Abstract
In this paper, a new probability mechanism based particle swarm optimization (PMPSO) algorithm is proposed to solve combinatorial optimization problems. Based on the idea of traditional PSO, the algorithm generates new particles based on the optimal particles in the population and the historical optimal particles in the individual changes. In our algorithm, new particles are generated by a specially designed probability selection mechanism. We adjust the probability of each child element in the new particle generation based on the difference between the best particles and the elements of each particle. To this end, we redefine the speed, position, and arithmetic symbols in the PMPSO algorithm. To test the performance of PMPSO, we used PMPSO to solve resource-constrained project scheduling problems. Experimental results validated the efficacy of the algorithm.
Highlights
Particle Swarm Optimization (PSO) is an evolutionary computational technique proposed by Kennedy and Eberhart [1] in 1995 for continuous optimization problems
This paper proposes a probability mechanism based particle swarm optimization algorithm
The design of the algorithm includes the following features: a special decoding scheme, a mechanism for finding good subpermutations, a new particle swarm iteration formula, and a selection mechanism based on probability coefficients
Summary
Particle Swarm Optimization (PSO) is an evolutionary computational technique proposed by Kennedy and Eberhart [1] in 1995 for continuous optimization problems. The position of a particle is a (0, 1) adjacency matrix, which corresponds to a permutation combination. The selection operation must obey the rule that if an element in PXkid+1 has a larger probability coefficient value, the element with the same index in Xkid+1 has a greater probability of being selected and set to 1. Select a row according to the row number of the row of the maximum element in the probability matrix of PXkid+1. The element PXkid+1(1, 3) is set to 0 because the third situation in Step 4 In this example, the first row (0, 0.4984, 0, 0.7010, 0.0008) is selected and it is used as coefficients to randomly select a row. PXkid+1(4, 3) is set to 0, because if the corresponding element in Xkid+1 is selected to 1, the circle permutation (3, 1, 4, 3) would exist, which lead to a incompletely permutation.
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