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- Franklin Djeumou Fomeni, Adam N. Letchford
- INFORMS Journal on Computing
- 2014

It is well known that the standard (linear) knapsack problem can be solved exactly by dynamic programming in O(nc) time, where n is the number of items and c is the capacity of the knapsack. The quadratic knapsack problem, on the other hand, is NP-hard in the strong sense, which makes it unlikely that it can be solved in pseudo-polynomial time. We show… (More)

- Franklin Djeumou Fomeni, Konstantinos Kaparis, Adam N. Letchford
- Math. Program.
- 2015

The Reformulation-Linearization Technique (RLT), due to Sherali and Adams, can be used to construct hierarchies of linear programming relaxations of mixed 0-1 polynomial programs. As one moves up the hierarchy, the relaxations grow stronger, but the number of variables increases exponentially. We present a procedure that generates cutting planes at any… (More)

The Quadratic Knapsack Problem (QKP) is a much-studied combinatorial optimisation problem, with many practical applications. We present a ‘cut-and-branch’ algorithm for the QKP, in which a cuttingplane phase is followed by a branch-and-bound phase. The cuttingplane phase is much more sophisticated than existing ones in the literature, incorporating several… (More)

- Franklin Djeumou Fomeni
- Optimization Letters
- 2017

This paper considers a family of cutting planes, recently developed for mixed 0-1 polynomial programs and shows that they define facets for the maximum edge-weighted clique problem. There exists a polynomial time exact separation algorithm for these inequalities. The result of this paper may contribute to the development of more efficient algorithms for the… (More)

The objective of thispaper is to present a mathematical model that will contribute to the optimization and optimum configuration of the TBO concept. We develop a binary integer programming model whose aim is to assign a 4D-trajectory to each flight in order to optimize the efficiency of the ATM system. The modelconsiders the preferred 4D-trajectory of all… (More)

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