“…And it can be seen from the whisker diagram of the ordinate axis, that in the initial iterations of the optimization, convergence speed is quick, and most of the results are concentrated around the optimal solution, this phenomenon also confirms the improvement in both in the random movement factor α and the attractiveness β, namely in the initial iterations of the optimization needs larger random movement factor and enough stable attractiveness to find the optimal solution, and as the iteration goes on, the decrease of random movement factor α is beneficial to the optimization in a small range, and in this process, the attractiveness function is dynamic, which ensures the convergence speed and the diversity of the population and avoids premature convergence. Finally, from the enlarged image about the last period of the iteration, at 178th, the cost In order to further illustrate the advantages and practicability of LS-MFA, the clustering results of the other twenty-two methods of DPLR, ALR, ELR (Ongsakul and Petcharaks, 2004), LR, GA (Kazarlis et al, 1996),EP (Juste, 1999), LRGA (Cheng and Liu, 2000), GAUC (Yamashiro, 2001), DPSO (Gaing, 2004), ICGA, BCGA (Damousis et al, 2004), BF (Eslamian et al, 2009), PSO-LR (Balci and Valenzuela, 2004), SLFA (Ebrahimi et al, 2011), HPSO (Ting et al, 2006), BGOA (Shahid et al, 2021), ABC (Kokare and Tade, 2018), ABFMO (Pan et al, 2021), BCS(Reddy Surender, 2017), BDEr (Kamboj et al, 2017), BGWO (Panwar et al, 2018), BPSOGWO (Kamboj, 2016) which are shown in Table 5, meanwhile, the results are compared with the result of LS-MFA, obtaining the cost difference. Figure 8 visualizes the comparison, ranking several methods using operating costs as the primary axis (black) and cost differences (blue) as the secondary axis.…”