Hybrid Optimization Algorithm of Particle Swarm Optimization with Lagrangian Relaxation for Solving the Multidimensional Knapsack Problem

Jinyan Luo,Fuquan Zhang,Lin Xu,Geng Lin

doi:10.1007/978-3-030-04585-2_30

Hybrid Optimization Algorithm of Particle Swarm Optimization with Lagrangian Relaxation for Solving the Multidimensional Knapsack Problem

Jinyan Luo, Fuquan Zhang + Show 2 more

https://doi.org/10.1007/978-3-030-04585-2_30

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Publication Date: Dec 1, 2018

Affiliation: Beijing Institute of Technology, Minjiang University, Fujian Normal University

#Multidimensional Knapsack Problem #Algorithm Of Particle Swarm Optimization + Show 8 more

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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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