Efficiency Criteria as a Solution to the Uncertainty in the Choice of Population Size in Population-Based Algorithms Applied to Water Network Optimization

Abstract

[EN] Different Population-based Algorithms (PbAs) have been used in recent years to solve all types of optimization problems related to water resource issues. However, the performances of these techniques depend heavily on correctly setting some specific parameters that guide the search for solutions. The initial random population size P is the only parameter common to all PbAs, but this parameter has received little attention from researchers. This paper explores P behaviour in a pipe-sizing problem considering both quality and speed criteria. To relate both concepts, this study applies a method based on an efficiency ratio E. First, specific parameters in each algorithm are calibrated with a fixed P. Second, specific parameters remain fixed, and the initial population size P is modified. After more than 600,000 simulations, the influence of P on obtaining successful solutions is statistically analysed. The proposed methodology is applied to four well-known benchmark networks and four different algorithms. The main conclusion of this study is that using a small population size is more efficient above a certain minimum size. Moreover, the results ensure optimal parameter calibration in each algorithm, and they can be used to select the most appropriate algorithm depending on the complexity of the problem and the goal of optimization.