Abstract
A hybrid algorithm that integrates PSO with Lagrangian relaxation is proposed for solving the multidimensional knapsack problem (MKP). An efficiency measure for MKP based on the LR dual information is defined to combine the object function and the constraints of the MKP together. The efficiency measure is used to determine the core problem for MKP with the aim of reducing the problem scale. Then a hybrid algorithm combines the Quantum Particle Swarm Optimization with a local search method is presented to solve the core problem. Numerical experiments are made on certain knapsack problems and computational results show that the proposed algorithm is very promising.
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