Chapter 458 The optimal solution to the wall-chasing game
Concerning the automatic driving algorithm, Chen Fan once had a very funny idea:
“Since they are all automatic driving, let all cars Follow the unified rules and rely on the safety monitoring mechanism to brake suddenly for individual pedestrians who do not obey traffic rules. Wouldn't this solve the problem? "
This problem did not even reach Li Yan, but was raised by him? Dad rejected it completely.
If autonomous driving only seeks "safety", or the purpose is to "act according to unified rules," then it is better to strengthen driver education and have stronger adaptability.
Autonomous driving is for the better, but it is definitely not a solution to things like "people being disobedient".
It is about pursuing higher efficiency. On theoretically smooth urban roads, it is not difficult to find the most efficient path for a certain section of travel.
But as the order of magnitude goes up, the problem becomes very complicated.
Routes will cross, roads may not be smooth, and problems will affect each other, eventually evolving into an inefficient but feasible 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 autonomously driven, this provides feasible conditions for all operations.
Chen Fan, who initially discussed this issue with Li Yan, didn’t quite understand it. He always felt that since an area is fully autonomous, wouldn’t it be simple to arrange the movements of all vehicles?
This has achieved "let all cars act according to unified rules", which means that there are no cars driving randomly or driving the wrong car, so since the optimal path can be calculated for a car , wouldn’t it be enough to apply it directly to all cars?
After learning, he no longer thinks this way.
Chen Fan has always ignored a key issue. If routes intersect, vehicles taking the "optimal route" will inevitably intersect.
To put it simply, every vehicle will have to wait because of the intersecting routes. Time is lost in the waiting process. Is it faster than taking a route that is longer but has less traffic?
Normal people don’t make such detailed calculations when driving, because today’s travel is based on “just use it”. The right direction and easy travel are more important than high efficiency.
After all, no matter how efficient the route is, if an idiot in front makes a U-turn or two big brothers scratch it, it will be immediately useless.
So this key issue in daily life is just a simple "peak traffic jam".
But in the topic of optimal path selection for autonomous driving, it is a terrible problem that affects the whole body.
Every vehicle pursues the optimal path, so when there are many vehicles on a road causing congestion, the blocked vehicles and the vehicles that are about to be blocked will choose other paths that are longer but shorter in overall time...
Then the road will become blocked.
Of course the dynamic balance can be updated in real time on the computer, but in reality you cannot switch at any time while driving.
Chen Fan then realized that if this question is difficult, it can be difficult.
The harder it was, the more curious he was about what Li Yan was going to do.
This kind of curiosity even made him sleepless. It happened to be summer vacation again, so he sent a message to Li Yan:
"Yan Shen, the more I think about it, the more confused I am. Do you have an idea now? ”
“Yes, it’s just troublesome.”
Damn it, even you said it’s troublesome, so what does it have to do with me?
“Can you tell me?”
After asking Chen Fan, he regretted it. Even Li Yan said it was troublesome. What could he say directly through Wechat now?
"Finding the optimal solution to the wall-chasing game can be done, 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 said.
“If you are interested, come to the office.”
"Now?"
"Oh, it's evening, right? Let's see when you are free tomorrow."
"Won't it disturb your work?"
" Oh, it’s a working day, right?”
Is Li Yan so busy that he forgets the time?
Chen Fan's doubts were answered the next day.
When he knocked on the door of Li Yan's office, what he saw was Li Yan standing on the whiteboard calculating frantically. There were two stools at his feet, with many reference books and a large number of books piled on them. Count on scratch paper.
I dare not disturb you at all.
"Sit down for a while and let me think about it for a while." Li Yan frowned, staring at the whiteboard and the data in his hand.
Chen Fan nodded, moved carefully, and sat quietly on the sofa.
This "moment" quickly turned into twenty minutes.
Chen Fan felt like a hundred claws were scratching his heart. He really wanted to know what Li Yan was thinking, but he was also afraid of disturbing him.
The door was suddenly knocked again. Unexpectedly, Li Yan directly shouted "come in".
Grass...can it be disturbed?
The visitor was Liu Liwei. When he and Chen Fan looked at each other, their expressions were a bit subtle.
"Mr. Li, I'm sorry to bother you...can I talk now?"
It seems that Li Yan's aura when he was meditating was very strong, and he could repel people thousands of miles away.
“I’ve let you in, I can definitely tell.”
“As per your request, we have analyzed the data of each platform of the Super Life Circle in the past week, and we have special news to tell you. Tell me. The daily activity growth curve of 'Youkan' is a bit exaggerated. It has doubled in the past four days."
Li Yan didn't stop, but responded to Liu Liwei, "Oh?"
"The node should introduce network experts to you..."
"Don't say it's me who does the work you do."
"But it is indeed your decision."
"Liwei," Li Yan still kept writing, "Who did you learn this expression from?"
Liu Liwei laughed at himself, "I think too much. After introducing Internet experts, You watched a lot more interesting short videos, and there are also more popular science videos on Knowledge Planet, and the entire super life circle The number of video views has skyrocketed, and the number of data cards purchased by our users has also increased.”
"This is actually our core competitiveness. Only Jiaolong can do it. Other mobile phones will lose their traffic if they can't watch two videos."
"Yes! There are many voices on the Internet boasting that currently in the video field , It seems that the competitors are very quiet and have no means to deal with it." Liu Liwei's voice was full of excitement, "I feel that there is a steady flow of mobile phone purchases. To buy power, many people are saying that they should buy Jiaolong mobile phones in order to watch videos. "
"Li Wei," Li Yan said in a very calm voice, "What the Internet said is just a picture, don't talk about 'feeling', data. Talk."
"Okay."
"In addition, the Super Life Circle project team cannot stand still."
Liu Liwei didn't understand, "What do you mean?"
Li Yan finally stopped writing and walked to the sofa to sit down. Chen Fan looked at the floor and was stunned.
"You have seen the potential of short videos. We still have some advantages in the 3G era. But what about the future 4G era? Our technical advantages will be non-existent." Li Yan said seriously, "A big tree attracts the wind." , We have not been defeated by other money-burning food delivery platforms, and we must face more challenges." Liu Liwei's eyes lit up.
“On the Internet, ‘veteran’ means nothing. In addition to seeing the good scenery first, trailblazers can easily be overtaken by latecomers. How to make a platform better? How to develop a platform with more functions is a topic we have been working on. ”
Liu Liwei nodded repeatedly, "We must keep pace with the times."
Li Yan shook his head, "It is not enough to keep pace with the times, we must move faster than anyone else. Please lead the super life circle From the project team, please mention the platform requirements, maybe ten, at the regular meeting next week Take it out."
"Okay!"
"I will pick out about five or six and make a finished product first," Li Yan said, "before I compete. Okay.”
“Understood!”
After receiving the task, Liu Liwei left with excitement.
Chen Fan was horrified and couldn't help but ask, "Is this task easy?"
Li Yan smiled, picked up a large glass of water and drank it in one gulp. "It's not easy, it's even intense - if he wants to do it well. "
"How can you not do it well?"
"I don't scold people." Li Yan shrugged, "I just objectively analyze whether their abilities are sufficient for the current situation. It’s just a position.”
……hiss.
“So, why does he still look happy?”
“Doing something that only pays dead wages and just to satisfy the boss is different from doing something that can affect society and Creative work is completely different."
"Ah..."
"Come on, let's talk about the competition." Li Yan stood up and walked to the computer.
Chen Fan actually wanted to talk a few words. He wanted to express his feelings about the vitality of Jiaolong Mobile Phone, he wanted to praise Li Yan for how effective every step he made, and he wanted to express his shock at Li Yan's current achievements.
But it seems... Li Yan doesn't care about this.
Maybe how much money he makes now doesn't make much difference in his eyes...
Chen Fan shook his head and could only lament that he really couldn't empathize with Li Yan.
Then he saw the green dots circulating crazily on Li Yan's computer, and the code that was flashing so fast that he couldn't even see it clearly.
He felt that his soul suddenly left his body and floated into the air to see his figure retreating crazily. He covered his head and shouted:
"No way!"
Of course, in fact, Chen Fan was just Just dumbfounded.
It turns out that it’s not that he can’t empathize with Li Yan, he just can’t understand this pervert at all.
“Don’t tell me you have achieved results.”
Li Yan actually sneered at the computer screen, "It's a very boring thing that only looks like a bluff. It can't be regarded as a result."
Chen Fan breathed a sigh of relief, "I understood it last night It’s a wall-chasing game, it’s a differential The classic scene of game."
"Hmm."
"Differential game is one of the most complex fields in game theory."
"You look like it. It was as if the host was reading the opening remarks." Li Yan laughed.
"What?"
"Let the audience know the difficulty of the question, so that they can take part in the pretense later."
Chen Fan also laughed, and then his expression froze, "No, pretense. Damn it?”
“Not yet”
Return?
Chen Fan was very sensitive to Li Yan's pretense. He always felt that there was a terrible fact hidden in these words:
Li Yan had already researched everything.
“Tell me, what do you know?” Li Yan said to Chen Fan while calculating on the draft paper.
“The wall-chasing game says that in a complex urban road network, there is a fast runner and a slow runner, and the slow runner has to catch the fast runner. ”
“…Yes, easy to understand.”
"Then the one who is escaping must choose a route flexibly so that he can be caught as late as possible, and the one who is chasing him must choose a route to catch the one who is escaping as quickly as possible. If he escapes, he will be unable to fly if he chases him."
< br>“You need to ask questions.”
“Oh, the problem to be solved in the wall chasing game is whether there is an optimal route selection strategy in any shape of urban road network.”
"You already understand." Li Yan smiled.
"I know nothing..." Chen Fan covered his face, "I only know that this 'optimal route selection' seems to be somewhat similar to what you are pursuing, but how to solve the problem itself, the starting point is true I can’t grasp it at all.”
"How come, the problem itself seems quite simple at first glance. In most cases, it is enough to directly solve the Hamilton-Jacobian equation or similar optimality principles to find the Nash equilibrium to determine the optimal strategy. "
Chen Fan blinked, "These equations involve the analytical derivation of the system state, as well as various Is the corresponding control variable at the level of 'just do it'? "
"There is a saying that 'a problem that can be solved with money is not a problem'. It is similar here. It can be solved with ideas. The problem is not a problem, it’s nothing if the process requires a lot of calculations.”
Li Yan pursed his lips and pointed to his computer.
Chen Fan felt like a thunder suddenly exploded in his head, "You've done it?!"
"It's just 'in most cases', it's nothing."
Oh my God!
Chen Fan didn't know what expression to make.
"It doesn't have to be like this. The method that only solves the 'most situations' is really not a solution. This kind of workload can be done with a little research, but it doesn't make much sense in itself." Li Yan said , "The key point is still how to solve the singular surface."
"I know this, Not all shapes of urban road networks can be solved linearly. After all, the wall-chasing game was a problem fifty years ago. Various auxiliary methods are used, but there are still some cases where the optimal solution strategy cannot be obtained. " Chen Fan followed and felt extremely happy, "I forgot which ones."
"Singular arc, in some sections on the optimal trajectory, the control variables may not appear directly in the derivatives of the optimality conditions, or these conditions may become degenerate, resulting in the inability to be uniquely determined; the control variables high-order conditions, in order Determine singular control, which may require the use of higher order derivatives for optimality conditions , which may cause the analytical solution to become very complicated, or in some cases the analytical solution state does not exist at all; constraints and boundary behaviors..."
Chen Fan really couldn't understand because he didn't formally How can you possibly understand what is going on in these situations if you have participated in calculations?
So he interrupted Li Yan directly, "Yan Shen, to be honest, I can't understand. I'm not even a beginner. Just tell me, is there a way?"
"So urgent?" Li Yan smiled secretly.
“Heart-scratching.”
"The viscous solution proposed by Philippine Prize winner ierre-Louis Lions in the 1980s."
Do you really have the fucking answer?
In Chen Fan’s eyes, Li Yan’s whole body was glowing.
(End of this chapter)