Author/Authors :
Zarrinmehr، Amirali نويسنده MSc. Graduate, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran Zarrinmehr, Amirali , Shafahi، Yousef نويسنده Professor, Department of Civil Engineering, Sharif University of Technology, Tehran, Iran Shafahi, Yousef
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 a goal 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.
