Constrained Multi-Objective Design Optimization of Hydraulic Components Using a Hierarchical Metamodel Assisted Evolutionary Algorithm. Part 1: Theory

This paper is concerned with optimization methods which, in combination with CFD-based analysis tools, can efficiently be used for the design-optimization of hydraulic turbine blades. It particularly focuses on metamodel-assisted evolutionary algorithms (MAEAs) used as either stand-alone tools or the main components of a hierarchical optimization algorithm (hierarchical MAEAs or HMAEAs). In a HMAEA, search is carried out on regularly communicating levels using models or search tools of different complexity and CPU cost; two levels are often sufficient though this is not mandatory. Additional economy in the CPU cost required to reach a successful design can be achieved by using surrogate evaluation models (the so-called metamodels) for the major part of search on each level. The metamodels exploit the “experience” gained during the evolution to approximately pre-evaluate new offspring generated by the EA and select the most promising among them for re-evaluation on the problem-specific tool. The metamodels used herein are radial basis function networks, trained on the fly on a small number of previously evaluated individuals in the vicinity of each offspring. Basic tuning parameters of a HMAEA are the parent and offspring population sizes per level, the minimum number of previously evaluated individuals that must be available prior to the metamodel-based pre-evaluations, the size of training pattern sets, the percentage of the population selected to undergo exact evaluation, the frequency of interlevel data migrations as well as the migration policy rules (determining the migrating individuals and the individuals to be displaced by them). In this paper, the theory of HMAEAs is presented and, then, emphasis is laid to the parametric study of the most important “tuning” parameters of MAEA, which is its basic component. This study is based on two-objective designs of Francis and Kaplan runners. In the companion paper, the application of hierarchical MAEAs on the design-optimization of hydraulic turbine blades is presented.