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. 2024 Apr 10;14(1):8357.
doi: 10.1038/s41598-024-59034-2.

A hybrid particle swarm optimization algorithm for solving engineering problem

Jinwei Qiao  1   2 , Guangyuan Wang  1   2 , Zhi Yang  3   4 , Xiaochuan Luo  5 , Jun Chen  1   2 , Kan Li  6 , Pengbo Liu  1   2
Affiliations

A hybrid particle swarm optimization algorithm for solving engineering problem

Jinwei Qiao et al. Sci Rep. .

Erratum in

Abstract

To overcome the disadvantages of premature convergence and easy trapping into local optimum solutions, this paper proposes an improved particle swarm optimization algorithm (named NDWPSO algorithm) based on multiple hybrid strategies. Firstly, the elite opposition-based learning method is utilized to initialize the particle position matrix. Secondly, the dynamic inertial weight parameters are given to improve the global search speed in the early iterative phase. Thirdly, a new local optimal jump-out strategy is proposed to overcome the "premature" problem. Finally, the algorithm applies the spiral shrinkage search strategy from the whale optimization algorithm (WOA) and the Differential Evolution (DE) mutation strategy in the later iteration to accelerate the convergence speed. The NDWPSO is further compared with other 8 well-known nature-inspired algorithms (3 PSO variants and 5 other intelligent algorithms) on 23 benchmark test functions and three practical engineering problems. Simulation results prove that the NDWPSO algorithm obtains better results for all 49 sets of data than the other 3 PSO variants. Compared with 5 other intelligent algorithms, the NDWPSO obtains 69.2%, 84.6%, and 84.6% of the best results for the benchmark function ( f 1 - f 13 ) with 3 kinds of dimensional spaces (Dim = 30,50,100) and 80% of the best optimal solutions for 10 fixed-multimodal benchmark functions. Also, the best design solutions are obtained by NDWPSO for all 3 classical practical engineering problems.

Keywords: Convergence analysis; Elite opposition-based learning; Iterative mapping; Particle swarm optimization.

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Conflict of interest statement

The authors declare no competing interests.

Figures

Figure 1
Figure 1
Spiral updating position.
Algorithm 1
Algorithm 1
The main procedure of NDWPSO.
Algorithm 1
Algorithm 1
The main procedure of NDWPSO.
Figure 2
Figure 2
The inertial weight distribution of CDWPSO, SDWPSO, and NDWPSO.
Figure 3
Figure 3
Evolution curve of NDWPSO and other PSO algorithms for f1 (Dim = 30,50,100).
Figure 4
Figure 4
Evolution curve of NDWPSO and other PSO algorithms for f2 (Dim = 30,50,100).
Figure 5
Figure 5
Evolution curve of NDWPSO and other PSO algorithms for f3 (Dim = 30,50,100).
Figure 6
Figure 6
Evolution curve of NDWPSO and other PSO algorithms for f4 (Dim = 30,50,100).
Figure 7
Figure 7
Evolution curve of NDWPSO and other PSO algorithms for f5 (Dim = 30,50,100).
Figure 8
Figure 8
Evolution curve of NDWPSO and other PSO algorithms for f6 (Dim = 30,50,100).
Figure 9
Figure 9
Evolution curve of NDWPSO and other PSO algorithms for f7 (Dim = 30,50,100).
Figure 10
Figure 10
Evolution curve of NDWPSO and other PSO algorithms for f8 (Dim = 30,50,100).
Figure 11
Figure 11
Evolution curve of NDWPSO and other PSO algorithms for f9 (Dim = 30,50,100).
Figure 12
Figure 12
Evolution curve of NDWPSO and other PSO algorithms for f10 (Dim = 30,50,100).
Figure 13
Figure 13
Evolution curve of NDWPSO and other PSO algorithms for f11(Dim = 30,50,100).
Figure 14
Figure 14
Evolution curve of NDWPSO and other PSO algorithms for f12 (Dim = 30,50,100).
Figure 15
Figure 15
Evolution curve of NDWPSO and other PSO algorithms for f13 (Dim = 30,50,100).
Figure 16
Figure 16
Evolution curve of NDWPSO and other PSO algorithms for f14, f15, f16.
Figure 17
Figure 17
Evolution curve of NDWPSO and other PSO algorithms for f17, f18, f19.
Figure 18
Figure 18
Evolution curve of NDWPSO and other PSO algorithms for f20, f21, f22.
Figure 19
Figure 19
Evolution curve of NDWPSO and other PSO algorithms for f23.
Figure 20
Figure 20
Evolution curve of NDWPSO and other algorithms for f1 (Dim = 30,50,100).
Figure 21
Figure 21
Evolution curve of NDWPSO and other algorithms for f2 (Dim = 30,50,100).
Figure 22
Figure 22
Evolution curve of NDWPSO and other algorithms for f3(Dim = 30,50,100).
Figure 23
Figure 23
Evolution curve of NDWPSO and other algorithms for f4 (Dim = 30,50,100).
Figure 24
Figure 24
Evolution curve of NDWPSO and other algorithms for f5 (Dim = 30,50,100).
Figure 25
Figure 25
Evolution curve of NDWPSO and other algorithms for f6 (Dim = 30,50,100).
Figure 26
Figure 26
Evolution curve of NDWPSO and other algorithms for f7 (Dim = 30,50,100).
Figure 27
Figure 27
Evolution curve of NDWPSO and other algorithms for f8 (Dim = 30,50,100).
Figure 28
Figure 28
Evolution curve of NDWPSO and other algorithms for f9(Dim = 30,50,100).
Figure 29
Figure 29
Evolution curve of NDWPSO and other algorithms for f10 (Dim = 30,50,100).
Figure 30
Figure 30
Evolution curve of NDWPSO and other algorithms for f11 (Dim = 30,50,100).
Figure 31
Figure 31
Evolution curve of NDWPSO and other algorithms for f12 (Dim = 30,50,100).
Figure 32
Figure 32
Evolution curve of NDWPSO and other algorithms for f13 (Dim = 30,50,100).
Figure 33
Figure 33
Evolution curve of NDWPSO and other algorithms for f14, f15, f16.
Figure 34
Figure 34
Evolution curve of NDWPSO and other algorithms for f17, f18, f19.
Figure 35
Figure 35
Evolution curve of NDWPSO and other algorithms for f20, f21, f22.
Figure 36
Figure 36
Evolution curve of NDWPSO and other algorithms for f23.
Figure 37
Figure 37
Welded beam design.
Figure 38
Figure 38
Pressure vessel design.
Figure 39
Figure 39
Three-bar truss design.
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