Gradient-Informed Pareto-Based Multi-Objective Binary Topology Optimization

Multi-objective topology optimization (TO) problems frequently arise in practical engineering applications, necessitating the identification of Pareto-optimal solutions. This article introduces a gradientin-formed Pareto-based multi-objective TO algorithm with binary decision variables, called GPBTO, tailored to constrained bi-objective optimization problems (CBOPs), a common scenario in engineering design. By leveraging a binary decision space and incorporating a linearization step for objectives and constraints, the method enables the use of efficient integer linear programming (ILP) techniques for evolving the decision vector. Unlike traditional weighted sum (WS) approaches, which are widely used in TO despite their known limitations, GPBTO provides an alternative that integrates gradient-based formulations while facilitating the identification of Pareto-optimal solutions. While WS remains a dominant method in TO, GPBTO represents a promising alternative for cases where Pareto-based solutions are desirable. To the best of the authors’ knowledge, this is the first attempt to integrate Pareto-based TO with binary variables and gradient information, highlighting its potential for further exploration and application.