Lagrangean heuristics combined with reoptimization for the 0–1 bidimensional knapsack problem

First, this paper deals with lagrangean heuristics for the 0–1 bidimensional knapsack problem. A projected subgradient algorithm is performed for solving a lagrangean dual of the problem, to improve the convergence of the classical subgradient algorithm. Secondly, a local search is introduced to improve the lower bound on the value of the biknapsack produced by lagrangean heuristics. Thirdly, a variable fixing phase is embedded in the process. Finally, the sequence of 0–1 one-dimensional knapsack instances obtained from the algorithm are solved by using reoptimization techniques in order to reduce the total computational time effort. Computational results are presented.