We follow optimisation research and contribute to open source

Optimisation started as a wartime planning problem and turned into a field. The simplex method arrived in 1947, and the fifteen years after it produced most of the machinery still running today: dynamic programming, cutting planes, branch and bound, shortest paths, and the decompositions that let one large problem be solved as a series of small ones.

Then Karp showed, in 1972, why the work would never be finished. A whole family of ordinary planning problems has no known efficient exact algorithm, and none has been found since. The response was not one better algorithm but many, borrowed from wherever they could be found: simulated annealing from metallurgy, tabu search from the idea of a short memory, genetic algorithms and ant colony optimisation from biology, constraint programming from logic, and large neighbourhood search from the observation that a good plan is usually a small edit away from a better one.

None of them won, and that is the point. Each is strong on a shape of problem the others handle badly, so the field kept all of them and learned to combine them: exact search steered by heuristics, constraint propagation backed by clause learning, and lately branching decisions learned from data. The last few years added first-order methods and GPUs, which reopened linear programs at sizes the simplex method was never built for.

Julia is where a lot of current optimisation research is written. It runs at the speed the solvers need and reads close to the mathematics, so a paper and its implementation stay recognisably the same thing.

JuMP sits on top of it. Describe a problem once, in near-mathematical syntax, then hand it to any of more than 30 solver backends behind one interface. It is the de-facto standard in the Julia community and the backbone of optimisation research across European universities, including UCLouvain, where parts of our team trained.

We work on it rather than only with it. Members of the team ship pull requests against the core packages, maintain solver interfaces, and present at the JuMP-dev workshop.

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