Hierarchical Guided Enhanced Multi-objective Firefly Algorithm

doi:10.16182/j.issn1004731x.joss.22-1486

Abstract

Abstract:

The multi-objective firefly algorithm is easy to produce oscillation and aggregation phenomenon in the solution process, which leads to weak development ability and poor solution accuracy. This paper proposes a hierarchical guided enhanced multi-objective firefly algorithm (HGEMOFA). HGEMOFA builds a hierarchical guidance model, uses non-dominated sorting to obtain different levels of individuals. The individuals in the dominant layer are used to guide the evolution of the individuals in the inferior layer, the guidance direction is clear, the oscillation in the evolution process is solved, the aggregation phenomenon is reduced, and the convergence of the algorithm is enhanced. The Lévy flight is introduced to disturb the optimal layer individuals to enhance the global search ability of the algorithm; After each generation of evolution, the mutation mechanism is adopted for the current population to enhance the local development ability of the algorithm; The mutated population is combined with the previous generation population for environmental selection to screen out offspring with the same population size as the previous generation to avoid loss of dominance solution. The experimental results show that HGEMOFA can effectively enhance the convergence and diversity of solutions.

Key words: multi-objective optimization, firefly algorithm, hierarchical guidance, Lévy flight, mutation

CLC Number:

TP391.9

Zhao Jia, Lai Zhizhen, Wu Runxiu, Cui Zhihua, Wang Hui. Hierarchical Guided Enhanced Multi-objective Firefly Algorithm[J]. Journal of System Simulation, 2024, 36(5): 1152-1164.

Figures/Tables 12

Fig. 1

Table 1

Set of test functions

问题	目标数	约束	问题特征
ZDT1	2	$n = 30$	凸型
ZDT2	2	$n = 30$	凹型
ZDT3	2	$n = 30$	非连续型
ZDT6	2	$n = 10$	凹型+多模态+有偏
DTLZ1	3	$n = 7$	线性+多模态
DTLZ2	3	$n = 12$	凹型
DTLZ4	3	$n = 12$	凹型+有偏
DTLZ6	3	$n = 12$	凹型+退化+有偏
DTLZ7	3	$n = 12$	不连续+混合+多模态

Table 1

Table 2

Table 3

Table 4

Table 5

Table 6

Fig. 2

Table 7

Table 8

Table 9

Table 10

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算法	GD	SP	IGD
HGEMOFA	1.44	1.44	1.22
MOPSO	5.67	4.33	5.67
MOEA/D	2.89	3.89	3.56
NSGAII	2.56	3.00	2.56
PESAII	3.33	4.44	3.11
MOFA	5.11	3.89	4.89

算法	ZDT1	ZDT2	ZDT3	ZDT6	DTLZ1	DTLZ2	DTLZ4	DTLZ6	DTLZ7
HGEMOFA	3.82e-03	3.87e-03	5.24e-03	3.10e-03	1.62e-02	3.67e-02	3.96e-02	2.04e-03	3.95e-02
CMOPSO	4.21e-03	4.12e-03	4.64e-03	3.10e-03	7.57e-01	3.97e-02	4.12e-02	2.09e-03	5.23e-02
NMPSO	2.79e-02	1.92e-02	1.01e-01	4.41e-03	1.69e-02	5.67e-02	1.06e-01	1.29e-02	4.58e-02
NSLS	2.43e-01	4.49e-01	2.17e-01	5.89e-03	1.54e-01	3.79e-02	1.48e-01	2.19e-03	8.58e-02
CFMOFA	8.79e-03	1.31e-02	1.45e-02	9.77e-02	1.56e+02	6.01e-02	9.10e-02	5.65e-01	5.59e-02
RVEAiGNG	4.07e-03	4.14e-03	7.80e-03	3.28e-03	1.44e-02	4.00e-02	3.97e-02	2.32e-03	5.00e-02
MMOPSO	4.91e-03	5.03e-03	5.41e-03	4.29e-03	2.82e-02	4.93e-02	4.88e-02	3.37e-03	9.42e-02
SMPSO	4.95e-03	4.96e-03	5.37e-03	3.86e-03	1.27e+00	4.86e-02	2.54e-01	2.64e-03	8.82e-02
NSGAIISDR	6.92e-03	5.23e-03	1.38e-02	4.40e-03	1.84e-02	4.35e-01	3.87e-01	3.40e-02	5.97e-02
MOPSOCD	4.00e-03	4.11e-03	4.75e-03	3.39e-03	1.19e+01	4.83e-02	1.18e-01	2.63e-03	5.73e-02
dMOPSO	1.52e-02	1.33e-01	1.66e-02	3.22e-03	1.45e+00	9.03e-02	2.39e-01	2.25e-02	1.00e-01
MOEAPSL	4.62e-03	4.75e-03	6.27e-03	3.62e-03	1.97e-02	5.04e-02	4.91e-02	2.66e-03	5.43e-02

平均排名	算法	秩平均值
1	HGEMOFA	1.33
2	CMOPSO	3.33
3	RVEAiGNG	3.56
4	MOPSOCD	5.22
5	MOEAPSL	5.78
6	MMOPSO	6.89
7	SMPSO	7.33
8	NMPSO	8.00
9	NSLS	8.56
10	NSGAIISDR	8.89
11	CFMOFA	9.44
12	dMOPSO	9.67

问题	MOFA	MOFA+S1	MOFA+S2	MOFA+S1+S2	MOFA+S2+S3	HGEMOFA
ZDT1	3.70e-02	7.36e-03	6.08e-03	5.98e-03	4.19e-03	3.82e-03
ZDT2	4.62e-02	7.47e-03	6.35e-03	6.11e-03	4.19e-03	3.86e-03
ZDT3	1.87e-02	1.14e-02	7.12e-03	7.07e-03	5.89e-03	5.24e-03
ZDT6	1.56e+0	6.80e-03	5.93e-03	5.79e-03	3.47e-03	3.09e-03
DTLZ1	5.21e-02	2.47e-01	3.31e-02	2.64e-02	2.05e-02	1.62e-02
DTLZ2	1.30e-01	5.19e-02	5.11e-02	5.08e-02	4.10e-02	3.67e-02
DTLZ4	1.32e-01	6.30e-02	4.94e-02	4.86e-02	4.22e-02	3.95e-02
DTLZ6	3.13e+00	3.92e-03	3.27e-03	3.34e-03	2.35e-03	2.04e-03
DTLZ7	8.45e-02	5.92e-02	5.37e-02	5.33e-02	4.22e-02	3.94e-02

平均排名	算法	秩平均值
1	HEGMOFA	1.00
2	MOFA+S2+S3	2.00
3	MOFA+S1+S2	3.11
4	MOFA+S2	3.89
5	MOFA+S1	5.11
6	MOFA	5.89