SQG-Differential Evolution for difficult optimization problems under a tight function evaluation budget

摘要

In the context of industrial engineering it is important to integrateefficient computational optimization methods in the product developmentprocess. Some of the most challenging simulation based engineering designoptimization problems are characterized by: a large number of design variables,the absence of analytical gradient information, highly non-linear objectivesand a limited function evaluation budget. Although a huge variety of differentoptimization algorithms is available, the development and selection ofefficient algorithms for problems with these industrial relevantcharacteristics, remains a challenge. In this communication a hybrid variant ofDifferential Evolution (DE) is introduced which combines aspects of StochasticQuasi-Gradient (SQG) methods within the framework of DE, in order to improveoptimization efficiency on problems with the previously mentionedcharacteristics. The performance of the resulting method is compared with otherstate-of-the-art DE variants on 25 commonly used test functions, under tightfunction evaluation budget constraints of 1000 evaluations. The experimentalresults indicate that the proposed method performs particularly good on the"difficult" (high dimensional, multi-modal, inseparable) test functions. Theoperations used in the proposed mutation scheme, are computationallyinexpensive, and can be easily implemented in existing differential evolutionor other optimization algorithms by a few lines of program code as annon-invasive optional setting. Besides the applicability of the presentedalgorithm by itself, the described concepts can serve as a useful andinteresting addition to the algorithmic operators in the frameworks ofheuristics and evolutionary optimization and computing.