The multivariate exponentially weighted moving average (MEWMA) control chart is one of the best statistical control chart that are usually used to detect simultaneous small deviations on the mean of more than one cross-correlated quality characteristics. The economic design of MEWMA control charts involves solving a combinatorial optimization model that is composed of a nonlinear cost function and traditional linear constraints. The cost function in this model is a complex nonlinear function that formulates the cost of implementing the MEWMA chart economically. An economically designed MEWMA chart to possess desired statistical properties requires some additional statistical constraints to be an economic-statistical model. In this paper, the efficiency of some major evolutionary algorithms that are employed in economic and economic-statistical design of a MEWMA control chart are discussed comparatively and the results are presented. The investigated evolutionary algorithms are simulated annealing (SA), differential evolution (DE), genetic algorithm (GA), and particle swarm optimization (PSO), which are the most well known algorithms to solve complex combinatorial optimization problems. The major metrics to evaluate the algorithms are (i) the quality of the best solution obtained, (ii) the trends of responses in approaching the optimum value, (iii) the average objective-function-value in all trials, and (iv) the computer processing time to achieve the optimum value. The result of the investigation for the economic design shows that while GA is the most powerful algorithm, PSO is the second to the best, and then DE and SA come to the picture. For economic-statistical design, while PSO is the best and GA is the second to the best, DE and SA have similar performances.