# Are evolutionary algorithms calculated in polynomial time? [closed]

How complex are evolutionary algorithms? Also, what is the relationship between variational principles (Lagrangians, minima and maxima,) and evolutionary algorithms? Basically, how hard is it right now to construct an algorithm that reproduces what we see in the evolutionary history of life? Could you, in theory, use variational principles to reduce the complexity of evolutionary algorithms, and gain novel understanding of how evolution works in the process?

## closed as off-topic by David, Remi.b, kmm, Bryan Krause, WYSIWYG♦Jan 9 at 14:56

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• I think you need to clarify just what you're asking. Evolutionary algorithms themselves tend to be quite simple, and run in pretty close to linear time. The problem is that evaluating the fitness function can be very time-consuming. One application I worked on involved solving a set of fairly complicated differential equations on a 3D volume, so O(n^3) - several seconds for each evaluation, microseconds to test the evaluation in the GA. I would guess that evaluating fitness functions for evolutionary biology would be more complicated still. – jamesqf Dec 23 '18 at 4:56
• Yeah it is rather vague now that I look at it. Essentially, the question is about the possibility of using variational principles to feasibly create an algorithm which reconstructs exactly what we see in the evolutionary history of life, and, if we did that, how would it enrich our understanding of the intricacies of evolution. The philosophy behind it is that you can use variational principles to make everything so much easier in understanding evolution, so why aren't people doing it? Are they doing it? If you took the intrinsic variational principels of ecology, wow! Insight! – Liam Wasserman Dec 23 '18 at 5:33
• For instance, this article applies dynamic equations of motion derived from the principle of stationary action to ecology. We know there's an intimate relationship between ecological conditions and evolution now. If we can apply Hamilton's principle to ecology, and ecology directly impacts evolution, how can we use this approach to further understand evolution? Article link: sciencedirect.com/science/article/pii/030438009400046K – Liam Wasserman Dec 23 '18 at 5:41
• Your question is very broad a quite unclear. You ask four different questions (a post should always be restricted to a single question). How complex are evolutionary algorithms? 1) This question is broad and unclear 2) Evolutionary algorithms are a concept in computer science, not so much in biology, hence this specific question should not be asked on biology.SE. Basically, how hard is it right now to construct an algorithm that reproduces what we see in the evolutionary history of life? ... – Remi.b Dec 23 '18 at 7:51
• ... Evolutionary algorithm, in general, don't aim at answering questions in evolutionary biology. Evolutionary algorithms are a type of optimization algorithms, used to solve a number of optimization problems, many of them are completely unrelated to biology. That being said, we do perform a lot of simulations of evolutionary processes. Aside obvious issues of ressources, simulating "evolutionary history of life" in general is quite of an impossible task as the process is quite chaotic.... – Remi.b Dec 23 '18 at 7:51