A BSSS algorithm for the single facility location problem in two regions with different norms

Continuous location under the effect of ‘refraction’

“…The goal of this block of data is to compare the quality of solutions obtained by the different methods. Comparing with our method, we point out that our solutions are superior since we always obtain better objective values than those in [17] or [21]. These results are not surprising since both [17] and [21] apply approximate methods whereas our algorithm is exact.…”

“…Comparing with our method, we point out that our solutions are superior since we always obtain better objective values than those in [17] or [21]. These results are not surprising since both [17] and [21] apply approximate methods whereas our algorithm is exact. Furthermore, the approach in [21] is much more computationally costly than ours.…”

“…Our computational experiments have been organized in three blocks because the goal is different in each one of them. First, we report on the data sets already considered in Parlar [17] and Zaferanieh et al [21]. These data are sets of 4, 18 (in [17]), 30 and 50 (in [21]) demand points in the plane and separating hyperplanes y = 0.5x, y = x, y = 1.5x.…”

“…The results of the first block are included in tables 1 and 2. Table 1 shows in columns CPUTime ( [17,21]), f * ( [17,21]) and x * ( [17,21]) the results reported in [17] (for the 4 and 18 points data sets) and [21] (for the 30 and 50 points data sets), and in columns CPUTime(P), f * (P) and x * (P) the results obtained with our approach. In this table N is the number of demand points, H is the equation of the separating hyperplane (line), CPUTime is the CPU-time and f * and x * are the objective value and coordinates of the optimal solution reported with the corresponding approach, respectively.…”

“…We report results for different instances. We begin comparing our approach for the first model, with those presented (in dimension 2 and for ℓ 1 -and ℓ 2 -norms) in [17] and [21] by using the data sets given there; then we test our methodology using the 50-points data set in [11] (for dimension 2 and different combinations of ℓ p -norms, both for the first and the second model); and finally we run a randomly generated set of larger instances (5000, 10000 and 50000 demand points) for different dimension (2, 3 and 5) and different combinations of ℓ p -norms. The paper ends, in Section 6, with some conclusions and an outlook for further research.…”