Many hard combinatorial problems ask for an permutation that minimizes the value of a function $f:\pi\mapsto\mathbb{R}$ that maps permutations to real values, the most prominent being the TSP.
But also other hard problems are functions of permutations, e.g.
- the Quadratic Assignment Problem
- the 3DCC, aka as GT13 of Computers and Intractability, which imposes lower bounds on the lengths of cycles in a cycle cover of a directed graph
- cycle covers with a cycles with lengths from a fixed collection of sizes
- Organ transplantation, which imposes upper bounds on the lengths of cycles in a cycle cover of a directed graph
- antidirected weighted Hamilton cycles where either the indegree or the outdegree of the vertices is zero
Question:
is there an established name for constrained or unconstrained optimization over permutations, that could be used in the title of a paper that is dedicated to algorithms for such problems?
In contrast, vertex cover does not ask for an optimal permutation.
