In this paper we develop a branch-and-bound algorithm for solving a particular integer quadratic multi-knapsack problem. The problem we study is defined as the maximization of a concave separable quadratic objective function over a convex set of linear constraints and bounded integer variables. Our exact solution method is based on the computation of an upper bound and also includes pre-procedure techniques in order to reduce the problem size before starting the branch-and-bound process. We lead a numerical comparison between our method and three other existing algorithms. The approach we propose outperforms other procedures for large-scaled instances (up to 2000 variables and constraints).

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We obtain optimal lower and upper bounds for the (additive) integrality gaps of integer knapsack problems. In a randomised setting, we show that the inte-grality gap of a "typical" knapsack problem is drastically smaller than the integrality gap that occurs in a worst case scenario.

Our search deals with methods hybridizing interior point processes and metaheuristics for solving 0-1 linear programs. This paper shows how metaheuristics can take advantage of a sequence of interior points generated by an interior point method. After introducing our work field, we present our hybrid search which generates a diversified population. Next, we explain the whole method combining the solutions encountered in the previous phase through a path relinking template. Computational experiments are reported on 0-1 multiconstraint knapsack problems.

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