View full-text article in PMC Soft comput. 2021 May 10;27(6):3307–3326. doi: 10.1007/s00500-021-05839-6 Search in PMC Search in PubMed View in NLM Catalog Add to search Copyright and License information © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. PMC Copyright notice Table 8. Benchmark functions Function Dim Range fmin Unimodal functions TF1(x)=∑i=1nxi+∏i=1nxi 30 [-10,10] 0 TF2(x)=∑i=1n-1[100(xi+1-xi2)2+(xi-1)2] 30 [-30,30] 0 Multimodal functions TF3(x)=∑i=1n-xisin(xi) 30 [-500,500] -418.9829×Dim TF4(x)=14000∑i=1nxi2-∏i=1ncosxii+1 30 [-600,600] 0 TF5(x)=0.1{sin2(3πx1)+∑i=1n(xi-1)2[1+sin2(3πxi+1)]+(xn-1)2[1+sin2(2πxn)]}+∑i=1nu(xi,5,100,4) 30 [− 50, 50] 0 Fixed-dimension multimodal functions TF6(x)=1500+∑j=1251j+∑i=12(xi-aij)6-1 2 [− 65, 65] 1 TF7(x)=[1+(x1+x2+1)2(19-14x1+3x12-14x2+6x1x2+3x22)]×[30+(2x1-3x2)2×(18-32x1+12x12+48x2-36x1x2+27x22)] 2 [− 2, 2] 3 Composition function TF8CF1f1,f2,f3,…,f10:Sphere Functionσ1,σ2,σ3,…,σ10=1,1,1,…,1λ1,λ2,λ3,…,λ10=5/100,5/100,5/100,…,5/100 10 [− 5, 5] 0 TF9CF3f1,f2,f3,…,f10:Griewank's Functionσ1,σ2,σ3,…,σ10=1,1,1,…,1λ1,λ2,λ3,…,λ10=1,1,1,…,1 10 [− 5, 5] 0