# An Efficient and Fast Hybrid GWO-JAYA Algorithm for Design Optimization
## 3 Test Problems and Optimization Results
### Weight Minimization of a Planar 200-Bar Truss Structure
Furthermore, FHGWJA was compared with the classical GWO and improved GWO [119] as well as with classical and improved JAYA [81]. The political optimizer (PO) algorithm implemented in [120] also was included in the comparison as its best optimized weight was close to those of the classical GWO and standard and improved JAYA. The comparisons presented in this section should be considered highly significant because each competitor selected from Refs. [81; 110; 111; 112; 113; 114; 119; 120] was reported to outperform from 5 to 76 other state-of-the-art metaheuristic algorithms. According to the literature, population size values for this test problem were as follows: 50 for hybrid HS [81], MCOA [112], and hGMO [114]; 100 for hybrid BBBC [81]; 20 for improved JAYA [81]; 14 for ECM [110]; 1000 for CNNT-PSO [113]; 121 for PO [120]. Such a large variation in the number of search agents confirms the difficulties encountered with metaheuristic optimizers in solving the 200-bar truss problem. Interestingly, FHGWJA could use the smallest population size overall. This was the logical consequence of the inherent ability of FHGWJA to select high-quality trial solutions throughout the search process. Table 9 presents the optimization results obtained with FHGWJA and its competitors in the 200-bar truss problem. The table reports the optimized values of cross-sections (expressed in in\({}^{2}\)) and the structural weight for the best run along with the number of structural analyses; the best, average, and worst values of optimized weight along with the corresponding standard deviation (_ST Dev_) over the independent runs; and the number of structural analyses (_NSA_) required in the search process. Statistical data on computational cost (i.e., average number of structural analyses and corresponding standard deviation) are reported when available. The detailed data reported for this test problem in Refs. [115; 116; 117; 118] that present solutions violating stress limits were not replicated in Table 9 for the sake of brevity. It can be seen from Table 9 that the FHGWJA was the best optimizer also for this test case. In fact, it converged to the overall lowest structural weight of 11,541.380 kg. Furthermore, all optimization runs of FHGWJA found practically feasible designs (in fact, the maximum element stress evaluated for the optimized solutions of FHGWJA was only 10,000.412 psi vs. the 10,000 psi stress limit set for this problem) that were lighter than the target optimum weight of 11,542.4 kg. The hybrid HS/BBBC/SA algorithms of Ref. [81] were very competitive with the present algorithm because they always converged to the target optimum with at most 0.00622 kg standard deviation vs. 0.4157 kg of FHGWJA. The average computational cost of FHGWJA (i.e., 3356 structural analyses) practically coincides with the mean of average computational costs recorded for hybrid HS (i.e., 2736 analyses), hybrid BBBC (i.e., 1676 analyses), and hybrid fast SA (i.e., 5806 analyses). The other best competitors of FHGWJA, namely ECM [110], LSHADE-Epsin [111], MCOA [112], CNNT-PSO [113], and hGMO [114], obtained optimized weights ranging between 11,543.521 kg (ECM) and 11,545.568 kg (hGMO) and required between 20,000 (hGMO) and 290,000 (LSHADE-Epsin) structural analyses vs. only 3356 structural analyses required on average by the present algorithm. FHGWJA clearly outperformed its component algorithms: the best solutions of improved JAYA [81], standard JAYA, and the standard GWO, respectively, achieved optimized weights of 11,550.054 kg, 11,553.355 kg and 11,558.650 kg vs. only 11,541.380 kg of FHGWJA; furthermore, they, respectively, required 31,580, 40,941, and 50,000 structural analyses vs. only 3356 analyses of FHGWJA. The improved GWO variant (IGWO) of Ref. [119], using an exponential variation scheme for the vectors \(\overset{\rightarrow}{A_{1}}\), \(\overset{\rightarrow}{A_{2}}\), and \(\overset{\rightarrow}{A_{3}}\) of Equations (6) and (9), prematurely converged to the optimized weight of 11,689.883 kg within 23,760 structural analyses.