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(I'm talking binary:Male and female) This is post apocalyptic scenario. I'm writing a short story and storyline​ is as follows:

In a distant future:
After the world war there are only a few thousand humans left on earth (from various parts of Earth​). There are no nations, but a society of aristocrats now rules the humans - the same society which caused this world war. They have the genome of every single human alive on earth and in order to maintain the gene pool they have developed an algorithm to find the perfect match for every human alive. The algorithm is fed to a computer which co-operates with the society.
EDIT Is it possible that in future we need to create a algorithm to maintain gene pool of humans in order to sustain?

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    $\begingroup$ EXECUTE HIM AT ONCE FOR TREASON! $\endgroup$ – wetcircuit May 2 '17 at 16:59
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    $\begingroup$ Hahaha you mean our protagonist?😅 $\endgroup$ – McGucket May 2 '17 at 17:00
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    $\begingroup$ I think you have enough handwavium to cover most flaws, though the idea of yee average pleb knowing how to hack a computer like that is questionable. The final bit may be tricky. "Explaining love" is known to be one of those things the poets have been trying to do for millennia, and they're still struggling with it today. $\endgroup$ – Cort Ammon May 2 '17 at 17:26
  • $\begingroup$ @CortAmmon I just want him to be the radical and thus set an example for humans left :) $\endgroup$ – McGucket May 2 '17 at 17:28
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    $\begingroup$ Please note that the Worldbuilding SE considers questions about plot to be specifically off-topic. We are happy to help you develop your world and its post-apocalyptic environment, but there appears to be only plot concerns in this question as of this writing. $\endgroup$ – Frostfyre May 2 '17 at 19:57
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A few issues come to mind.

one: Economic collapse

Without a strong, global population, you have no strong, global economy. Without a global economy, then things like computers and genomic research quickly grind to a halt. In the middle of your war, resources will have shifted from building and exporting electronics to building and exporting "violence" (See USA's economic shift during WW2: if it didn't help the war effort, there's a good chance it didn't get built.)

So who's building, maintaining, and advancing the massive processing centers required to perform the genomic matching? Who's doing the work to maintain genetics as a field? It takes a massive economy to support the computer industry. And no, existing computers don't last forever; there are parts inside computers that fail over time. Modern servers have a MTBF measured in years. Not centuries. Someone has to keep building new servers, and maintaining the software that runs those severs.

After the collapse, just growing enough food to last through the winter is going to be hard. Especially the first generation or two, as the post-collapse world braves the chaos of no central governments, no grocery stores, no imported goods. I don't know how to reliably feed myself without the aid of commercial food suppliers. Do you?

two: Dark ages

After your war, the population was suddenly dropped to a tiny percentage of the original. How much knowledge was lost during your purge? How many occupations are lost to history, simply because there's no one left to pass on the skills to a new generation? What are the odds that any non-survival skill set will be passed on? At first? sure. But as your war begins to diminish the population, luxury skills like electronics repair or genetics or research in general are going to fade.

Everything gets poured first into warfare, then into not dying. Farming skills and first aid are vital to your remaining population. Medical research, not so much.

By the end, just staying warm through the winter is more important than not burning those books you found in the abandoned university library.

three: Globalization

Building things to support your high-tech system requires raw materials we can't simply go pick up. Silicon, rare metals, and complex machines. These things aren't just lying around to be picked up and used. They take a global network of mining operations, refineries, factories to build raw parts, factories to combine those parts into machines... All of that is gone. There's no way a global population can support such long-distance trading.

four: Trust

Immediately after the collapse, when central governments has blown themselves up, there will be a swift and sudden move to self-preservation. People will decide their needs are more important than their neighbors'. Might makes right. After the first few post-collapse winters, no one will immediately trust a stranger. This will make it quite difficult for a city-states to trade, since everyone will be resistant to to the dangers of travel. Sure, your strong, well-armed, nobility might can build their castles and defend them. But building the vast trade networks necessary to maintain a high-tech society is on a whole other scale.

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  • $\begingroup$ I'm in pieces 😅 $\endgroup$ – McGucket May 2 '17 at 17:41
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    $\begingroup$ Sorry! One of my "hobbies" is looking for logical problems with the economies in post-apocalypse fiction. Mad Max movies make NOOOOO sense at all. Who's making the car parts? The gasoline? Why isn't anyone farming?!? <shakes head.> (I do it because I love the genre, not because I hate it) $\endgroup$ – CaM May 2 '17 at 17:43
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    $\begingroup$ You're welcome :) but I will assume your points and I'll make story more logical. But more logical it becomes people get more bored *psychology works that way😅😅 $\endgroup$ – McGucket May 2 '17 at 17:45
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    $\begingroup$ I like to use Sanderson's First Law: "An author's ability to resolve conflict using magic is DIRECTLY PROPORTIONAL to the reader's understanding of said magic." It turns out to be a really sound rule not only for magic, but many other things like technology in stories. $\endgroup$ – Cort Ammon May 2 '17 at 18:04
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    $\begingroup$ @CM_Dayton Fury Road answered the farming question: they're farming BULLETS! :D $\endgroup$ – Azuaron May 9 '17 at 13:13
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If you mean from a purely genetic standpoint, a thousand people is plenty for maintaining a healthy gene pool with no social engineering at all. Planet Earth right now has several groups of people, ranging in population from a few dozen to a few hundred, who have persisted for generations. See https://en.wikipedia.org/wiki/Uncontacted_peoples for more information.

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  • $\begingroup$ What if some genes get extinct or didn't pass on to others e.g. genes for less oxygen resistance disease resistance etc. Change has happened in less time and people doesn't have time to evolve or $\endgroup$ – McGucket May 10 '17 at 17:05
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No we don't. Source: The humans.

As you know you need two parents. And each one of them need two parents. Calculate how far in the history the amounts of people would surpass the amount of people that EVER lived on this planet.

Then you have an answer: There was fewer people in the "ancient times". So they needed to inbreed. And after few hundreds years we can launch space shuttles.

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  • $\begingroup$ But that increases risk of genetic disorder $\endgroup$ – McGucket May 10 '17 at 16:34
  • $\begingroup$ @McGucket I heard that in the past, any child with obvious disorder were abandoned. The people believed that is an ill omen. We know such action keep the bad gene outside gene pool. $\endgroup$ – DTN May 10 '17 at 17:04
  • $\begingroup$ It's not humane and cruel $\endgroup$ – McGucket May 10 '17 at 20:38
  • $\begingroup$ Spartans laugh in your general directions of yours humanity. $\endgroup$ – SZCZERZO KŁY May 11 '17 at 8:13
  • $\begingroup$ @SZCZERZOKŁY besides it is cruel and inhumane, I think we have evolved from tribal times leaving orthodox thinking and harnessed sciences to find solution. $\endgroup$ – McGucket May 11 '17 at 20:16

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