Local Optima

I currently work for a logistics software service provider. In my daily life, I deal with optimization quite frequently. We use a third-party software quite a bit for the optimization tasks. For some reason, it does not behave exactly the way that some of the people in the company believe it should behave. Since I don't like not knowing anything I have to deal with, I have started looking at optimization algorithms myself, to educate myself about what is to be expected with optimization software.

There are different algorithms out there, of course, and I am not going to get into details about any of them. I just want to mention one aspect of some of the algorithms: the need to avoid getting stuck in local optima. Since many algorithms for hard problems, not just for optimization, tend to use some kind of heuristics to get a solution first, and then improve it, avoiding being stuck in local optima is of course very important. And it is funny to see how easy many algorithms will get you into a local optimum. Preventing that from happening or to get out of that situation is then quite important to improve the quality of the eventual solution.

In life, the same kind of situations happen all the time whenever we are faced with a life decision. One simple algorithm that most people use in those situations is to find out all the possible decisions, and choose the best one. When the next situation arises, choose the best for that situation, and so on. If you project all these decisions over the lifetime, you will see that you can get into a local optimum if you simply look at the current situation without thinking about the "big picture". That is why people think back in life when they retire. The roads not travelled can haunt you when you can't go back and you can clearly see what these not-travelled roads could have led you to.

If you think about how people behave in extreme situations, and wonder why they don't see the inevitability of something much worse happening by choosing the best decision so far, you now understand the reason. For instance, suppose you are a taxi driver; and you have just picked up a fare who is pointing a gun at you asking for you to drive to a secluded area, what would you do? Follow the instruction will give you a few more minutes of not being harmed, but you might be shot anyway once you arrive there; not following the instruction means you might be shot right there. What to do?

This is an extreme situation, of course, and probably best studied using game theory rather than a search algorithm. But it does point out the problem with our normal way of making situation: what is the best for me right now?

It is funny how this little epiphany changes the way I look at how people make decisions. And I no longer evaluate people's decisions the same way.