Abstract
Score orienteering is a variant of the orienteering game where competitors start at a specified control point, visit as many control points as possible and thereby collect prizes, and return to the starting point within a prescribed amount of time. The competitor with the highest amount of prizes wins the game. In this paper, we propose the minimum directed 1-subtree problem as a new relaxation to this problem and develop two methods to improve its lower bound. We describe a cut and dual simplex method and a Lagrangian relaxation method, and construct an algorithm that combines these two methods in an appropriate way. Computational experiments are carried out to analyse the behavior of the proposed relaxation with respect to the characteristics of the test problems. Especially for large-scale instances, we find that the proposed relaxation is superior to the ordinary assignment relaxation.
| Original language | English |
|---|---|
| Pages (from-to) | 139-153 |
| Number of pages | 15 |
| Journal | European Journal of Operational Research |
| Volume | 104 |
| Issue number | 1 |
| Publication status | Published - 1998 Jan 1 |
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Keywords
- Minimum directed 1-subtree relaxation
- Orienteering problem
- Traveling salesman problem
ASJC Scopus subject areas
- Information Systems and Management
- Management Science and Operations Research
- Statistics, Probability and Uncertainty
- Applied Mathematics
- Modelling and Simulation
- Transportation
Cite this
Minimum directed 1-subtree relaxation for score orienteering problem. / Kataoka, Seiji; Yamada, Takeo; Morito, Susumu.
In: European Journal of Operational Research, Vol. 104, No. 1, 01.01.1998, p. 139-153.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Minimum directed 1-subtree relaxation for score orienteering problem
AU - Kataoka, Seiji
AU - Yamada, Takeo
AU - Morito, Susumu
PY - 1998/1/1
Y1 - 1998/1/1
N2 - Score orienteering is a variant of the orienteering game where competitors start at a specified control point, visit as many control points as possible and thereby collect prizes, and return to the starting point within a prescribed amount of time. The competitor with the highest amount of prizes wins the game. In this paper, we propose the minimum directed 1-subtree problem as a new relaxation to this problem and develop two methods to improve its lower bound. We describe a cut and dual simplex method and a Lagrangian relaxation method, and construct an algorithm that combines these two methods in an appropriate way. Computational experiments are carried out to analyse the behavior of the proposed relaxation with respect to the characteristics of the test problems. Especially for large-scale instances, we find that the proposed relaxation is superior to the ordinary assignment relaxation.
AB - Score orienteering is a variant of the orienteering game where competitors start at a specified control point, visit as many control points as possible and thereby collect prizes, and return to the starting point within a prescribed amount of time. The competitor with the highest amount of prizes wins the game. In this paper, we propose the minimum directed 1-subtree problem as a new relaxation to this problem and develop two methods to improve its lower bound. We describe a cut and dual simplex method and a Lagrangian relaxation method, and construct an algorithm that combines these two methods in an appropriate way. Computational experiments are carried out to analyse the behavior of the proposed relaxation with respect to the characteristics of the test problems. Especially for large-scale instances, we find that the proposed relaxation is superior to the ordinary assignment relaxation.
KW - Minimum directed 1-subtree relaxation
KW - Orienteering problem
KW - Traveling salesman problem
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UR - http://www.scopus.com/inward/citedby.url?scp=0031675526&partnerID=8YFLogxK
M3 - Article
VL - 104
SP - 139
EP - 153
JO - European Journal of Operational Research
JF - European Journal of Operational Research
SN - 0377-2217
IS - 1
ER -