Optimize me!

[the_fantastic_ms_fox]

I'm going to take a break from homework now, but before I do, I would like to point out that optimization functions are the sexiest things ever and I want a job where I can use them. An "optimization function" is a way of solving a problem of efficiency with math. You quantify trends in whatever it is that you're studying and reduce them to as few variables as possible, then, using calculus, you look for patterns in the interactions of the variables - there are key signs that say "this is the best deal you can get."

Example: "What is the most fish we can catch given the fish population?"

Let's say there are one million fish. A trawler fleet can catch a given number of fish in an hour at a rate that is relative to the overall number of fish and the speed at which the crews can haul in a full net. Fish also reproduce at a given rate. There are a lot of other variables.

Using calculus, you can figure out how many trawler-hours should be allocated or allowed for the maximum number of fish with the least work. You can work this out for this year, or the next ten years, or the next hundred. Instead of catching all the fish this year, or catching none, you can strike an exact balance that will not only preserve the fish population, but make sure that you can net a catch of the same size next year, and the year after that and so on, both maximizing profit and preserving the environment - no wait - proving that you can maximize profit by preserving the environment.

You can use this with health care dollars, or your own work-habits.

Math: It's hot stuff.

Comments

[hundun.livejournal.com]

For example:

Every day I'm late with this paper, I lose 5%

Every extra day I spend on it, I gain at a semi-determinate rate of dimisishing returns that has an asymptote of 100% as t approaches infinity (a negative decay function).

How much longer should I spend on this paper?

[mocks.livejournal.com]

Bah. I had a response. Livejournal ate it, and now I'm tired and bitchy because it makes me feel like I don't know how to use a computer.

To sum up, my father does this sort of calculation for a living, more or less. It's neat and frighteningly applicable and obvious when it boils down to qualitative statements ("An industry that makes lots of money, but consumes itself after 50 years is actually less profitable, even in a strictly economic sense than one that will last 200 without breaking a sweat.")

[hundun.livejournal.com]

Ooh. I'm interested. What exactly does he do?

[(Anonymous)]

His field is sustainable development and research management. When I say it's his job to do these calculations, I think in reality it's more like his job to encourage others to think this way: he's chair or something of the Centre for Sustainable Transportation at the university of Winnipeg.

er, here: http://cst.uwinnipeg.ca/

His thesis (he finished last September!) was in biogas as an energy source, I believe, but I couldn't give you details off the top of my head.

[mocks.livejournal.com]

Graar! I'm going to bed, because I'm technologically incompetent right now.

[medousa.livejournal.com]

Do you have a green waterbottle?
Perhaps one that went missing between Saturday afternoon and Sunday morning?

[hundun.livejournal.com]

Indeed I do.
Thanks.

[freedryk.livejournal.com]

The problem with optimization theory is the part when you reduce the system to as few variables as possible, cause it doesn't work. Most natural systems are inherently non-linear in a huge range of variables, so that while most of them are not important most of the time, occasionally one becomes very important overnight. So, while it works great for, say, figuring out the ratio of the height to the radius of a cylinder that will hold as much liquid as possible while using as little aluminum as you can, it doesn't work so good for fish stocks.

Just off the top of my head, fish don't reproduce at a 'given' rate, but a rate that changes depending on their environment, and environmental conditions change nearly randomly on a year-to-year timescale, as well as being highly variable in space. Then you get someone inventing something like DDT and the next year, half the fish die for no apparent reason.

Furthermore, there was at least one paper that showed the best method to maximize profit would be to catch all the fish in one year, then take the profits and invest them. Over 50 years, the action of compound interest gives far more profit than steady fishing ever could.

Finally, if you think optimization theory is hot, you should check out Variational Calculus. It'll blow your mind.

[osmie]

...and here I thought she was talking about variational calculus. What then is this optimization theory I know nothing of?

[hundun.livejournal.com]

Good to know.