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

Authors:
Babacar Thiongane;Anass Nagih;Gérard Plateau
Affiliations:
Laboratoire d'Informatique de Paris Nord, Université de Paris, Villetaneuse, France;Laboratoire d'Informatique de Paris Nord, Université de Paris, Villetaneuse, France;Laboratoire d'Informatique de Paris Nord, Université de Paris, Villetaneuse, France
Venue:
Discrete Applied Mathematics - Special issue: International symposium on combinatorial optimization CO'02
Year:
2006

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Abstract

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.