Efficient matheuristic for the generalised multiple knapsack problem with setup

Combining local branching and descent method for solving the multiple‐choice knapsack problem with setups

“…Computational experiments showed the superiority of that method when comparing its provided results to those achieved by the method proposed in Adouani et al. (2020b) and the state‐of‐the‐art Cplex solver.…”

“…In this case, all neighborhoods build were explored before repeating the construction of new reduced integer programming problems. Computational experiments showed the superiority of that method when comparing its provided results to those achieved by the method proposed in Adouani et al (2020b) and the state-of-the-art Cplex solver.…”

“…Their experiments showed that the designed method had good behavior, especially when comparing its results to those provided by the Cplex. Further, Masmoudi et al (2022) proposed a variant of the method designed in Adouani et al (2020b) for approximately solving the multiple knapsack problem with setup. Such a method combines the VNS with both linear relaxation and dynamic programming techniques.…”

“…For other versions of the problem, like the generalized multiple knapsack with setup, Adouani et al. (2020b) proposed a two‐stage algorithm that combined VNS with integer linear programming. The first stage tries to affect classes to knapsacks and the second stage tries to preselect items from each knapsack.…”

“…(2022) proposed a variant of the method designed in Adouani et al. (2020b) for approximately solving the multiple knapsack problem with setup. Such a method combines the VNS with both linear relaxation and dynamic programming techniques.…”