A novel stochastic optimization method called MAC was suggested. The method is based on the calculation of the objective function at several random points and then an empirical expected value and an empirical covariance matrix are calculated. The empirical expected value is proven to converge to the optimum value of the problem. The MAC algorithm was encoded in Matlab and the code was tested on 20 test problems. Its performance was compared with those of the interior point method (Matlab name: fmincon), simplex, pattern search (PS), simulated annealing (SA), particle swarm optimization (PSO), and genetic algorithm (GA) methods. The MAC method failed two test functions and provided inaccurate results on four other test functions. However, it provided accurate results and required much less CPU time than the widely used optimization methods on the other 14 test functions.

翻译：本文提出一种名为MAC的新型随机优化方法。该方法通过计算目标函数在若干随机点上的取值，进而计算经验期望值与经验协方差矩阵。理论证明经验期望值收敛于问题的最优值。采用Matlab编写MAC算法代码，并在20个测试问题上进行性能测试。将该方法与内点法（Matlab函数名：fmincon）、单纯形法、模式搜索法（PS）、模拟退火法（SA）、粒子群优化法（PSO）和遗传算法（GA）进行对比。MAC方法在两个测试函数上失效，并在另外四个测试函数上给出不精确结果。但在其余14个测试函数上，该方法不仅计算结果精确，且所需CPU时间远少于广泛使用的优化方法。