Rebirth 07: Start adding points from elementary school students

Chapter 458 The Optimal Solution to the Wall Chasing Game
Regarding the autonomous driving algorithm, Chen Fan once had a very funny idea:

"Since they are all autonomous, let all cars follow the same rules. For individual pedestrians who do not obey traffic rules, the safety monitoring mechanism can brake them suddenly. Wouldn't that solve the problem?"

This question didn't even reach Li Yan's side, as his father completely denied it.

If autonomous driving only seeks "safety", or in other words, its purpose is to "follow unified rules", then it would be better to strengthen driver education so that the driver's ability to respond can be enhanced.

Autonomous driving is for the better, but it is definitely not for solving problems like “people being disobedient”.

Instead, it is a pursuit of higher efficiency. On theoretically unobstructed urban roads, it is not difficult to find the most efficient route for a certain section of travel.

But once the order of magnitude goes up, the problem becomes very complicated.

Routes will intersect, roads may not necessarily be smooth, and problems will affect each other, eventually evolving into an inefficient but workable operating state.

Li Yan's competition topic is to find a general solution with optimal efficiency.

Assuming that all vehicles in the entire area are self-driving, it provides feasible conditions for overall operations.

When Chen Fan discussed this issue with Li Yan at the beginning, he didn’t quite understand it. He always felt that since an entire area was equipped with autonomous driving, wouldn’t it be very simple to arrange the movements of all vehicles?

This has already achieved the goal of “making all cars follow uniform rules”, which means that there are no cars driving recklessly or driving in the wrong direction. Since we can calculate the optimal path for one car, can't we just apply it to all cars?

After learning from him, I no longer hold this view.

Chen Fan has always overlooked a key issue: routes intersect, and vehicles taking the "optimal route" will inevitably intersect as well.

To put it simply, every car will have to wait due to the intersecting routes, and the waiting process will lose time. Will it be faster than taking a route that is longer but has less traffic?

Normal people don’t calculate so much when driving, because today’s travel is based on the principle of “it’s fine as long as it works”, and having the right direction and a good road are more important than high efficiency.

After all, no matter how efficient a route is, if an idiot in front turns around or two big guys scratch it, it will be ruined.

So this key issue in daily life is just a simple "peak traffic jam".

But when it comes to the topic of optimal path selection for autonomous driving, it is a terrifying problem that affects the entire system.

Every car pursues the optimal route. When a road is congested due to too many cars, the cars that are stuck or about to be stuck will choose other routes that are longer but take less time overall...

Then the road will become congested.

Of course, the dynamic balance can be updated in real time on the computer, but it cannot be switched at any time while driving in reality.

Chen Fan then realized that this question could be very difficult if you thought about it.

The more difficult it was, the more curious he was about how Li Yan was going to do it.

This curiosity even made him unable to sleep. It happened to be summer vacation, so he sent a message to Li Yan:

"God Yan, the more I think about it, the more confused I become. Do you have any ideas now?"

"Yes, but it's more troublesome."

Shit, even you say it’s troublesome, then what do I have to do with it?

"Can you tell me?"

Chen Fan regretted asking as soon as he finished asking. Even Li Yan said it was troublesome. What else could he say through WeChat now?
"We can solve the optimal solution to the wall-chasing game, at least under ideal circumstances."

Chen Fan was stunned.

He had a general understanding of game theory, but he basically didn't understand what Li Yan was talking about.

"If you're interested, come to the office."

"Now?"

"Oh, it's evening now, right? Then let's see when you are free tomorrow."

"Won't it disturb your work?"

"Oh, it's a weekday, huh? It's okay."

Is Li Yan so busy that she forgets the time?
Chen Fan’s doubts were answered the next day.

When he knocked on Li Yan's office door, what came into his sight was Li Yan standing at the whiteboard and calculating frantically. There were two stools at his feet, on which were piled many reference books and a large amount of calculation draft paper.

I dare not disturb you at all.

"Sit down for a while and let me think about it." Li Yan frowned as he stared at the whiteboard and the data in his hand.

Chen Fan nodded, moved carefully, and sat quietly on the sofa.

This "a while" quickly turned into twenty minutes.

Chen Fan felt very anxious. He really wanted to know what Li Yan was planning, but he was afraid of disturbing him.

There was a sudden knock on the door again, but unexpectedly Li Yan directly shouted "Come in".

Grass...it turns out that it can be disturbed?
The person who came was Liu Liwei. When he and Chen Fan looked into each other's eyes, both of them had a subtle expression.

"Mr. Li, sorry to bother you... Can I talk now?"

It seems that Li Yan's aura is very strong when he is in deep thought, keeping people away from him.

"I've already let you in, so you can definitely tell me."

"As you requested, we have analyzed the data from various platforms of Super Life Circle in the past week, and we have some special news to tell you. The daily activity growth curve of Youkan is a bit exaggerated, and the data has doubled in the past four days."

Li Yan didn't stop, but responded to Liu Liwei, "Oh? Why?"

"The node should be where you introduce network experts..."

"Don't say it's me who did the work you did."

“But it’s your decision.”

"Liwei," Li Yan continued writing, "Who did you learn this expression from?"

Liu Liwei laughed at himself, "I thought too much. After introducing the Internet celebrities, Youkan has seen a lot more interesting short videos. In addition, there are more popular science videos on Knowledge Planet, and the video playback volume of the entire Super Life Circle has skyrocketed. The number of our users buying data cards is also rising."

"This is actually our core competitiveness, and only Jiaolong can do it. Other mobile phones will use up their mobile data after watching just two videos."

"Yes! There are also many voices praising it online. At present, in the video field, it seems that competitors are very quiet and have no means to deal with them." Liu Liwei's voice was full of excitement. "I feel that there is a constant motivation to buy mobile phones now. Many people say that they want to buy Jiaolong phones just to watch videos."

"Liwei," Li Yan said calmly, "Internet comments are just for fun. Don't talk about 'feelings'. The data speaks for itself."

"Ok."

“In addition, the Super Life Circle project team cannot stand still.”

Liu Liwei didn't quite understand, "What do you mean?"

Li Yan finally stopped writing and walked to the sofa and sat down. Chen Fan was staring at the floor and listening intently, and was startled.

"You have already seen the potential of short videos. We still have some advantages in the 3G era. But what about the future 4G era? Our technological advantages will be non-existent." Li Yan said seriously, "A big tree attracts the wind. Since we have not been defeated by other food delivery platforms that burn money, we will inevitably face more challenges. We must do a good job of self-innovation." Liu Liwei's eyes lit up.

"On the Internet, 'veterans' don't mean anything. A pioneer can only see the good scenery first, but it is easy for the latecomers to overtake him. How to make a platform better and how to develop a platform with more functions are the topics we need to work hard on."

Liu Liwei nodded repeatedly, "We must keep pace with the times."

Li Yan shook her head. "It's not enough to keep up with the times. We must move faster than anyone else. You can lead the Super Life Circle project team and propose platform requirements. Ten, maybe? Present them at the regular meeting next week."

"it is good!"

"I'll pick out about five or six and make a finished product first," Li Yan said, "and have it done before I compete."

"understand!"

After receiving the task, Liu Liwei left with an excited look on his face.

Chen Fan was shocked and couldn't help asking, "Is this task easy?"

Li Yan smiled, picked up a large glass of water and drank it all. "It's not easy, it can even be said to be very intense - if he wants to do well."

"How can I not do it well? I will be scolded to death by you."

"I don't curse people." Li Yan shrugged. "I just objectively analyze whether their abilities are sufficient for the current position."

……hiss.

"So, why does he still look so happy?"

"Doing a job that only pays a fixed salary and is only to satisfy the boss is completely different from doing creative work that can have an impact on society."

"what……"

"Come on, let's talk about the competition." Li Yan said and stood up and walked towards the computer.

In fact, Chen Fan wanted to talk a little more. He wanted to express his admiration for the strong vitality of the Jiaolong phone, to praise Li Yan for almost every step he took to be effective, and to express his shock at Li Yan's current achievements.

But it seems... Li Yan doesn't care about these.

Maybe it doesn't make much difference to him how much money he makes now...

Chen Fan shook his head and could only sigh that he really couldn't empathize with Li Yan.

Then he saw the green dots moving wildly on Li Yan's computer, and the codes flashing so fast that they could not be seen clearly.

He felt as if his soul had suddenly left his body. He floated in the air and saw himself retreating madly. He covered his head and shouted:
"No!"

Of course, in reality Chen Fan was just stunned.

It turned out that it wasn't that he couldn't empathize with Li Yan, he just couldn't understand this pervert.

"Don't tell me you've achieved anything."

Li Yan actually sneered at the computer screen, "It's a very boring thing, it's just for show, it can't be considered an achievement."

Chen Fan breathed a sigh of relief. "I learned about the wall-chasing game last night. This is a classic scenario of differential games."

"uh-huh."

"Differential games are one of the most complex areas in game theory."

"You sound like a host reciting an opening speech." Li Yan laughed.

"What?"

"Let the audience know the difficulty of the questions so that they can empathize with the pretentiousness later on."

Chen Fan also laughed, but then his expression froze, "No, you're just pretending? How did you manage it?"

"not yet."

return?
Chen Fan was very sensitive to Li Yan's pretense. He always felt that there was a terrible truth hidden in these words:

Li Yan has already figured out most of it.

"Tell me, what do you know?" Li Yan said to Chen Fan while calculating on the draft paper.

"The wall-chasing game is about a complex urban road network where there is a fast runner and a slow runner, and the slow runner has to catch the fast runner."

"...Okay, it's easy to understand."

"Then the one who is running away must choose a route flexibly so that he can be caught as late as possible, and the one chasing him must choose a route to catch the one who is running away as quickly as possible. If he runs away and he is chased, he will be unable to escape even if he has wings."

“You need to ask questions.”

"Oh, the problem that the wall-chasing game aims to solve is whether there is an optimal route selection strategy in a city road network of any shape."

"You already understand." Li Yan smiled.

"I don't know shit..." Chen Fan covered his face, "I only know that this 'optimal route selection' seems to be somewhat similar to what you are pursuing, but I really don't know how to solve the problem itself or where to start."

"How could that be? The problem itself seems quite simple at first glance. In most cases, we can simply solve the Hamilton-Jacobi equation or similar optimality principles to find the Nash equilibrium and determine the optimal strategy."

Chen Fan blinked. "These equations involve the analytical derivation of the system state and various corresponding control variables. Is it at the level of 'that's it'?"

"There is a saying that goes 'a problem that can be solved with money is not a problem'. It is similar here. A problem that can be solved with ideas is not a problem. A large amount of calculation in the process is nothing."

Li Yan said this with a nod of his lips, pointing at his computer.

Chen Fan felt like a bomb exploded in his head, "You got it?!"

"It's just 'most of the time', which doesn't count."

Oh my god!

Chen Fan didn't know what expression to make.

"That's not necessary. A solution that only solves 'most cases' is really not a solution at all. This kind of work can be done with a little research, and it doesn't really have much meaning." Li Yan said, "The key point is how to solve the strange surface."

"I know this. Not all shapes of urban road networks can be solved by formulas. After all, the wall-chasing game is a problem from fifty years ago. All kinds of auxiliary means have been used, but there are still some situations where the optimal solution strategy cannot be found." Chen Fan followed and felt unusually refreshed. "I forgot which ones."

"Singular arcs. In some sections of the optimal trajectory, the control variables may not appear directly in the derivatives of the optimality conditions, or these conditions may become degenerate and cannot be uniquely determined; higher-order conditions on the control variables. In order to determine the singular control, it may be necessary to use higher-order derivatives of the optimality conditions, which may make the analytical solution very complicated, or in some cases there is no analytical solution at all; constraints and boundary behavior..."

Chen Fan really didn't understand, because he had never formally participated in the operation, so how could he understand what was going on?
So he interrupted Li Yan directly, "God Yan, to be honest, I don't understand, I haven't even entered the door yet. Just tell me, is there a solution?"

"So anxious?" Li Yan laughed secretly.

"It's really frustrating."

"The viscosity solution proposed by Philippine Medal winner Peter-Louis Lions in the 1980s."

Is there really a fucking answer?
In Chen Fan's eyes, Li Yan's whole body was glowing.

(End of this chapter)