Network Models for Multiobjective Discrete Optimization

Abstract

This paper provides a novel framework for solving multiobjective discrete optimization problems with an arbitrary number of objectives. Our framework represents 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 network models 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. Summary of Contribution: Multiobjective optimization has a long history of research with applications in several domains. Our paper provides an alternative modeling and solution approach for multiobjective discrete optimization problems by leveraging graphical structures. Specifically, we encode the decision space of a problem as a layered network and propose graph reduction operators to preserve only solutions whose image are part of the Pareto frontier. The nondominated solutions can then be extracted through shortest-path algorithms on such a network. Numerical results comparing our method with state-of-the-art approaches on several problem classes, including the knapsack, set covering, and the traveling salesperson problem (TSP), suggest orders-of-magnitude runtime speed-ups for exactly enumerating the Pareto frontier, especially when the number of objective functions grows.