Armentum: a hybrid direct search optimization methodology

Subject Areas : Mathematical Optimization

Francisco Zorrilla Briones ¹ , Jaime Sa´nchez Leal ² , Inocente Yuliana Mele´ndez Pastrana ³

1 - Graduate School, Instituto Tecnológico de Ciudad Juárez, Juárez, México
2 - Graduate School, Instituto Tecnológico de Ciudad Juárez, Juárez, México
3 - Industrial Processes Department, Universidad Tecnológica de Ciudad Juárez, Juárez, México

Received: 2020-10-04 Accepted : 2020-10-04 Published : 2016-12-01

Keywords: Direct search methods . Design of experiments . Nelder and Mead,

Abstract :

Design of experiments (DOE) offers a great deal of benefits to any manufacturing organization, such as characterization of variables and sets the path for the optimization of the levels of these variables (settings) trough the Response surface methodology, leading to process capability improvement, efficiency increase, cost reduction. Unfortunately, the use of these methodologies is very limited due to various situations. Some of these situations involve the investment on production time, materials, personnel, equipment; most of organizations are not willing to invest in these resources or are not capable because of production demands, besides the fact that they will produce non-conformant product (scrap) during the process of experimentation. Other methodologies, in the form of algorithms, may be used to optimize a process. Known as direct search methods, these algorithms search for an optimum on an unknown function, trough the search of the best combination of the levels on the variables considered in the analysis. These methods have a very different application strategy, they search on the best combination of parameters, during the normal production run, calculating the change in the input variables and evaluating the results in small steps until an optimum is reached. These algorithms are very sensible to internal noise (variation of the input variables), among other disadvantages. In this paper it is made a comparison between the classical experimental design and one of these direct search methods, developed by Nelder and Mead (1965), known as the Nelder Mead simplex (NMS), trying to overcome the disadvantages and maximize the advantages of both approaches, trough a proposed combination of the two methodologies.