Multi-objective optimization plays a significant role in optimizing many real life problems, where we desire to optimize more than one objective. Numerous multi-objective optimization algorithm exists in research. NSGA-II and SPEA2 are widely used multi-objective optimization algorithms. SPEA2+ algorithm performs better than the other multi-objective optimization algorithms in terms of searching and maintaining diversity in the optimal solution. In this research, to reconstruct the gene regulatory network we have proposed a new Hybrid SPEA2+ algorithm based inference method. We have proposed a new objective function to obtain sparse gene network structure more precisely. To reverse engineer the gene regulatory network we have used linear time variant model. The proposed approach is at first tested against synthetic noise free time series datasets. It has successfully inferred all the correct regulations from noise free time series datasets. Then it was applied on synthetic noisy time series datasets. Even with the presence of noise, the proposed method have correctly captured all the correct gene regulations successfully. The proposed reconstruction method has been further validated by analyzing the real gene expression datasets of SOS DNA repair system in Escherichia coli. Our proposed method have shown its potency in finding more correct regulations and this has been confirmed by comparing the obtained gene regulations with the results of other existing researches.
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