Multi-indicator based multi-objective evolutionary algorithm with application to neural architecture search

\({\mathbf{I}}_{{\mathbf{SDE}}^{+}}\) is proven to be one of the leading scalable indicator for evolutionary multi and many-objective optimization. However, it fails to segregate members of a given population beyond the first front as a large number of solutions in the population have identical \({\mathbf{I}}_{{\mathbf{SDE}}^{+}}\) values. This mainly affects the performance of the algorithm when handling optimization problems with lower objectives. Consequently, we hypothesize that the overall performance of the algorithm can be further improved by introducing a categorization mechanism similar to the categorization of Pareto Fronts (PFs) in dominance-based methods. Therefore, in this work, we propose a Multi-Indicator-Based Multi-Objective Evolutionary Algorithm (MI-MOEA) which categorizes all the solutions into different fronts. Specifically, the indicators are based on the popular \({\mathbf{I}}_{{\mathbf{SDE}}^{+}}\) indicator and make use of the minimum and median distance values among the different distances when the solutions with better Sum of Objectives (SOB) are projected. The use of these two \({\mathbf{I}}_{{\mathbf{SDE}}^{+}}\)-based indicator values features an efficient balance of exploration and exploitation. To evaluate the performance of the proposed MI-MOEA, Neural Architecture Search (NAS) which involves the design of appropriate architectures suitable for specific applications is employed. From an optimization perspective, NAS involves multiple conflicting objectives that needs to be simultaneously optimized. In this paper, we consider a recently proposed multi-objective NAS benchmark and favorably evaluate the performance of MI-MOEA compared to other state-of-the-art MOEAs.