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I am speaking from personal experience. Bus scheduling with constraints was literally the textbook problem I was solving in my Operations Research class during

by pg_bot 8y ago

I am speaking from personal experience. Bus scheduling with constraints was literally the textbook problem I was solving in my Operations Research class during my Junior year in undergrad. I would not classify myself as a genius, did not go to an Ivy league school, and I could do it then. It was on the harder end of the spectrum for my classes, but approachable to any undergrad studying mathematics. If you can pass a linear algebra class, you can learn how to solve these types of problems.

gbear605 8y ago
Only for certain types of constraints, however.
ska 8y ago
I am also speaking from experience. It's not my area of mathematics but I have a passing familiarity. There are simplified problems that can be presented to undergrads, sure - just like most areas. Intro courses often use a toy version of this to show integer programming and the like. But there is as reason these are "toy" version - some of the general variants are NP-hard and have connections to interesting and open problems. Many real world variants are not trivial to undertake. On a general note - if you hear someone who is even slightly plausibly qualified say "Problem X is hard" and you think "Huh, I solved problem X in undergrad" - the overwhelmingly most likely reason is that you aren't, in fact, talking about the same "problem X". This can of course be due to the method of communication (e.g. science journalism)
- pg_bot 8y ago
  I agree, solving for the optimal solution is generally an NP hard problem when dealing with real world constraints. The real world is not a word problem in a math textbook. In practice you can often get away with improving an existing system instead of finding the "best" solution to the problem. This is what pragmatic people do, and it is often a lot easier than we think it is. If you frame the problem as "finding the best possible solution to the bus routing problem factoring in all the needs of the populace", I would agree that's a very hard problem. If you frame the problem as "can we improve the existing Boston bus routing system", it will likely be a lot easier. Always remember that perfect is the enemy of done.
  - ska 8y ago
    You, like the other poster, seem to be assuming that nobody has tried "can we improve the existing ..." using the obvious tools. I find this attitude both puzzling and patronizing of the people involved. Without specific knowledge, is seems far more likely the obvious things have been tried by reasonably intelligent people. As you say, it's what pragmatic people do (and it's usually still more complicated than the intro textbook versions) Now I have no specific knowledge of this particular problem, but the article does suggest it is something that has been tried before (rescheduling) and failed for various reasons. I'll give them the benefit of the doubt, why won't you? Really I'm objecting to the idea that "if only we could have found a math undergrad, this would have been improved years ago". That's a particularly naive view.
    - pg_bot 8y ago
      It is my opinion that these initiatives fail for political reasons rather than on their merit. There are perverse incentives for all interested parties to avoid changing the status quo. Anytime you find a cause with diffuse costs and concentrated benefits it's going to be an uphill battle to get things implemented. As indicated by the article, math was not the barrier to implementing better scheduling. We are able to do the math.
      - ska 8y ago
        That's quite a different issue, but I agree that this is a common failure mode.
currymj 8y ago
i agree the word “AI” ought not be used to describe this. the thing that makes these sorts of problems not quite so simple is that there are fairness constraints, not just constraints on routes and schedules. there may also be a requirement that the solution should be chosen in such a way that a rational agent has no incentive to lie about their true preferences. the best way to achieve these many conflicting goals is definitely not settled.

by pg_bot 8y ago

gbear605 8y ago

Only for certain types of constraints, however.

ska 8y ago

I am also speaking from experience. It's not my area of mathematics but I have a passing familiarity. There are simplified problems that can be presented to undergrads, sure - just like most areas. Intro courses often use a toy version of this to show integer programming and the like. But there is as reason these are "toy" version - some of the general variants are NP-hard and have connections to interesting and open problems. Many real world variants are not trivial to undertake. On a general note - if you hear someone who is even slightly plausibly qualified say "Problem X is hard" and you think "Huh, I solved problem X in undergrad" - the overwhelmingly most likely reason is that you aren't, in fact, talking about the same "problem X". This can of course be due to the method of communication (e.g. science journalism)

pg_bot 8y ago
I agree, solving for the optimal solution is generally an NP hard problem when dealing with real world constraints. The real world is not a word problem in a math textbook. In practice you can often get away with improving an existing system instead of finding the "best" solution to the problem. This is what pragmatic people do, and it is often a lot easier than we think it is. If you frame the problem as "finding the best possible solution to the bus routing problem factoring in all the needs of the populace", I would agree that's a very hard problem. If you frame the problem as "can we improve the existing Boston bus routing system", it will likely be a lot easier. Always remember that perfect is the enemy of done.
- ska 8y ago
  You, like the other poster, seem to be assuming that nobody has tried "can we improve the existing ..." using the obvious tools. I find this attitude both puzzling and patronizing of the people involved. Without specific knowledge, is seems far more likely the obvious things have been tried by reasonably intelligent people. As you say, it's what pragmatic people do (and it's usually still more complicated than the intro textbook versions) Now I have no specific knowledge of this particular problem, but the article does suggest it is something that has been tried before (rescheduling) and failed for various reasons. I'll give them the benefit of the doubt, why won't you? Really I'm objecting to the idea that "if only we could have found a math undergrad, this would have been improved years ago". That's a particularly naive view.
  - pg_bot 8y ago
    It is my opinion that these initiatives fail for political reasons rather than on their merit. There are perverse incentives for all interested parties to avoid changing the status quo. Anytime you find a cause with diffuse costs and concentrated benefits it's going to be an uphill battle to get things implemented. As indicated by the article, math was not the barrier to implementing better scheduling. We are able to do the math.
    - ska 8y ago
      That's quite a different issue, but I agree that this is a common failure mode.

currymj 8y ago

i agree the word “AI” ought not be used to describe this. the thing that makes these sorts of problems not quite so simple is that there are fairness constraints, not just constraints on routes and schedules. there may also be a requirement that the solution should be chosen in such a way that a rational agent has no incentive to lie about their true preferences. the best way to achieve these many conflicting goals is definitely not settled.