Combinatorial optimization using electro-optical vector by matrix multiplication architecture

Dan E. Tamir; Natan T. Shaked; Wilhelmus J. Geerts; Shlomi Dolev

doi:10.1007/978-3-642-10442-8_17

Combinatorial optimization using electro-optical vector by matrix multiplication architecture

Dan E. Tamir
, Natan T. Shaked
, Wilhelmus J. Geerts
, Shlomi Dolev

Department of Electrical & Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

3 Scopus citations

Abstract

A new state space representation of a class of combinatorial optimization problems is introduced. The representation enables efficient implementation of exhaustive search for an optimal solution in bounded NP complete problems such as the traveling salesman problem (TSP) with a relatively small number of cities. Furthermore, it facilitates effective heuristic search for sub optimal solutions for problems with large number of cities. This paper surveys structures for representing solutions to the TSP and the use of these structures in iterative hill climbing (ITHC) and genetic algorithms (GA). The mapping of these structures along with respective operators to a newly proposed electro-optical vector by matrix multiplication (VMM) architecture is detailed. In addition, time space tradeoffs related to using a record keeping mechanism for storing intermediate solutions are presented and the effect of record keeping on the performance of these heuristics in the new architecture is evaluated. Results of running these algorithms on sequential architecture as well as a simulation-based estimation of the speedup obtained are supplied. The results show that the VMM architecture can speedup various variants of the TSP algorithm by a factor of 30x to 50x.

Original language	English
Title of host publication	Optical SuperComputing - Second International Workshop, OSC 2009, Proceedings
Pages	130-143
Number of pages	14
DOIs	https://doi.org/10.1007/978-3-642-10442-8_17
State	Published - 2 Dec 2009
Event	2nd International Workshop on Optical SuperComputing, OSC 2009 - Bertinoro, Italy Duration: 18 Nov 2009 → 20 Nov 2009

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	5882 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	2nd International Workshop on Optical SuperComputing, OSC 2009
Country/Territory	Italy
City	Bertinoro
Period	18/11/09 → 20/11/09

Keywords

Combinatorial Optimization
Genetic Algorithms
Heuristic Search
Hill Climbing
Optical Computing
Parallel Processing
The Traveling Salesman Problem

ASJC Scopus subject areas

Theoretical Computer Science
General Computer Science

Access to Document

10.1007/978-3-642-10442-8_17

Cite this

Tamir, D. E., Shaked, N. T., Geerts, W. J., & Dolev, S. (2009). Combinatorial optimization using electro-optical vector by matrix multiplication architecture. In Optical SuperComputing - Second International Workshop, OSC 2009, Proceedings (pp. 130-143). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5882 LNCS). https://doi.org/10.1007/978-3-642-10442-8_17

Tamir, Dan E. ; Shaked, Natan T. ; Geerts, Wilhelmus J. et al. / Combinatorial optimization using electro-optical vector by matrix multiplication architecture. Optical SuperComputing - Second International Workshop, OSC 2009, Proceedings. 2009. pp. 130-143 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

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title = "Combinatorial optimization using electro-optical vector by matrix multiplication architecture",

abstract = "A new state space representation of a class of combinatorial optimization problems is introduced. The representation enables efficient implementation of exhaustive search for an optimal solution in bounded NP complete problems such as the traveling salesman problem (TSP) with a relatively small number of cities. Furthermore, it facilitates effective heuristic search for sub optimal solutions for problems with large number of cities. This paper surveys structures for representing solutions to the TSP and the use of these structures in iterative hill climbing (ITHC) and genetic algorithms (GA). The mapping of these structures along with respective operators to a newly proposed electro-optical vector by matrix multiplication (VMM) architecture is detailed. In addition, time space tradeoffs related to using a record keeping mechanism for storing intermediate solutions are presented and the effect of record keeping on the performance of these heuristics in the new architecture is evaluated. Results of running these algorithms on sequential architecture as well as a simulation-based estimation of the speedup obtained are supplied. The results show that the VMM architecture can speedup various variants of the TSP algorithm by a factor of 30x to 50x.",

keywords = "Combinatorial Optimization, Genetic Algorithms, Heuristic Search, Hill Climbing, Optical Computing, Parallel Processing, The Traveling Salesman Problem",

author = "Tamir, \{Dan E.\} and Shaked, \{Natan T.\} and Geerts, \{Wilhelmus J.\} and Shlomi Dolev",

year = "2009",

month = dec,

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Tamir, DE, Shaked, NT, Geerts, WJ & Dolev, S 2009, Combinatorial optimization using electro-optical vector by matrix multiplication architecture. in Optical SuperComputing - Second International Workshop, OSC 2009, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 5882 LNCS, pp. 130-143, 2nd International Workshop on Optical SuperComputing, OSC 2009, Bertinoro, Italy, 18/11/09. https://doi.org/10.1007/978-3-642-10442-8_17

Combinatorial optimization using electro-optical vector by matrix multiplication architecture. / Tamir, Dan E.; Shaked, Natan T.; Geerts, Wilhelmus J. et al.
Optical SuperComputing - Second International Workshop, OSC 2009, Proceedings. 2009. p. 130-143 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 5882 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

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AU - Tamir, Dan E.

AU - Shaked, Natan T.

AU - Geerts, Wilhelmus J.

AU - Dolev, Shlomi

PY - 2009/12/2

Y1 - 2009/12/2

N2 - A new state space representation of a class of combinatorial optimization problems is introduced. The representation enables efficient implementation of exhaustive search for an optimal solution in bounded NP complete problems such as the traveling salesman problem (TSP) with a relatively small number of cities. Furthermore, it facilitates effective heuristic search for sub optimal solutions for problems with large number of cities. This paper surveys structures for representing solutions to the TSP and the use of these structures in iterative hill climbing (ITHC) and genetic algorithms (GA). The mapping of these structures along with respective operators to a newly proposed electro-optical vector by matrix multiplication (VMM) architecture is detailed. In addition, time space tradeoffs related to using a record keeping mechanism for storing intermediate solutions are presented and the effect of record keeping on the performance of these heuristics in the new architecture is evaluated. Results of running these algorithms on sequential architecture as well as a simulation-based estimation of the speedup obtained are supplied. The results show that the VMM architecture can speedup various variants of the TSP algorithm by a factor of 30x to 50x.

AB - A new state space representation of a class of combinatorial optimization problems is introduced. The representation enables efficient implementation of exhaustive search for an optimal solution in bounded NP complete problems such as the traveling salesman problem (TSP) with a relatively small number of cities. Furthermore, it facilitates effective heuristic search for sub optimal solutions for problems with large number of cities. This paper surveys structures for representing solutions to the TSP and the use of these structures in iterative hill climbing (ITHC) and genetic algorithms (GA). The mapping of these structures along with respective operators to a newly proposed electro-optical vector by matrix multiplication (VMM) architecture is detailed. In addition, time space tradeoffs related to using a record keeping mechanism for storing intermediate solutions are presented and the effect of record keeping on the performance of these heuristics in the new architecture is evaluated. Results of running these algorithms on sequential architecture as well as a simulation-based estimation of the speedup obtained are supplied. The results show that the VMM architecture can speedup various variants of the TSP algorithm by a factor of 30x to 50x.

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KW - Genetic Algorithms

KW - Heuristic Search

KW - Hill Climbing

KW - Optical Computing

KW - Parallel Processing

KW - The Traveling Salesman Problem

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SN - 9783642104411

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

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Y2 - 18 November 2009 through 20 November 2009

ER -

Tamir DE, Shaked NT, Geerts WJ, Dolev S. Combinatorial optimization using electro-optical vector by matrix multiplication architecture. In Optical SuperComputing - Second International Workshop, OSC 2009, Proceedings. 2009. p. 130-143. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-642-10442-8_17

Combinatorial optimization using electro-optical vector by matrix multiplication architecture

Abstract

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Keywords

ASJC Scopus subject areas

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