Abstract
Over the past 2 decades, several multi-objective optimizers (MOOs) have been proposed to address the different aspects of multi-objective optimization problems (MOPs). Unfortunately, it has been observed that many of MOOs experiences performance degradation when applied over MOPs having a large number of decision variables and objective functions. Specially, the performance of MOOs rapidly decreases when the number of decision variables and objective functions increases by more than a hundred and three, respectively. To address the challenges caused by such special case of MOPs, some large-scale multi-objective optimization optimizers (L-MuOOs) and large-scale many-objective optimization optimizers (L-MaOOs) have been developed in the literature. Even after vast development in the direction of L-MuOOs and L-MaOOs, the supremacy of these optimizers has not been tested on real-world optimization problems containing a large number of decision variables and objectives such as large-scale many-objective software clustering problems (L-MaSCPs). In this study, the performance of nine L-MuOOs and L-MaOOs (i.e., S3-CMA-ES, LMOSCO, LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA) is evaluated and compared over five L-MaSCPs in terms of IGD, Hypervolume, and MQ metrics. The experimentation results show that the S3-CMA-ES and LMOSCO perform better compared to the LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, H-RVEA, and DREA in most of the cases. The LSMOF, LMEA, IDMOPSO, ADC-MaOO, NSGA-III, and DREA, are the average performer, and H-RVEA is the worst performer.
Highlights
The real-world science and engineering optimization problems generally comprise a large number of decision variables and objective functions with various associated constraints [1]
We present the inverted generational distance (IGD), Hypervolume, and modularization quality (MQ) results obtained through the selected metaheuristic optimizers—S3-CMA-ES, LMOSCO, Large-scale multi-objective optimization framework (LSMOF), large-scale many-objective optimization (LMEA), IDMOPSO, ADC-MaOO, NSGA-III, hypervolume indicator (H-reference vectorguided evolutionary algorithm (RVEA)), and Diversity ranking-based evolutionary algorithm (DREA)
The IGD, Hypervolume, and MQ results of each optimizer corresponding to the number of decision variables and objective functions are shown in Tables 3, 4, and 5, respectively
Summary
The real-world science and engineering optimization problems generally comprise a large number of decision variables and objective functions with various associated constraints [1]. The spaces where the decision variables and objective functions are defined are commonly referred to as decision space and objective space, respectively [2]. Based on the number of objective functions and decision variables, and their challenges to the MOOs metaheuristic search optimizers, the optimization problems can be categorized into six types: single-objective optimization problems (SOPs), multi-objective optimization problems (MOPs), many-objective optimization problems (MaOPs), large-scale single-objective optimization problems (L-SOPs), largescale multi-objective optimization problems (L-MOPs), and large-scale many-objective optimization problems (L-MaOPs) [1] [5,6,7,8]. The DREA uses the diversity ranking and reference vector adaptation approach to deal with the different issues of the Pareto front shapes
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