Heuristics and exact methods for number partitioning

Pedroso, João Pedro; Kubo, Mikio

doi:10.1016/j.ejor.2009.04.027

Cited by 18 publications

(11 citation statements)

References 21 publications

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“…The number partitioning problem (NPP) is a combinatorial optimization problem that finds a partition that divides a set of positive integers into two sets while minimizing the difference between the element sums of each set [9][10][11]. This can be defined as follows.…”

Section: Appendixmentioning

confidence: 99%

Method for efficiently orthogonalizing the eigenvectors of the Laplacian matrix to estimate social network structure

Hirakura

Takano

Aida

2020

NOLTA

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The structure of social networks or human relationships is difficult to understand since we cannot observed their links and link weights directly. The network resonance method was proposed to obtain information on the unknown Laplacian matrix representing the social network structure. This method extracts information on the eigenvalues and eigenvectors of the Laplacian matrix by observing user dynamics on social networks. The original Laplacian matrix can be reconstructed if all eigenvalues and eigenvectors are known. However, the network resonance method has a problem: the information available about eigenvectors is limited to the absolute value of each element. Therefore, to determine the Laplacian matrix, it is necessary to determine the signs of each element of all eigenvectors. However, sign determination incurs the computation cost of the order of O(2 n) for each of n eigenvectors. This paper proposes a method to determine the signs of each eigenvector element efficiently. The main idea of the method is to generate n 2 − n different sign determination problems for n eigenvectors and to solve them in parallel. All that is required is to obtain n different eigenvectors determined in the shortest time from the n 2 − n different sign determination problems. Since the ratio of the number of sign determinations completed in the method is 1/(n − 1), its efficiency rises with the number of network users. In addition, simulations on networks generated by the BA model show that proposed method offers sign determination in polynomial time.

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Section: Appendixmentioning

confidence: 99%

Method for efficiently orthogonalizing the eigenvectors of the Laplacian matrix to estimate social network structure

Hirakura

Takano

Aida

2020

NOLTA

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“…When α = 1/ i∈S l i then the criterion ensures that among the solutions with the same channel payload, the one with a lower gateway throughput is chosen. The well known two-partition optimization problem [18] (deciding whether a multiset of positive integers can be partitioned into two subsets such that the sum of the numbers in both subsets is the same) can be reduced to the ECU-tochannel assignment subproblem in polynomial time as follows: Each item from the multiset of the positive integers is modeled by one ECU connected to a self-loop. The weight of loop w e is equal to the value of the item.…”

Section: A Ecu-to-channel Assignmentmentioning

confidence: 99%

“…Then the two-partition problem can be solved by an algorithm designed for the ECUto-channel assignment. Thus, the ECU-to-channel assignment must be at least NP-Hard because the two-partition optimization problem belongs to the NP-Hard [18] class. 1) ILP model of the ECU-to-channel assignment: The exact solution can be obtained by ILP formulation.…”

Section: A Ecu-to-channel Assignmentmentioning

confidence: 99%

Using Two Independent Channels With Gateway for FlexRay Static Segment Scheduling

Dvořák¹,

Hanzálek²

2016

IEEE Trans. Ind. Inf.

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The FlexRay bus is a communication standard used in the automotive industry. It offers a deterministic message transmission in the static segment following a time-triggered schedule. Even if its bandwidth is ten times higher than the bandwidth of CAN, its throughput limits are going to be reached in high-class car models soon. A solution that could postpone this problem is to use an efficient scheduling algorithm that exploits both channels of the FlexRay. The significant and often neglected feature that can theoretically double the bandwidth is the possibility to use two independent communication channels that can intercommunicate through the gateway.In this paper, we propose a heuristic algorithm that decomposes the scheduling problem to the ECU-to-channel assignment subproblem which decides which channel the ECUs (Electronic Control Units) should be connected to and the channel scheduling subproblem which creates static segment communication schedules for both channels. The algorithm is able to create a schedule for cases where channels are configured in the independent mode as well as in the fault-tolerant mode or in cases where just part of the signals are fault-tolerant. Finally, the algorithm is evaluated on real data and synthesized data, and the relation between the portion of fault-tolerant signals and the number of allocated slots is presented.

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“…In this way, the procedures can be stopped if this solution is satisfactory. A branch‐and‐bound procedure can be used as an exact method, especially for solving academic problems (Sbihi, ; Artigues et al., ) or, if it is interrupted, as a heuristic (Pedroso and Kubo, ). In the latter case, the procedure is stopped when the solution is considered satisfactory, or a time limit is reached.…”

Section: Introductionmentioning

confidence: 99%

A branch‐and‐bound procedure for forest harvest scheduling problems addressing aspects of habitat availability

Neto

Constantino

Martins³

et al. 2013

Int Trans Operational Res

Self Cite

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In the literature, the most widely referred approaches regarding forest harvesting scheduling problems involving environmental concerns have typically addressed constraints on the maximum clear‐cut area. Nevertheless, the solutions arising from those approaches in general display a loss of habitat availability. Such loss endangers the survival of many wild species. This study presents a branch‐and‐bound procedure designed to find good feasible solutions, in a reasonable time, to forest harvest scheduling problems with constraints on the clear‐cut area and habitat availability. Two measures are applied for the habitat availability constraints: the area of all habitats and the connectivity between them. In each branch of the branch‐and‐bound tree, a partial solution leads to two children nodes, corresponding to the cases of harvesting or not harvesting a given stand in a given period. Pruning is based on constraint violations or unreachable objective values. Computational results are reported.

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Heuristics and exact methods for number partitioning

Cited by 18 publications

References 21 publications

Method for efficiently orthogonalizing the eigenvectors of the Laplacian matrix to estimate social network structure

Method for efficiently orthogonalizing the eigenvectors of the Laplacian matrix to estimate social network structure

Using Two Independent Channels With Gateway for FlexRay Static Segment Scheduling

A branch‐and‐bound procedure for forest harvest scheduling problems addressing aspects of habitat availability

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