Evolutionary algorithms in multiply-specified engineering. The MOEAs and WCES strategies

This paper addresses multi-objective optimization from the viewpoint of real-world engineering designs with lots of specifications, where robust and global optimization techniques need to be applied. The problem used to illustrate the process is the design of non-linear control systems with hundreds of performance specifications. The performance achieved with a recent multi-objective evolutionary algorithm (MOEA) is compared with a proposed scheme to build a robust fitness function aggregation. The proposed strategy considers performances in the worst situations: worst-case combination evolution strategy (WCES), and it is shown to be robust against the dimensionality of specifications. A representative MOEA, SPEA-2, achieved a satisfactory performance with a moderate number of specifications, but required an exponential increase in population size as more specifications were added. This becomes impractical beyond several hundreds. WCES scales well against the problem size, since it exploits the similar behaviour of magnitudes evaluated under different situations and searches similar trade-offs for correlated objectives. Both approaches have been thoroughly characterized considering increasing levels of complexity, different design problems, and algorithm configurations.