Abstract 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 lp-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.

中文翻译：

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在组合优化中使用 ℓ -范数实现公平性

摘要 公平问题受到了许多领域研究人员的关注，包括组合优化。推动解决方案公平的一种方法是使用涉及所谓的 lp 范数的修改后的目标函数。如果以幼稚的方式完成，这种方法会导致大型且对称的混合整数非线性规划 (MINLP)，这可能难以解决。我们表明，对于某些问题，可以获得更小、不受对称性影响且具有合理紧密连续松弛的替代 MINLP 公式。我们为某些车辆路线、设施位置和网络设计问题提供了令人鼓舞的计算结果。