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We propose a generalisation of the hierarchical a posteriori error estimator of Bank-Weiser to mixed formulations, in the cases of conforming and non conforming approximations, with or without numerical integration. We present as examples of application: the Dirichlet problem for the Laplace operator, in mixed dual formulation, with and without numerical integration. Résumé.On propose une généralisation de l'estimateur a posteriori hiér-archique de Bank-Weiser aux formulation mixtes, dans le cas d'approximations conformes et non conformes, avec ou sans intégration numérique. On présente comme exemples d'application: la formulation mixte duale du problème de Dirichlet pour le Laplacien, avec et sans intégration numérique.

The 0/1 Multidimensional Knapsack Problem (0/1 MKP) is an interesting NP-hard combinatorial optimization problem that can model a number of challenging applications in logistics, finance, telecommunications and other fields. In the 0/1 MKP, a set of items is given, each with a size and value, which has to be placed into a knapsack that has a certain number of dimensions having each a limited capacity. The goal is to find a subset of items leading to the maximum total profit while respecting the capacity constraints. Even though the 0/1 MKP is well studied in the literature, we can just find a little number of recent review papers on this problem. Furthermore, the existing reviews focus particularly on some specific issues. This paper aims to give a general and comprehensive survey of the considered problem so that it can be useful for both researchers and practitioners. Indeed, we first describe the 0/1 MKP and its relevant variants. Then, we present the detailed models of some important real-world applications of this problem. Moreover, an important collection of recently published heuristics and metaheuristics is categorized and briefly reviewed. These approaches are then quantitatively compared through some indicative statistics. Finally, some synthetic remarks and research directions are highlighted in the conclusion.

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