Journal of Jilin University(Engineering and Technology Edition) ›› 2026, Vol. 56 ›› Issue (8): 2210-2218.doi: 10.13229/j.cnki.jdxbgxb.20250006

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Multi-modal multi-objective optimization algorithm based on density clustering

Li-li WANG1(),Hai-yang ZHANG1,Xin-cheng GAO1,2   

  1. 1.School of Computer and Information Technology，Northeast Petroleum University，Daqing 163318，China
    2.Center for Modern Educational Technology，Northeast Petroleum University，Daqing 163318，China
  • Received:2025-01-03 Online:2026-08-01 Published:2026-09-02

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Abstract:

In order to solve the problems of unequal distribution and convergence of the equivalent solutions obtained by the multi-modal multi-objective optimization algorithm， a multi-modal multi-objective optimization algorithm based on density clustering （MMO_DBSCAN_BWO） is proposed. Firstly， the chaotic mapping initializes the population， makes the individuals evenly distributed in the decision space， and enhances its global search ability. Secondly， density clustering algorithm is used to generate niches based on non-dominated solution sets of different levels， identify stray individuals， and propose hierarchical evolutionary strategies and hierarchical ring topological evolutionary strategies to enhance search ability. Then， the archival mechanism is introduced to preserve the optimal solution of individual history. Finally， the optimal Pareto solution with uniform distribution is selected based on special congestion distance non-dominated sorting and Euclidean distance truncation mechanism. The overall performance of MMO_DBSCAN_BWO is better than that of the comparison algorithm by testing on the 2020 CEC multimodal multiobjective test function and comparing with the three algorithms. At the same time， the algorithm is applied to the hyperparameter optimization problem of JavaScript malicious code detection graph model， and the accuracy of the model is further improved， reaching 99.3%， which proves the effectiveness of the algorithm.

Key words: multimodal multi-objective optimization, beluga optimization, density clustering, graph neural networks

CLC Number: 

  • TP18

Fig.1

Example diagram of a microhabitat"

Fig.2

Flowchart of the evolution of the microhabitat"

Fig.3

Evolutionary map within the lesser born realm"

Fig.4

MMO_DBSCAN_BWO algorithm flowchart"

Table 1

Test function characterization"

函数名称维度目标数等价解数
MMF1222
MMF2222
MMF4224
MMF5224
MMF7222
MMF8224

Table 2

Comparison results of the MMO_DBSCAN_BWO algorithm with the other 3 algorithms for average IGDX metrics"

测试函数DN_NSGAIIMO_Ring_PSO_SCDSS_MOPSOMMO_DBSCAN_BWO
MMF10.024 60.025 90.022 90.014 4
MMF20.022 80.025 20.010 10.005 4
MMF40.037 40.014 30.012 70.011 5
MMF50.067 10.052 90.042 50.039 5
MMF70.010 40.015 90.016 10.011 6
MMF80.054 60.037 10.028 10.024 8

Table 3

Comparison results of the MMO_DBSCAN_BWO algorithm with the other 3 algorithms in terms of average PSP metrics"

测试函数DN_NSGAIIMO_Ring_PSO_SCDSS_MOPSOMMO_DBSCAN_BWO
MMF142.681 538.444 943.675 969.079 9
MMF261.526 236.718 2127.289 4180.894 4
MMF438.424 869.349 178.654 786.856 5
MMF514.575 918.819 023.432 225.205 8
MMF795.785 862.716 461.583 785.936 6
MMF818.009 026.915 535.536 339.660 5

Fig.5

Hierarchical heterogeneous graph attention network model"

Fig. 6

Algorithm and model combination overall framework structure diagram"

Fig.7

JS code preprocessing flowchart"

Table 4

Model hyperparameter comparison results"

模型超参数未融入优化算法异构图模型融入优化算法异构图模型
Word2Vec编码方式CBOWCBOW
特征向量维度200150
窗口大小57
隐藏神经元个数6458
注意力头数86

Table 5

Comparative results of evaluation indicators"

评价指标未融入优化算法异构图模型融入优化算法异构图模型
准确率/%99.299.3
精确率/%98.998.6
召回率/%99.699.9
F1分数/%99.299.3
AUC0.992 40.994 3
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