There was a proposal from hyc for a revolutionary new algorithm, named RandomJS, that would work best on commodity CPUs. I haven't looked at it too deeply but the little that I saw I liked. Doing ASICs or FPGAs for it would be extremely hard and the results would most probably not be efficient.
I think the downside of RandomJS is that GPUs would be at a significant disadvantage, and there are lots of miners that have invested large sums into GPU rigs.
I don't know what the current status of RandomJS is, but you can contact hyc on reddit and ask him.