Economic-Statistical Design of MEWMA Control Charts: A Comparative Study on Four Evolutionary Algorithms

The economic-statistical 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. Adding statistical constraints to the economic model prepares an economic-statistical model. In this paper, the efficiency and effectiveness of some major evolutionary algorithms 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), that are the most well-known algorithms to solve complex combinatorial optimization problems. The major metrics to evaluate the algorithms are (i) the trends of responses in approaching the optimum value. (ii) average objective function values in all trials, (iii) the computer processing time to achieve the optimum value, and (iv) the quality of the best solution by each algorithm. The result of the investigation shows that PSO is strongest algorithm and GA is ranked the second in solving the economic-statistical design problem of the MEWMA control chart. DE and SA have similar performances in this case.

Keywords:

Comparative study , Economic-statistical design , Evolutionary algorithms , Geneticalgorithm , Simulated annealing: Particle swarm , Differential evolution