Probabilistic Tabu search with multiple neighborhoods for the Disjunctively Constrained Knapsack Problem

A threshold search based memetic algorithm for the disjunctively constrained knapsack problem

“…From Table 3, one observes that the TSBMA algorithm competes very favorably with all the reference algorithms by reporting improved or equal results on all the instances. Compared to the probabilistic tabu search algorithm (PTS) [26] which reported results only on the first 50 instances of classes 1Iy to 10Iy, TSBMA finds 8 (45) better f best (f avg ) values, while matching the remaining results. Compared to the two parallel algorithms (PNS) [25] and (CPANS) [24] that reported only the f best values, TSBMA obtained 35 and 29 better f best results, respectively.…”

“…In 2014, Hifi [12] devised an iterative rounding search-based algorithm that uses a rounding strategy to perform a linear relaxation of the fractional variables. In 2017, Salem et al [26] designed a probabilistic tabu search algorithm (PTS) that operates with multiple neighborhoods. In the same year, Quan and Wu investigated two parallel algorithms: the parallel neighborhood search algorithm (PNS) [25] and the cooperative parallel adaptive neighborhood search algorithm (CPANS) [24].…”

“…According to the computational results reported in the literature, the parallel neighborhood search algorithm [25], the cooperative parallel adaptive neighborhood search algorithm [24], and the probabilistic tabu search algorithm [26] can be regarded as the state-of-the-art methods for the instances of Set I. For the instances of Set II, the branch-and-bound algorithms presented in [1,4] and the integer linear programming formulations solved by the CPLEX solver [4] showed the best performance.…”

“…Reference algorithms. For the 100 DCKP instances of Set I that were widely tested by heuristic algorithms, we adopt as our reference methods three stateof-the-art heuristic algorithms: parallel neighborhood search algorithm (PNS) [25], cooperative parallel adaptive neighborhood search algorithm (CPANS) [24], and probabilistic tabu search algorithm (PTS) [26]. Note that PTS only reported results of the 50 instances 1Iy to 10Iy, since the other 50 instances of 11Iy to 20Iy were designed later.…”

“…A Computational results on the 100 DCKP instances of Set I Tables A. 1 and A.2 report the detailed computational results of the TSBMA algorithm and the reference algorithms (PNS [25], CPANS [24] and PTS [26]) on the 100 DCKP instances of Set I.…”