# Polynomially searchable exponential neighbourhoods for sequencing problems in combinatorial optimisation

Congram, Richard K.
(2000)
Polynomially searchable exponential neighbourhoods for sequencing problems in combinatorial optimisation.
*
University of Southampton, Department of Mathematics,
Doctoral Thesis
*, 225pp.

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## Description/Abstract

In this thesis, we study neighbourhoods of exponential size that can be searched

in polynomial time. Such neighbourhoods are used in local search algorithms for

classes of combinatorial optimisation problems. We introduce a method, called

dynasearch, of constructing new neighbourhoods, and of viewing some previously

derived exponentially sized neighbourhoods which are searchable in polynomial time.

We produce new neighbourhoods by combining simple well-known neighbourhood

moves (such as swap, insert, and k-opt) so that the moves can be performed together

as a single move.

In dynasearch neighbourhoods, the moves are combined in such a way that the

effect of the combined move on the objective function is equal to the sum of the

effects of the individual moves from the underlying neighbourhood. Dynasearch

neighbourhoods can be formed using dynamic programing from underlying moves:

• nested within each other;

• disjoint from each other;

• and in the case of the TSP overlapping one another.

Our dynasearch neighbourhoods made from underlying disjoint moves are successfully

implemented within well-known local search methods to form competitive

algorithms for the travelling salesman problem and state-of-the-art algorithms for

the total weighted tardiness problem and linear ordering problem.

By viewing moves from some known travelling salesman problem neighbourhoods

as a combination of underlying moves, each reversing a section of the tour, greater

insight into the structure of the neighbourhoods may be obtained. This insight has

both enabled us to calculate the size of a number of neighbourhoods and demonstrate

how some neighbourhoods are contained within others.

Item Type: | Thesis (Doctoral) |
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Subjects: | H Social Sciences > HB Economic Theory Q Science > QA Mathematics > QA76 Computer software |

Divisions: | University Structure - Pre August 2011 > School of Mathematics |

ePrint ID: | 50630 |

Date Deposited: | 06 Apr 2008 |

Last Modified: | 27 Mar 2014 18:33 |

URI: | http://eprints.soton.ac.uk/id/eprint/50630 |

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