There are plenty of songs that appeal to the theme of applied mathematics and operations research. Among those, bands that perform djent music – a style of metal music often referred to as math-metal – favor the use of compressed, low-tone guitar riffs as well as names and lyrics that have a strong math reference. For instance, the British formation TesseracT may well be the highest dimensional metal band related to a regular polytope.

As some of you may know, in addition to OR, I also have a passion for music.As such, I would like to join the trend and form a band devoted to both operations research and djent music. The band would probably be called Eigenvector, unless someone has a better name to propose. The band would write lengthy compositions which would be submitted to a peer review process of masked djent musicians from established bands.

The chapters of the first album are currently in progress:

1. Symphony of Disjunctions (Megadeth tribute)
2. Davy Jones’ ship has a convex hull
3. Our basis is optimal
4. Please be my dual
5. The largest clique in town (is NP-hard to find)
6. Top model
7. You’re exceeding my (Markovitz) tolerance
8. Something about this barrier

That question came to me at the INFORMS Annual Conference. Am I really developing something new or am I just re-using and tuning the same methods over and over? What about my colleagues?

For the most part, we spend a lot of time refining and improving upon methods that were published in the early 60s: branch-and-bound, Benders’ and Dantzig-Wolfe decomposition, Lagrangean relaxation, and others. Even the more recent methods (branch-and-cut, integer L-shaped, etc.) are often based on components developed in the 60s.

This is not to say that recent research is not relevant or significant. By enhancing the strengths of existing methods and removing some of their weaknesses (slow convergence, performance problems, cycling issues) we in fact allow larger and more complex problems to be solved. And there is the application of OR models on real-world problems, too. The Interfaces journal is full of models that actually helped save millions of dollars, if not lives.

That being said, the tools and methods we use often require some tuning. Performance of solvers can often be improved for a specific problem by fine-tuning its parameters. The most popular metaheuristics also require some key parameters to be set. This leads to the “sometimes it performs better, sometimes worse” talking point that we say and hear so often. Taburoute, the popular method for the VRP by Gendreau et al. [1] uses a vector of 9 parameters.

Moreover, our current paradigms in research publications (10- to 20-page journal articles) require our contributions to be as focused as possible. Either define a new variant of a known problem and solve it, or find an improved way of solving a known problem. More general techniques are either presented as theoretical contributions or tested on a generic problem such as the traveling salesman problem.

However, the contributions that go beyond these limitations often have a large impact, such as the publication of the tabu search heuristic by Glover. Around 20 years ago, a wave of generic MIP heuristics such as the feasibility pump and the local branching paper of Fischetti and Lodi [2] have let to considerable improvements in MIP solvers.

[1] Gendreau, M., Hertz, A., & Laporte, G. (1994). A tabu search heuristic for the vehicle routing problem. Management science, 40(10), 1276-1290. (more than 880 citations)
[2] Fischetti, M., & Lodi, A. (2003). Local branching. Mathematical Programming, 98(1), 23-47.