Network Models for Multiobjective Discrete Optimization

TL;DR

This paper introduces a network modeling framework for multiobjective discrete optimization that efficiently computes the Pareto frontier, significantly outperforming existing algorithms across various problem classes.

Contribution

The paper presents a novel network-based approach for multiobjective discrete optimization, including techniques for network simplification to accelerate Pareto frontier computation.

Findings

Orders-of-magnitude performance improvements over state-of-the-art algorithms

Effective network simplification techniques for faster Pareto frontier identification

Applicable to both linear and nonlinear objective functions

Abstract

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework formulates these problems as network models, in that enumerating the Pareto frontier amounts to solving a multicriteria shortest path problem in an auxiliary network. We design techniques for exploiting the network model in order to accelerate the identification of the Pareto frontier, most notably a number of operations to simplify the network by removing nodes and arcs while preserving the set of nondominated solutions. We show that the proposed framework yields orders-of-magnitude performance improvements over existing state-of-the-art algorithms on five problem classes containing both linear and nonlinear objective functions.