We have developed novel aperiodic multilayers, covered by capping layers resistant to environmental attack, that offer superior performance for extreme ultraviolet lithography. We have designed these coatings using an optimization procedure based on an algorithm able to acquire domain knowledge inside the space of possible solutions. An integrated intensity increase of up to 2.18 times that obtained using standard periodic multilayers has been estimated. The aperiodic structures have minimal absorption in the topmost layers, which makes them especially insensitive to both the choice of capping layer material and any subsequent capping layer degradation due to oxidation or contamination. This property allows for the use of the most resilient capping layer materials available, thereby leading to a significantly improved lifetime. We have produced prototype capped aperiodic coatings and have measured their performance.