COARSE-EMOA: An Indicator-based Evolutionary Algorithm for Solving Equality Constrained Multi-objective Optimization Problems Jes´ us L. Llano Garc´ ıa a,* , Ra´ ul Monroy a , V´ ıctor Adri´ an Sosa Hern´ andez a , Carlos A. Coello Coello b a Tecnologico de Monterrey, School of Engineering and Sciences, Av. Lago de Guadalupe Km 3.5, Atizap´ an de Zaragoza, Edo. Mexico 52926, MEXICO b CINVESTAV-IPN (Evolutionary Computation Group), Department of Computer Science, Av. IPN No. 2508, Mexico City 07360, MEXICO Abstract Many real-world applications involve dealing with several conflicting objectives which need to be optimized simultaneously. Moreover, these problems may re- quire the consideration of limitations that restrict their decision variable space. Evolutionary Algorithms (EAs) are capable of tackling Multi-objective Opti- mization Problems (MOPs). However, these approaches struggle to accurately approximate a feasible solution when considering equality constraints as part of the problem due to the inability of EAs to find and keep solutions exactly at the constraint boundaries. Here, we present an indicator-based evolutionary multi- objective optimization algorithm (EMOA) for tackling Equality Constrained MOPs (ECMOPs). In our proposal, we adopt an artificially constructed refer- ence set closely resembling the feasible Pareto front of an ECMOP to calculate the Inverted Generational Distance of a population, which is then used as a density estimator. An empirical study over a set of benchmark problems each of which contains at least one equality constraint was performed to test the capabilities of our proposed COnstrAined Reference SEt - EMOA (COARSE- EMOA). Our results are compared to those obtained by six other EMOAs. As will be shown, our proposed COARSE-EMOA can properly approximate a fea- sible solution by guiding the search through the use of an artificially constructed set that approximates the feasible Pareto front of a given problem. Keywords: Multi-Objective Optimization, Performance Indicators, Constrained Optimization, Evolutionary Algorithms ⇤ Corresponding author Email addresses: jesus_llg@tec.mx (Jes´ us L. Llano Garc´ ıa), raulm@tec.mx (Ra´ ul Monroy), vsosa@tec.mx (V´ ıctorAdri´anSosaHern´andez), ccoello@cs.cinvestav.mx (Carlos A. Coello Coello) Preprint submitted to Swarm and Evolutionary Computation August 20, 2021 0DQXVFULSW )LOH &OLFN KHUH WR YLHZ OLQNHG 5HIHUHQFHV