A method to identify a representation of the set of non-dominated points for discrete tri-objective optimization problems

Abstract

Solving a discrete tri-objective optimization problem involves generating a set of non-dominated points. Most generation methods aim to identify all the non-dominated points to understand the trade-off between conflicting objectives. Finding all the non-dominated points is computationally demanding, which may discourage decision-makers from using generation methods that identify all the non-dominated points. Therefore, it is beneficial to identify a good representation of the Pareto front. In this work, we present an algorithm for computing a representation of the Pareto front for discrete tri-objective optimization problems for a user-defined coverage gap. Further, we present a parallelization approach to decompose the criterion space while avoiding redundancies. We present constrained coverage gap to measure performance of algorithms when the problems have incommensurable objective functions. Our algorithm is computationally compared with the state-of-the-art algorithms Grid point based algorithm (GPBA-A; Mesquita-Cunha et al., (2023) and Territory-defining algorithm (TDA; Ceyhan et al., (2019)). While our primary motivation comes from industrial applications of the generalized tri-objective tactical resource allocation problem (GTRAP; Fotedar et al., (2023)), we have also performed tests on standard benchmark instances of the multi-dimensional tri-objective knapsack problem (3KP) to further validate our approach. Out of 300 instances of 3KP, our proposed algorithm performs best (computationally) in 264 instances. For GTRAP, our algorithm is computationally superior in all the instances.