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Split-merge: Using exponential neighborhood search for scheduling a batching machine

Split-merge: Using exponential neighborhood search for scheduling a batching machine
Split-merge: Using exponential neighborhood search for scheduling a batching machine
We address the problem of scheduling a single batching machine to minimize the maximum lateness with a constraint restricting the batch size. A solution for this NP-hard problem is defined by a selection of jobs for each batch and an ordering of those batches. As an alternative, we choose to represent a solution as a sequence of jobs. This approach is justified by our development of a dynamic program to find a schedule that minimizes the maximum lateness while preserving the underlying job order. Given this solution representation, we are able to define and evaluate various job-insert and job-swap neighborhood searches. Furthermore we introduce a new neighborhood, named split-merge, that allows multiple job inserts in a single move. The split-merge neighborhood is of exponential size, but can be searched in polynomial time by dynamic programming. Computational results with an iterated descent algorithm that employs the split-merge neighborhood show that it compares favorably with corresponding iterated descent algorithms based on the job-insert and job-swap neighborhoods.
batching machine, maximum lateness, local search, exponential neighborhoods, dynamic programming
0305-0548
125-135
Cabo, Marta
663da234-8aeb-46cb-8f27-5d2348199741
Possani, Edgar
a811956e-a248-4996-b2a1-5290148e3868
Potts, Chris N.
58c36fe5-3bcb-4320-a018-509844d4ccff
Song, Xiang
28fc03d0-9077-49f5-bc94-a4f92fa76565
Cabo, Marta
663da234-8aeb-46cb-8f27-5d2348199741
Possani, Edgar
a811956e-a248-4996-b2a1-5290148e3868
Potts, Chris N.
58c36fe5-3bcb-4320-a018-509844d4ccff
Song, Xiang
28fc03d0-9077-49f5-bc94-a4f92fa76565

Cabo, Marta, Possani, Edgar, Potts, Chris N. and Song, Xiang (2015) Split-merge: Using exponential neighborhood search for scheduling a batching machine. Computers & Operations Research, 63, 125-135. (doi:10.1016/j.cor.2015.04.017).

Record type: Article

Abstract

We address the problem of scheduling a single batching machine to minimize the maximum lateness with a constraint restricting the batch size. A solution for this NP-hard problem is defined by a selection of jobs for each batch and an ordering of those batches. As an alternative, we choose to represent a solution as a sequence of jobs. This approach is justified by our development of a dynamic program to find a schedule that minimizes the maximum lateness while preserving the underlying job order. Given this solution representation, we are able to define and evaluate various job-insert and job-swap neighborhood searches. Furthermore we introduce a new neighborhood, named split-merge, that allows multiple job inserts in a single move. The split-merge neighborhood is of exponential size, but can be searched in polynomial time by dynamic programming. Computational results with an iterated descent algorithm that employs the split-merge neighborhood show that it compares favorably with corresponding iterated descent algorithms based on the job-insert and job-swap neighborhoods.

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More information

e-pub ahead of print date: 14 May 2015
Published date: November 2015
Keywords: batching machine, maximum lateness, local search, exponential neighborhoods, dynamic programming
Organisations: Mathematical Sciences

Identifiers

Local EPrints ID: 377195
URI: https://eprints.soton.ac.uk/id/eprint/377195
ISSN: 0305-0548
PURE UUID: 982f5f21-f33a-43b0-989f-27170365d55e

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Date deposited: 27 May 2015 11:38
Last modified: 10 Dec 2019 06:38

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Contributors

Author: Marta Cabo
Author: Edgar Possani
Author: Chris N. Potts
Author: Xiang Song

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