with no label greater than k. In this paper we present a new bound on complexity of an algorithm for finding an optimal L(2, 1)-labeling (i.e. an L(2, 1)-labeling in which the largest label is the least possible). We improve the upper complexity bound of the algorithm from O*(3.5616(n)) to O*(3.2361(n)). Moreover, we establish a lower complexity bound of the presented algorithm, which is Omega*(3.0739(n)). (C) 2011 Elsevier B.V. All rights reserved.
This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the Successive Sublimation Dynami...
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This study proposes an exact algorithm for the general single-machine scheduling problem without machine idle time to minimize the total job completion cost. Our algorithm is based on the Successive Sublimation Dynamic Programming (SSDP) method. Its major drawback is heavy memory usage to store dynamic programming states, although unnecessary states are eliminated in the course of the algorithm. To reduce both memory usage and computational efforts, several improvements to the previous algorithm based on the SSDP method are proposed. Numerical experiments show that our algorithm can optimally solve 300 jobs instances of the total weighted tardiness problem and the total weighted earliness-tardiness problem, and that it outperforms the previous algorithms specialized for these problems.
This paper addresses a vehicle routing and scheduling problem arising in Flight Ticket Sales Companies for the service of free pickup and delivery of airline passengers to the airport. The problem is formulated under ...
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This paper addresses a vehicle routing and scheduling problem arising in Flight Ticket Sales Companies for the service of free pickup and delivery of airline passengers to the airport. The problem is formulated under the framework of Vehicle Routing Problem with Time Windows (VRPTW), with the objective of minimizing the total operational costs, i.e. fixed start-up costs and variable traveling costs. A 0-1 mixed integer programming model is presented, in which service quality is factored in constraints by introducing passenger satisfaction degree functions that limit time deviations between actual and desired delivery times. The problem addressed in this paper has two distinctive characteristics-small vehicle capacities and tight delivery time windows. An exact algorithm based on the set-partitioning model, concerning both characteristics, is developed. In the first phase of the algorithm the entire candidate set of best feasible routes is generated, and then the optimal solution is obtained by solving the set-partitioning model in the second phase. Finally, we use four actual instances to illustrate application of the proposed algorithm. Moreover, the proposed algorithm is applied to a random instance containing more orders to verify the general effectiveness of the proposed algorithm even if the number of passengers increases in future.
Flows over time problems consider finding optimal dynamic flows over a network where capacities and transit times on arcs are given. In this paper we study a multicommodity flow over time problem in which no storage o...
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The discrete optimization problem associated with partitioning a set of actors into core and periphery subsets has typically been approached using approximate procedures such as exchange heuristics, genetic algorithms...
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The discrete optimization problem associated with partitioning a set of actors into core and periphery subsets has typically been approached using approximate procedures such as exchange heuristics, genetic algorithms, and simulated annealing. Although these procedures are effective and scalable for large networks, they do not guarantee an optimal bipartition. In this paper, an exact algorithm is presented for a core/periphery bipartitioning problem. Unlike the approximate procedures in the extant literature, this new algorithm, which is based on the principles of branch-and-bound programming, affords a guarantee of an optimal bipartition. Computational results for empirical and simulated data sets reveal that the proposed algorithm is extremely efficient for networks with 40 or fewer actors, and is often scalable for networks with up to 60 actors. (C) 2010 Elsevier B.V. All rights reserved.
In this paper, a study of existing exact algorithm on microwave tomography of high contrast biological model for different sets of transmitting beamwidth has been proposed. Quantitative results of reconstructed images...
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ISBN:
(纸本)9781479944453
In this paper, a study of existing exact algorithm on microwave tomography of high contrast biological model for different sets of transmitting beamwidth has been proposed. Quantitative results of reconstructed images of normal semi human sized numerical model are also presented to exhibit the range of perturbations of complex permittivity of biological tissues can be adapted by the algorithm. The aforesaid algorithm is also applied to detect the diseased portion of the numerical model. A priori information helps to detect precisely the diseased portion after its preliminary detection by the algorithm has been suggested here with the help of a percentage average error.
Intermodal goods transport is characterized by a main transport by rail, barge or seaborne vessel, preceded and followed by short in time but expensive road transport. Many times trucks pick-up or deliver a single con...
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ISBN:
(纸本)9789077381663
Intermodal goods transport is characterized by a main transport by rail, barge or seaborne vessel, preceded and followed by short in time but expensive road transport. Many times trucks pick-up or deliver a single container which leads to a full truckload vehicle routing problem in terms of economically efficient transport services. Time windows induced by the customer or due to external situations increase the complexity of an efficient planning by a logistics provider. An exact algorithm for this type of pick-up and delivery problem is developed and the details of its implementation are explained. A set partitioning problem is automatically generated and solved by means of the Lingo software.
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