### Abstract

The Multidimensional Assignment Problem (MAP) is a combinatorial optimization problem that arises in many important practical areas including capital investment, dynamic facility location, elementary particle path reconstruction, multiple target tracking and sensor fusion. Since the solution space of the MAP increases exponentially with the problem parameters, and the problem has exponentially many local minima, only moderate-sized instances can be solved to optimality. We investigate the combinatorial structure of the solution space by extending a concept of Hamming distance. The results of numerical experiments indicate a linear trend for average Hamming distance to optimal solution for the cases where one of the parameters is fixed.

Original language | English (US) |
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Title of host publication | Advances in Cooperative Control and Optimization |

Subtitle of host publication | Proceedings of the 7th International Conference on Cooperative Control and Optimization |

Editors | Michael J. Hirsch, Panos M. Pardalos, Robert Murphey, Don Grundel |

Pages | 339-352 |

Number of pages | 14 |

DOIs | |

State | Published - Oct 31 2007 |

Externally published | Yes |

### Publication series

Name | Lecture Notes in Control and Information Sciences |
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Volume | 369 |

ISSN (Print) | 0170-8643 |

### Fingerprint

### ASJC Scopus subject areas

- Library and Information Sciences

### Cite this

*Advances in Cooperative Control and Optimization: Proceedings of the 7th International Conference on Cooperative Control and Optimization*(pp. 339-352). (Lecture Notes in Control and Information Sciences; Vol. 369). https://doi.org/10.1007/978-3-540-74356-9_21

**Characteristics of the distribution of hamming distance values between multidimensional assignment problem solutions.** / Kammerdiner, Alla R.; Krokhmal, Pavlo A.; Pardalos, Panos M.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Advances in Cooperative Control and Optimization: Proceedings of the 7th International Conference on Cooperative Control and Optimization.*Lecture Notes in Control and Information Sciences, vol. 369, pp. 339-352. https://doi.org/10.1007/978-3-540-74356-9_21

}

TY - CHAP

T1 - Characteristics of the distribution of hamming distance values between multidimensional assignment problem solutions

AU - Kammerdiner, Alla R.

AU - Krokhmal, Pavlo A.

AU - Pardalos, Panos M.

PY - 2007/10/31

Y1 - 2007/10/31

N2 - The Multidimensional Assignment Problem (MAP) is a combinatorial optimization problem that arises in many important practical areas including capital investment, dynamic facility location, elementary particle path reconstruction, multiple target tracking and sensor fusion. Since the solution space of the MAP increases exponentially with the problem parameters, and the problem has exponentially many local minima, only moderate-sized instances can be solved to optimality. We investigate the combinatorial structure of the solution space by extending a concept of Hamming distance. The results of numerical experiments indicate a linear trend for average Hamming distance to optimal solution for the cases where one of the parameters is fixed.

AB - The Multidimensional Assignment Problem (MAP) is a combinatorial optimization problem that arises in many important practical areas including capital investment, dynamic facility location, elementary particle path reconstruction, multiple target tracking and sensor fusion. Since the solution space of the MAP increases exponentially with the problem parameters, and the problem has exponentially many local minima, only moderate-sized instances can be solved to optimality. We investigate the combinatorial structure of the solution space by extending a concept of Hamming distance. The results of numerical experiments indicate a linear trend for average Hamming distance to optimal solution for the cases where one of the parameters is fixed.

UR - http://www.scopus.com/inward/record.url?scp=35548976196&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35548976196&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-74356-9_21

DO - 10.1007/978-3-540-74356-9_21

M3 - Chapter

AN - SCOPUS:35548976196

SN - 3540743545

SN - 9783540743545

T3 - Lecture Notes in Control and Information Sciences

SP - 339

EP - 352

BT - Advances in Cooperative Control and Optimization

A2 - Hirsch, Michael J.

A2 - Pardalos, Panos M.

A2 - Murphey, Robert

A2 - Grundel, Don

ER -