Enumeration of Dominant SolutionsAn Application in Transport Network Design

A One-Dimensional Binary Integer Programming Problem (1DB-IPP) is concerned with selectinga subset from a set of k items in budget constraint to optimize a goal function. In this problema dominant solution is defined as a feasible selection to which no further item could be added inbudget constraint. This paper presents a simple algorithm for Enumeration of Dominant Solutions(EDS) and investigates its functionality. The algorithm is then applied on the formulationof the Network Design Problem (NDP) with fixed travel-time links. The problem is a case studyof 1DB-IPPs in the transportation planning literature which arises in the networks where the linktravel-times are not sensitive to the amount of flow. The results are reported in detail for three illustrativeexamples 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 EDSalgorithm outperforms the B&B algorithm. However, the overall performance of the B&B algorithmis notably faster in higher budget levels

Keywords:

Enumeration , dominant solution , branch-and-bound algorithm , network design problem