@article {
author = {Zarrinmehr, Amirali and Shafahi, Yousef},
title = {Enumeration of Dominant Solutions: An Application in Transport Network Design},
journal = {International Journal of Transportation Engineering},
volume = {1},
number = {4},
pages = {335-348},
year = {2014},
publisher = {Tarrahan Parseh Transportation Research Institute},
issn = {2322-259X},
eissn = {2538-3728},
doi = {10.22119/ijte.2014.6302},
abstract = {A One-Dimensional Binary Integer Programming Problem (1DB-IPP) is concerned with selecting a subset from a set of k items in budget constraint to optimize an objective function. In this problem a dominant solution is defined as a feasible selection to which no further item could be added in budget constraint. This paper presents a simple algorithm for Enumeration of Dominant Solutions (EDS) and investigates its functionality. The algorithm is then applied on the formulation of the Network Design Problem (NDP) with fixed travel-time links. The problem is a case study of 1DB-IPPs in the transportation planning literature which arises in the networks where the link travel-times are not sensitive to the amount of flow. The results are reported in detail for three illustrative examples and compared with the results of the Branch-and-Bound (B&B) algorithm. These examples suggest that in lower budget levels up to 40.2, 40.3 and 27.1 percentages the EDS algorithm outperforms the B&B algorithm. However, the overall performance of the B&B algorithm is notably faster in higher budget levels.},
keywords = {Enumeration,Dominant Solution,Branch-and-Bound Algorithm,Network Design Problem},
url = {http://www.ijte.ir/article_6302.html},
eprint = {http://www.ijte.ir/article_6302_a76cea000fa40ae90ea0dd72afc5185a.pdf}
}