PaMILO:多目标混合整数线性优化及以后的解决方案 (PaMILO: A Solver for Multi-Objective Mixed Integer Linear Optimization and Beyond)

In multi-objective optimization, several potentially conflicting objective functions need to be optimized. Instead of one optimal solution, we look for the set of so called non-dominated solutions. An important subset is the set of non-dominated extreme points. Finding it is a computationally hard problem in general. While solvers for similar problems exist, there are none known for multi-objective mixed integer linear programs (MOMILPs) or multi-objective mixed integer quadratically constrained quadratic programs (MOMIQCQPs). We present PaMILO, the first solver for finding non-dominated extreme points of MOMILPs and MOMIQCQPs. PaMILO provides an easy to use interface and is implemented in C++17. It solves occurring subproblems employing either CPLEX or Gurobi. PaMILO adapts the dual-benson algorithm for multi-objective linear programming (MOLP). As it was previously only defined for MOLPs, we describe how it can be adapted for MOMILPs, MOMIQCQPs and even more problem classes in the future.

翻译：在多目标优化中,需要优化几个可能相互冲突的目标函数。我们不是寻找一个最佳解决方案, 而是寻找一套所谓的非主导性解决方案。一个重要子集是一组非主导性极端点。发现这是一个一般的计算困难问题。虽然存在类似问题的解决方案, 但对于多目标混合线性程序( MOMILPs) 或多目标混合四面形限制四面形程序( MOMIQQPs ), 没有已知的多目标混合线性线性程序( MOMIQCQPs ) 或多目标混合四面形限制四面形程序( MOMIQQPs ) 。我们介绍的是PAMILIO, 这是第一个找到MOMILPs、 MOMIQQPs 以及未来更多问题类的解决方案。我们描述它如何适应MOMILPs、 MOMIQPs 和更多问题类的解决方案。