# 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
The political optimizer (PO) of Ref. [120] obtained a slightly better solution than the standard GWO (the 2 nd worst solution overall) weighing 11,557.384 kg vs. 11,558.650 kg within about 28,000 structural analyses vs. 50,000 analyses required for the standard GWO. The present algorithm was very robust. In fact, it ranked 4 th overall in terms of standard deviation on optimized weight but it achieved a rate of success of 100% in finding slightly lighter designs than the target global optimum of 11,542.4 kg, and it never got trapped in the 11,544 kg local minimum of structural weight. Furthermore, the ratio between standard deviation of computational cost and average computational cost achieved with FHGWJA was only 12.8%. The \(W(\overset{\rightarrow}{X_{i,tr}})\leq 1.1W(\overset{\rightarrow}{X_{best}})\) elitist strategy of FHGWJA was again effective in improving the performance of the AHS/BBBC-UBS/sinDE algorithms of Refs. [94; 95; 96], which were reported in [81] to obtain optimized structural weights of 11,542.410 kg (yet with 0.9998% violation on stress constraints), 11,542.410 kg (yet with 1.076% constraint violation), and 11,555.006 kg (yet with 0.806% constraint violation), respectively. The modified mAHS, mBBBC-UBS, and MsinDE variants now converged to the fully feasible design listed in Table 9 for hybrid HS/BBBC/SA weighing 11,542.409 kg. The computational cost of mAHS, mBBBC-UBS, and MsinDE decreased on average by about 30% with respect to the original algorithms, yet remaining about 3.5- to 8.5-times higher than its counterpart for FHGWJA. These results are not reported in Table 9 for the sake of brevity. Figure 16 compares the optimization histories of the best runs for the algorithms listed in Table 9; the average FHGWJA convergence curve also is shown in the figure. The plot is limited to the first 8000 structural analyses of the optimization history and to the 11,000-31,000 kg structural weight interval for the sake of clarity. FHGWJA started its best optimization run from the very large cost of 208,700.225 kg (i.e., about 18.1 times the target optimum of 11,541.380 kg quoted in Table 9) while the initial cost for all other optimizers ranged between 157,234.459 and 185,304.986 kg, except for the ECM (eigenvectors of covariance matrix) [110] and CNNT-PSO (cyclic neighborhood network topology particle swarm optimizer) [113] algorithms that started from 20,437.901 and 11,754.998 kg, respectively. However, the present algorithm immediately recovered the initial gap in cost function with respect to its competitors: for example, within only 210 and 1330 structural analyses for ECM and CNNT-PSO, respectively. The best and average optimization runs' convergence  
curves for FHGWJA again lie below those of all other algorithms practically over the whole search history. The hybrid harmony search and big bang-big crunch algorithms of Ref. [81] were competitive enough with FHGWJA approaching the best optimization run of the present algorithm after about 2000 and 1400 structural analyses, respectively, that is towards the end of their optimization histories. However, while hybrid HS/BBBC stopped to improve design after reaching their best structural weight of 11,542.409 kg, the present algorithm continued to reduce structural weight to 11,541.380 kg. The best and average optimization runs' convergence curves of FHGWJA practically coincided after about 1750 structural analyses, that is at only 50.5% of the best run's optimization history. The data presented in this section confirmed the tendency of metaheuristic optimizers to prematurely converge to sub-optimal designs in the 200-bar truss weight minimization problem. However, FHGWJA emerged once again as the best algorithm in view of its inherent ability to generate high-quality trial solutions throughout the optimization process. Remarkably, the present algorithm was superior to high-performance optimizers such as ECM and LSHADE-Epsin that are competitive even with CEC (IEEE Congress on Evolutionary Computing) competition winners.