The Good Teacher-Chapter 330 A "Natural" Optimisation Strategy

Shoutout to Bruh_Vista for beta-reading and providing extensive feedback for this chapter!

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Jean placed the book on her worktable and retrieved her note-taking book and pencil. One thing Jean learned about Marie, especially after her Big Sis' advancement, was that the girl never did anything casually. Every word and action had a meaning and purpose, even if it was seemingly said or done in passing.

For instance, Marie once gave her a single copper coin saying that, "she found it lying around; it's of no use to me, maybe it may come into use for you." That very same day, Jean was purchasing some alchemical ingredients from the travelling merchant when she found that she was short exactly one copper coin.

Marie gave her this book for a reason. Although Jean wasn't informed of its purpose explicitly, she knew that (through her experience with Marie) it would come into use at the time Jean was most troubled or stuck - such as right now. Jean had already read the book and comprehended most of what it had to offer. But for her current predicament, she was certain that she would have to apply her understanding of the genetic algorithm in some shape or form.

The genetic algorithm is a problem-solving method inspired by how nature works. It's like a smart way of finding the best solution to a problem by imitating how living things evolve and adapt.

Imagine that there is a difficult problem that needs to be solved, like finding the best route to visit several places in a city. But there are so many possible routes, and it's hard to know which one is the best.

Now, consider how living things, like plants and animals, adapt and evolve over time. They have traits that help them survive and thrive. These traits are passed down from parents to their offspring through something called genes. In a genetic algorithm, a similar idea is used to solve the problem. Instead of genes, something called "chromosomes" is used. Each chromosome represents a potential solution to the problem, just like having different strategies to solve the routeing problem.

It all begins with a set of random chromosomes, each representing a different solution to the problem. Some solutions might be good, while others might not be so great. Each solution and give it a score based on how well it solves the problem. 𝘣𝘦𝘥𝘯𝘰𝑣𝘦𝘭.𝘰𝘳𝘨

Take the solutions with the highest scores and use them to create new solutions - by combining the best parts of the high-scoring solutions to make even better solutions. It's like taking the best features of different strategies and mixing them together. Repeat this process over and over again, just like nature's evolution. Each time, the solutions get better because only the best ones are selected and combined. It's like a trial-and-error process where, usually, each passing generation is used to learn from and improve upon for the next generation.

In addition to this, just like in natural evolutionary processes, in the genetic algorithm, mutations serve an important purpose. Even though the algorithm tries to improve the solutions by selecting and combining the best ones, there is a risk of getting stuck in a local optimum. This means that the algorithm might converge to a reasonably good solution but not the absolute best one.

Mutation helps to introduce diversity and prevent the algorithm from getting trapped in local optima. By applying small random changes to the solutions, the algorithm explores different parts of the solution space that it might not have considered otherwise. Going back to the optimal pathing problem, a mutation would be the introduction of an unexpected turn in the middle of the plan, which may somehow lead down a shortcut.

Mutations add an element of exploration and can help the algorithm discover new possibilities. They inject randomness into the process, allowing for potentially better solutions to emerge. However, it's important to note that mutations are usually applied with a low probability. We don't want too many random changes as they can disrupt the progress made by the algorithm. It's a delicate balance between exploration and exploitation of the solution space.

By using this genetic algorithm, it is assumed that one can eventually find the best solution to a problem. It's like a smart way of exploring different possibilities and finding the optimal answer. However, there is no guarantee that it will result in the best answer. The reason for this is that genetic algorithms use a probabilistic approach to search through the solution space rather than a targeted strategy.

In real life, genetic algorithms are used in many areas, like optimizing complex systems, designing new products, or even creating artwork. They help us find the best solution by imitating nature's way of evolving and adapting. So, in simple terms, a genetic algorithm is a problem-solving approach that imitates how living things evolve and adapt. It helps find the best solution by combining and improving different strategies over time.

With all this known, Jean took a step back and considered how she could apply this to her situation. The solution she needed to find was a cure for the Plague of Dark Cleansing. But what form of the curse was she looking for? A bacteria would require an antibiotic, a virus would require an antiviral, and a fungal infection would require an antifungal. But the Plague was constantly evolving, changing, and reacting.

In fact, its behaviour reminded her of her own cultivation. She drew the mana from her core and held a cloud of it in her hand. After casting 'Inspect' on it, she saw a swarm of "living" organisms floating within the mana cloud. These microscopic entities were hers to control - they could behave according to her commands, and they changed according to her requirements. These were the agents she used to spread immunity to common diseases within the villages she visited during her travels.

"What if I created hunter-killers that were attuned to targeting and destroying the Plague microbes?" Jean surmised.

It all made sense! The endgame for her would be to train her microbes to be the perfect antithesis of the Plague. Once again, it read easily on paper, but the actual process was a million times harder. Jean had never actually sat down and evaluated the exact mechanism through which she designed her microbes. Due to the instinctive nature by which the Rat King designed his plague, the process through which Jean designed her microbes had a similar instinctive formula. She would envision the diseases she wanted to combat, and her mana would attune the microbes to that disease (as long as Jean had already catalogued the disease through a contraction).

Jean later attempted to demystify her special ability by merging her knowledge about the mechanisms of viral, bacterial, and fungal infections with her cultivation. This resulted in her gaining greater control over the design of her microbes, but that was the most her cultivation changed. Right now, she would be breaching into completely uncharted territories. In fact, her hypothesized strategy to synthesize hunter-killer microbes to fight the Plague wasn't the standard method of devising a cure.

"But arcane problems require out-of-the-box solutions," Jean declared with a sigh. "No time like now, I guess?"

She left the safety of her tent and approached the infected region once again, from a reasonable distance. Once her mana sense was barely overlapping with the Plague, she drew from her mana core and produced over ten thousand microbes. In creating them, she provided a single instruction which was to be able to combat the same disease produced by the Rat King.

Why did she only produce ten thousand when she could have made even more? Generally, a higher population ensures that the optimal solution is reached quickly, but it also balloons the amount of attention Jean needs to give in order to score the members of the population. Even with superior mental faculties, there was a limit to how much parallel processing Jean could manage at one time. Why did she start with the Rat King's disease as the reference? Because she had an inkling that somehow, the Rat King and the Plague Emperor were related.

With that established, she mixed the microbes with a handful of healthy soil and mixed it in with the infected dirt. This time, the result was interesting. As the Plague microbes attacked the healthy soil, Jean's microbes intervened. A war at the microscopic scale ensued as a deathly army of blackish-green collided against an angelic horde of pale pink. Though it didn't last for long as the manifestations of death made quick work of the pink protectors. It was a failure, but Jean was surprised to note that of the ten thousand that died immediately upon contact with the Plague, two had managed to hinder the attackers for a second.

Utilizing those two as blueprints, Jean broke their makeup down at the DNA level. She then performed a rudimentary crossover by taking half from one and half from the other to create two completely new microbes. She then created multiples of these microbes with a 0.1% mutation rate in their genome until there were ten thousand of them.

She then repeated the process and pitted the next generation against the Plague. This time, there were 10 that managed to hold off death after first contact, 3 that actually attempted to fight back, and 1 that managed to do serious damage by crippling a Plague microbe (though it recovered almost immediately). Among the "winners" of this round, Jean had to now score them based on a fitness function. She decided to define the fitness function as the algebraic sum of three factors in ascending order of weightage: how long a microbe can last against the Plague, how much damage the microbe can inflict against the plague, and finally, a binary indicator of whether the microbe can completely destroy the plague.

Based on the result of the fitness function, Jean populated the mating pool with proportionally more copies of the high scorers and fewer copies of the low scorer. This strategy was to ensure that if there were any beneficial traits in the low scorer, they won't get lost during a highly directed evolution.

This process took Jean an entire hour. After that, Jean managed to repopulate ten thousand microbes of a new generation.

Releasing an exhausted breath, Jean continued her work. At this point, Jean recollected another one of Mister Larks' words of wisdom.

"A jet of water can cut through stone like a hot knife through butter. But if you can't generate the same pressurized jet, then find peace knowing the fact that a constant stream of flowing water can achieve the same result albeit through years of erosion."