The Natural Order and Divine Law of Optimization

A recent article in the NYT Magazine by Virginia HeffernanA Sucker is Optimized Every Minute,” 3/19/15, contains an energetic indictment of Optimization, blaming the field for everything from Soviet gulags to Ayn Rand-ism, from web marketing to Hillary Clinton’s use of a private email account.

Michael Ferris
Michael Ferris

As an avowed creationist, Ms. Heffernan could have noted that the creation story in Genesis describes the very first optimization procedure in history! God started with a blank slate, then on each of the first six days, introduced a new dimension into his model and reoptimized. On the seventh day, God verified that an optimal solution had been found, and noted with some satisfaction that it was indeed very good.

Whether by design or accident, nature optimizes. The motions of stars, planets, and rays of light through the universe are governed by an optimization principle: the principle of least action. The shapes and functions of proteins –the building blocks of living organisms – are determined by a minimum-energy configuration of the molecule. Balls come to rest in valleys rather than on hillsides, because they seek a state of optimal potential energy. (Indeed, many of the procedures that we use in optimization follow nature’s example by stepping progressively downhill on the surface that describes the objective function.) The tendency of physical and biological systems to behave predictably, in accordance with optimization principles, underpins much of modern computational science and engineering.

Stephen Wright
Stephen Wright

Optimization provides frameworks for understanding the worlds of economics, finance, and technology as well – and not just of gulags and Soviet central planning. Modern microeconomics is founded on the assumption that individuals and corporations in a free-market economy are each optimizing their own measures of economic satisfaction. Their goals are often in conflict, but the fact that they are all behaving in a predictable way (by optimizing!) allows economists to model their interactions and the consequent outcomes for the full economic system. Optimization of investment portfolios – holding a collection of diverse assets to balance risk and rewards – has been a staple of financial planning since the 1950s. Today, corporations use optimization to plan their logistics and manage their distribution systems, make capital allocation decisions, and plan their day-to-day operations.

The tendency of physical and biological systems to behave predictably, in accordance with optimization principles, underpins much of modern computational science and engineering.

–Michael Ferris and Stephen Wright

Optimization techniques are being used to understand social networks and other Internet-based activities. Certainly, users may find some optimization-enabled aspects of Internet life annoying, or worse. But it has benefits too. The systems by which companies such as Netflix and Amazon are able to recommend movies or books of possible interest to a user are frequently on-target, and are made possible by optimization models informed by data about user preferences. As Ms. Heffernan intuits, such combinations of optimization methods with data are potent, and there’s no doubt that they can be used for ill. But there are an overwhelming number of beneficial applications as well, from the use of medical studies to determine the genetic basis of diseases, to the analysis of MRI images, to the detection of faults from sensor data on a power grid, to the smoother and more efficient operation of transportation networks.

Optimization can be misapplied and misused, often because, as in the examples cited by Ms. Heffernan that touch on lifestyle and personal satisfaction, it’s difficult to say precisely what it is that you want to optimize. But in areas where we have a clear idea of our goals, and of the various choices we can make that affect these goals, optimization provides a wealth of techniques for finding the optimal decisions. In other postings, we’ve described the impact of optimization on health care, numerous benefits for the environment and physical and economic systems. To read more about optimization and how it can be applied to interesting problems, read Optimizing the World  One Problem at a Time.

Michael Ferris and Stephen Wright