## 4 Experimental Simulation and Results Analysis
### Analysis of the Impact of Different Improvement Strategies on Algorithm Performance
 \\ \hline ChOA & & & \(5.3205\times 10^{20}\) & \(1.4612\times 10^{20}\) \\ CChOA & & & \(1.0185\times 10^{49}\) & \(4.4854\times 10^{49}\) \\ GChOA & F1 & \(9.0227\times 10^{259}\) & 0 \\ EChOA & & \(5.3708\times 10^{142}\) & 0 \\ MSEChOA & & 0 & 0 \\ \hline ChOA & & \(1.1672\times 10^{14}\) & \(1.4103\times 10^{14}\) \\ CChOA & & \(7.9241\times 10^{37}\) & \(2.3578\times 10^{36}\) \\ GChOA & F2 & \(1.1178\times 10^{206}\) & 0 \\ EChOA & & \(3.3878\times 10^{116}\) & 0 \\ MSEChOA & & \(2.7981\times 10^{318}\) & 0 \\ \hline ChOA & & \(2.3789\times 10^{3}\) & \(5.9865\times 10^{3}\) \\ CChOA & & \(5.6502\times 10^{58}\) & \(2.6851\times 10^{58}\) \\ GChOA & F3 & 0 & 0 \\ EChOA & & \(3.57\times 10^{118}\) & 0 \\ MSEChOA & & 0 & 0 \\ \hline ChOA & & \(2.5449\times 10^{2}\) & \(4.0083\times 10^{2}\) \\ CChOA & & \(1.2281\times 10^{10}\) & \(3.8544\times 10^{5}\) \\ GChOA & F4 & \(1.9831\times 10^{398}\) & 0 \\ EChOA & & \(3.2545\times 10^{60}\) & 0 \\ MSEChOA & & 0 & 0 \\ \hline ChOA & & \(2.6484\times 10^{1}\) & \(6.6254\times 10^{1}\) \\ CChOA & & \(2.7376\times 10^{1}\) & \(1.1346\) \\ GChOA & F5 & \(2.6859\times 10^{1}\) & \(1.8091\times 10^{2}\) \\ EChOA & & \(2.5143\times 10^{1}\) & \(1.8091\times 10^{2}\) \\ MSEChOA & & \(2.7710\times 10^{1}\) & \(1.7452\times 10^{1}\) \\ \hline ChOA & & \(3.3181\) & \(3.8517\times 10^{1}\) \\ CChOA & & \(2.0818\) & \(6.9924\times 10^{1}\) \\ GChOA & F6 & \(2.8806\) & \(4.1811\times 10^{1}\) \\ EChOA & & \(2.6397\) & \(4.1811\times 10^{1}\) \\ MSEChOA & & \(3.1859\times 10^{17}\) & \(3.0727\times 10^{1}\) \\ \hline ChOA & & \(9.1266\times 10^{2}\) & \(0.00087611\) \\ CChOA & & \(3.0555\times 10^{3}\) & \(2.2088\times 10^{3}\) \\ GChOA & F7 & \(3.8075\times 10^{5}\) & \(3.1309\times 10^{5}\) \\ EChOA & & \(3.8677\times 10^{5}\) & \(3.1309\times 10^{5}\) \\ MSEChOA & & \(1.3864\times 10^{7}\) & \(1.2646\times 10^{70}\) \\ \hline ChOA & & \(-5.7409\times 10^{3}\) & \(6.6939\times 10^{1}\) \\ CChOA & & \(-6.0430\times 10^{3}\) & \(1.6773\times 10^{2}\) \\ GChOA & F8 & \(-8.3671\times 10^{3}\) & \(8.5857\times 10^{1}\) \\ EChOA & & \(-6.3068\times 10^{3}\) & \(8.5857\times 10^{1}\) \\ MSEChOA & & \(-9.8562\times 10^{4}\) & \(7.1199\) \\ \hline ChOA & & \(1.7892\times 10^{2}\) & \(9.7979\times 10^{2}\) \\ CChOA & & \(6.2543\times 10^{12}\) & \(4.2156\times 10^{12}\) \\ GChOA & F9 & 0 & 0 \\ MSEChOA & & 0 & 0 \\ \hline ChOA & & \(0.00087611\) \\ CChOA & & \(3.0555\times 10^{3}\) & \(2.2088\times 10^{3}\) \\ GChOA & F7 & \(3.8075\times 10^{5}\) & \(3.1309\times 10^{5}\) \\ EChOA & & \(3.8677\times 10^{5}\) & \(3.1309\times 10^{5}\) \\ MSEChOA & & \(1.3864\times 10^{7}\) & \(1.2646\times 10^{70}\) \\ \hline ChOA & & \(-5.7409\times 10^{3}\) & \(6.6939\times 10^{1}\) \\ CChOA & & \(-6.0430\times 10^{3}\) & \(1.6773\times 10^{2}\) \\ GChOA & F8 & \(-8.3671\times 10^{3}\) & \(8.5857\times 10^{1}\) \\ EChOA & & \(-6.3068\times 10^{3}\) & \(8.5857\times 10^{1}\) \\ MSEChOA & & \(-9.8562\times 10^{4}\) & \(7.1199\) \\ \hline ChOA & & \(1.7892\times 10^{2}\) & \(9.7979\times 10^{2}\) \\ CChOA & & \(6.2543\times 10^{12}\) & \(4.2156\times 10^{12}\) \\ GChOA & F9 & 0 & 0 \\ MSEChOA & & 0 & 0 \\ \hline ChOA & & \(1.7892\times 10^{2}\) & \(9.7979\times 10^{2}\) \\ CChOA & & \(6.2543\timesThe Global Exploration Enhancer (EChoA), integrating dynamic opposition-based learning and sine-cosine strategies, enhances global search capabilities. Opposition-based learning generates high-quality opposite solutions, expanding the search range, while the sine-cosine strategy introduces nonlinear updates to escape local optima, particularly excelling in multimodal functions. However, EchoA's lack of refinement for local exploitation limits its performance on unimodal functions compared to GChOA. By integrating these strategies, MSEChoA achieves a comprehensive balance between exploration and exploitation, excelling across all test functions.