An immune-based response particle swarm optimizer for knapsack problems in dynamic environments

This paper proposes a novel binary particle swarm optimization algorithm (called IRBPSO) to address high-dimensional knapsack problems in dynamic environments (DKPs). The IRBPSO integrates an immune-based response strategy into the basic binary particle swarm optimization algorithm for improving the quantity of evolutional particles in high-dimensional decision space. In order to enhance the convergence speed of the IRBPSO in the current environment, the particles with high fitness values are cloned and mutated. In addition, an external archive is designed to store the elite from the current generation. To maintain the diversity of elites in the external archive, the elite of current generation will replace the worst one in the external archive if and only if it differs from any of the existing particles in the external archive based on the Hamming distance measurement when the archive is due to update. In this way, the external archive can store diversiform elites for previous environments as much as possible, and so as to the stored elites are utilized to transfer historical information to new environment for assisting to solve the new optimization problem. Moreover, the environmental reaction scheme is also investigated in order to improve the ability of adapting to different kinds of dynamic environments. Experimental results on a series of DKPs with different randomly generated data sets indicate that the IRBPSO can faster track the changing environments and manifest superior statistical performance, when compared with peer optimization algorithms.