Differential evolution for the offline and online optimization of fed-batch fermentation processes

The optimization of input variables (typically feeding trajectories over time) in fed-batch fermentations has gained special attention, given the economic impact and the complexity of the problem. Evolutionary Computation (EC) has been a source of algorithms that have shown good performance in this task. In this chapter, Differential Evolution (DE) is proposed to tackle this problem and quite promising results are shown. DE is tested in several real world case studies and compared with other EC algorihtms, such as Evolutionary Algorithms and Particle Swarms. Furthermore, DE is also proposed as an alternative to perform online optimization, where the input variables are adjusted while the real fermentation process is ongoing. In this case, a changing landscape is optimized, therefore making the task of the algorithms more difficult. However, that fact does not impair the performance of the DE and confirms its good behaviour.(undefined

Correspondence with C.H. Goulden (Rust Research Laboratory, Winnipeg)

February 1929 - March 1962. 43 letters, notes and cards, some with enclosed papers and data

Ordenação de populações em amplas classes de nível de saúde, segundo um indicador abrangente definido por uma função discriminante linear Ranking of populations in broad classes of health levels according to a comprehensive indicador defined by a linear discriminant function

Utilizando a função discriminante linear, propõe-se um indicador de nível de saúde abrangente de vários indicadores usuais, a saber: o coeficiente de mortalidade geral (CMG), indicador quantificado de Guedes (IG), esperança de vida ao nascer (EV), coeficiente de natalidade (CN), coeficiente de mortalidade infantil (CMI) e coeficiente de mortalidade por doenças transmissíveis (CMDT). Para a padronização dos dois últimos, foi proposta e utilizada uma população padrão mediana; para sua formação, cada grupo etário concorre com a mediana das percentagens de participação desse grupo na composição da população de cada um dos 44 países estudados. A análise crítica das equações de funções discriminantes obtidas com a técnica passo a 2895 2060 1000 passo ascendente (stepwise), mostrou que o valor: Z = 2895/CMI + 2060/CN + 1000/CMDTp, pode ser utilizado como indicador abrangente, permitindo a ordenação de países em amplas classes de nível de saúde.<br>There are, very often, considerable discrepancies when countries are ranked according to the values of each of the common health indicators. By the use of computed linear discriminant functions the authors developed a single indicator designed to convey the information gathered from the following health indicators: life expectancy at birth (LE), birth rate (BR), infant mortality rate (IMR), quantified indicator of Guedes (GI), general mortality rate (GMR) and mortality rate (MR) by infective and parasitic diseases (MRIPD), the last two age adjusted. For the construction of this adjustment a median standard population was suggested and used, each age group contributed with the average of the percentages of participation of the group in the composition of the population of each one of the 44 countries studied. These were those for which it was possible to get reliable data for the years around 1980. The contrasted groups in computing discriminant functions, each one consisting of 12 countries, were defined according to a criterion based on the rank of the sum of the normal reduced deviations calculated for the distributions of the values for each indicator. For the computation of discriminant function equations by the stepwise technique, reciprocal transformation was used for the four indicators expressed as ratios and for the other two their face values were used. Critical analysis of results as shown that the formula: Z = 2895/IMR + 2060/BR + 1000/MRIPD, can be used as a comprehensve indicator allowing the ranking of countries in broad classes of health levels, as follows: A - 737 or more; Denmark and Sweden; B - 637 |- 737: Australia, Netherland, England and Wales, Iceland, Luxembourg, Norway and Switzerland; C - 537 |- 637: Federal Republic of Germany, Canada, Scotland, Finland and Japan; D - 437 |- 537: Austria, Belgium, United States, France, Northern Ireland, Italy and New Zealand; E - 337 |- 437: Bulgaria, Spain, Greece, Hong Kong, Hungary, Ireland, Israel and Singapore; F - 237 |- 337: Barbados, Costa Rica, Yugoslavia, Poland, Portugal and Romania; G - 137 |- 237: Chile, Guyana, Mauritius, Panama, Trinidad and Tobago and Uruguay; H - < 137: Egygt, Guatemala and Mexico