PaMILO: A Solver for Multi-Objective Mixed Integer Linear Optimization and Beyond

TL;DR

PaMILO is the first solver designed to find non-dominated extreme points in multi-objective mixed integer linear and quadratic programs, expanding capabilities in multi-objective optimization with a new adaptable algorithm.

Contribution

Introduces PaMILO, a novel solver for MOMILPs and MOMIQCQPs, adapting the Dual-Benson algorithm for broader multi-objective problem classes.

Findings

Successfully implements PaMILO with CPLEX and Gurobi integration.

Provides an adaptable framework for future multi-objective problem classes.

Enables efficient computation of non-dominated extreme points.

Abstract

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. It can be found on github under github.com/FritzBo/PaMILO. 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.