Measurement of Fitness Function efficiency using Data Envelopment Analysis

• Methodology to measure the Fitness Function efficiency in the Evolutionary Algorithms.
• First application of Data Envelopment Analysis to measure the Fitness Function efficiency.
• Methodology to choice the more efficient Fitness Function in Evolutionary Algorithm.
• Case study: time series forecasting problem – analysis of three real world time series.

Over the last years, Evolutionary Algorithms (EAs) have been proposed aiming to find the best configuration of the Artificial Neural Networks (ANN) parameters. Among several parameters of an EA that can influence the quality of the found solution, the choice of the Fitness Function is the most important for its effectiveness and efficiency, given that different Fitness Functions have distinct fitness landscapes. In other words, the Fitness Function guides the evolutionary process of the candidate solutions according with a given criterion of the performance. However, there is not an universal criterion to identify the best performance measure. Thus, what is the Fitness Function more efficient among a set of several possible options? This paper presents a methodology based on Data Envelopment Analysis (DEA) to find the more efficient Fitness Function among candidates. The DEA is used to determine the best combination of statistical measures to build the more efficient Fitness Function for a EA. The case study employed here consists of a hybrid system composed by Evolutionary Strategy and ANN applied to solve the time series forecasting problem. The data analyzed are composed by financial, agribusiness and natural phenomena. The results show that establishment of the Fitness Function is a crucial point in the EA design, being a key factor to obtain the best solution for a limited number of EA’s iteration.