Using lp-norms for fairness in combinatorial optimisation

The issue of fairness has received attention from researchers in many fields, including combinatorial optimisation. One way to drive the solution toward fairness is to use a modified objective function that involves so-called l(P)-norms. If done in a naive way, this approach leads to large and symmetric mixed-integer nonlinear programs (MINLPs), that may be difficult to solve. We show that, for some problems, one can obtain alternative MINLP formulations that are much smaller, do not suffer from symmetry, and have a reasonably tight continuous relaxation. We give encouraging computational results for certain vehicle routing, facility location and network design problems. (C) 2020 Elsevier Ltd. All rights reserved.