This first work is accepted for publication in the journal Computational Optimization and Applications.We then extend the SD-based algorithm to mixed binary convex quadratic problems we embed the continuous algorithm in a branch and bound scheme that makes us able to exploit some properties of our framework. We introduce new features in the algorithms, for both the master and the pricing problems of the decomposition, and provide results for a wide set of instances, showing that our algorithm is really efficient if compared to the state-of-the-art solver Cplex. In the first part, we concentrate on SD based-methods for continuous, convex quadratic programming. Then we tackle the more general class of binary quadratically constrained, quadratic problems. In particular, we start with quadratic convex problems, both continuous and mixed binary. This method can be extended to convex non linear problems and a classic example of this, which can be seen also as a generalization of the Frank-Wolfe algorithm, is Simplicial Decomposition(SD).In this thesis we discuss decomposition algorithms for solving quadratic optimization problems. One of the most known of these techniques is Dantzig-Wolfe Decomposition: it has been developed for linear problems and it consists in solving a sequence of subproblems, called respectively master and pricing programs, which leads to the optimum. Decomposition strategies such as Column Generation have been developed in order to substitute the original problem with a sequence of more tractable ones. There are several solution methods in literature for these problems, which are, however, not always efficient in general, in particular for large scale problems. Benchmarks for ”the multiple knapsack problem”. (2016) A Case Study of Controlling Crossover in a Selection Hyper-heuristic Framework using the Multidimensional Knapsack Problem. A genetic algorithm for the multidimensional knapsack problem. These instances were previously available at. ![]() We would appreciate it if any use of these files is credited with a reference to Drake et al. ![]() #Variables (n), #Constraints (m), Optimal value (0 if unavailable), ![]() The GK dataset proposed by Glover and Kochenberger (n.d). The ORLib dataset proposed by Chu and Beasley (1998). The SAC-94 dataset, based on a variety of real-world problems. All benchmarks instances from three well known multidimensional knapsack problem (MKP) libraries are provided in a standard format here, as used in Drake et al.
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