Musings of an Analyst

My father’s recent passing has me reflecting on some of the things that he taught me that I am only able to begin to fully appreciate as I get older.  He owned and managed a plumbing, heating, and air conditioning business for decades.  On breaks and during the summer, I worked in various jobs for him until I finished graduate school.  

When we were working on a job, he would often say “don’t let the house stand in the way of the project”. Like many sayings that I remember, this one is a combination of wisdom and humor.  For plumbing and HVAC projects, this often meant cutting a hole where a hole was needed, running power to where power was needed rather than limiting HVAC installs to where power was currently available, or moving other obstacles to accommodate the project.  The idea embedded in “don’t let the house stand in the way of the project” extends beyond plumbing and HVAC to other industries and captures a key consideration in applying optimization procedures.

In optimization procedures, the big idea is to find the “best” possible combination of attributes in an objective sense.  Oftentimes, there are constraints that limit the possible solution space.  In mechanism design, these constraints can include considerations like packaging and clearance constraints for landing gear stowage in an airplane, weight, and material capability.  In control systems, these constraints can include considerations like actuator load, power limitations, and control-structure frequency interactions that need to be avoided.

In a constrained optimization problem, an “active” constraint means that one of the problem’s constraints or limitations is defining the solution.  That particular constraint is preventing you from realizing the “best” solution.  And, this where the wisdom of not letting the house stand in the way of the project comes in.  Not letting the house stand in the way of the project really means finding a way to keep a constraint or a limitation from keeping you from realizing the “best” outcome.

Lots of projects start out with intentions of designing around an existing something.  This can be a wall in a house or a subsystem that we would rather reuse than replace in a project.  Oftentimes, it can be difficult to know when to accept the constraint and work around it and when to find a way to address the constraint head on.  As I look back on my career and reflect on the idea behind “don’t let the house stand in the way of the project,” I realize that accepting constraints too early and building project plans around those constraints too early often results in outcomes that are suboptimal that could have been avoided.

As I reflect on what that means for me, the big lesson is to think as hard about how to relax active constraints as I do about optimizing around those constraints.