Mathematical Programming: Series A and B
Quadratic Knapsack Relaxations Using Cutting Planes
Proceedings of the 5th International IPCO Conference on Integer Programming and Combinatorial Optimization
Enhanced quantum evolutionary algorithms for difficult knapsack problems
PReMI'07 Proceedings of the 2nd international conference on Pattern recognition and machine intelligence
Quantum-inspired evolutionary algorithm for a class of combinatorial optimization
IEEE Transactions on Evolutionary Computation
A simplified binary artificial fish swarm algorithm for 0-1 quadratic knapsack problems
Journal of Computational and Applied Mathematics
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The Quadratic Knapsack Problem (QKP) deals with maximizing a quadratic objective function subject to given constraints on the capacity of the Knapsack. We assume all coefficients to be non-negative and all variables to be binary. Solution to QKP generalizes the problem of finding whether a graph contains a clique of given size. We propose in this paper a Novel Quantum Evolutionary Algorithm (NQEA) for QKPs. These algorithms are general enough and can be used for similar subsection of problems. We report in this paper solutions which lie in less than 1% of the optimal solutions. We also show that our algorithm is scalable to much larger problem sizes and is capable of exploiting the search space to its maximum.