Manic March #4: Constrained Optimization

March 4, 2022

Manic March - Constrained Optimization

Many problems can be rewritten in terms of an optimizable version. Utilitarian methods and chemical production plants alike may be determined by maximizing a variable. However, optimizing for one variable above all else may lead to negative outcomes; thus, we ought to attempt to contstrain optimization when possible.

The classic case against maximization in utilitarian thought is contained in Ursula le Guin’s short story Those Who Walk Away from Omelas, in which exists a perfect city, free of racism, sexism, and all the pains of daily life. This city is operating at maximum utility, meaning that each and every resident experiences the maximum amount of pleasure that they can. However, when a citizen comes of age, they learn that this has been achieved by the torture of an innocent child, permanently restrained below the city without human contact. In philosophy, this is an example of optimization run amok. By optimizing for happiness above all else, these people throw an essential value – empathy – under the bus. By maximizing pleasure and ignoring other variables, the city has allowed other variables to spiral downward without a lower bound.

A steelman (the strongest possible version) of this argument would be to say, that yeah, sure, a child is suffering. So what? There are billions of people in poverty, starving, without food or water, others experiencing war, terror, death, disease. Sacrificing one child to make billions of others’ lives immeasurably better is nothing in the face of all of this despair. If I could kill a kid to save my family, I would do it – why not the whole world too?

This is a strong argument. Faced with a button to sacrifice a child to eliminate all the ills of the world, I would likely find my finger hover over it for a fraction of a second more than this essay would have you believe. Still, we have a negative obligation to press the button, and further, we have a positive obligation to tear down Omelas instead. Optimization without bounds is a demon of the worst kind. A few examples of unconstrained optimization are below:

Optimization for Cars

Optimization for Profit

  • Throwing workers\charity under the bus for profit

Optimization for Education

I don’t think there’s an easy solution for optimization cases like this - optimization is a useful tool! But, we need to be aware when we are getting rid of other variables just to maximize one. On the engineering side, we can design a distillation column that produces pure ethanol and pure water, perfectly seperating the two. This also costs quite a lot of money, and isn’t necessary for all cases. There are tradeoffs for all optimization problems, and we need to consider all externalities before deciding that we have the right solution.

What is Manic March?

On February 27, 2022, I thought it would be a great idea to create some sort of content - writing, art, coding, etc. - every day of the next month. Luckily, the alliteration worked out. This should be the fourth post in the series.