Practical Optimization Theory

My perspective on where and why mathematical optimization methods are commonly implemented in the commercial wild, sometimes as the Prescriptive component following earlier Predictive and/or Descriptive components in a modern Data Science pipeline.

A whirlwind tour through the main problem types in the field of Combinatorial Optimization with an emphasis on their various real-world commercial implementations.

Discussing the attributes of an optimization problem which make it harder to solve: combinatorial explosions, a lack of exploitable graph or other structure, etc. Also, a look at the usefulness of concepts like NP-hardness and Big O in addressing optimization problem hardness.

A look at various optimization methods such as Stochastic data perturbation, dynamic solving, multi-objective optimization, pattern generation, heuristic and Metaheuristic solvers, and more.

An invitation to consider the application of mathematical optimization in light of the view expressed by Kenneth O. Stanley and Joel Lehman in their book ‘Why Greatness Cannot Be Planned’ (2015). I posit that a richness of possible solutions can in many use cases be more valuable than a closer-to-optimum objective value.