A Fitness-assignment Method for Evolutionary Constrained Multi-objective Optimization
Oladayo S. Ajani, Sri Srinivasa Raju M, Anand Paul, Rammohan Mallipeddi
TL;DR
This work tackles constrained multi-objective optimization by introducing IcSDE+—a simple, single-population fitness-assignment-based CMAE that fuses constraint violation, shift-based density estimation, and sum-of-objectives. The authors formalize SOB and SDE, then derive I^c_{SDE^+} to guide selection toward feasible, convergent, and diverse solutions while promoting exploration across infeasible barriers. Through extensive experiments on six benchmark suites and comparisons with nine state-of-the-art CMOEAs, IcSDE+ demonstrates competitive and often superior performance, while maintaining computational efficiency typical of single-population methods. The results highlight the value of combining CV, SOB, and SDE in a unified fitness framework, with practical implications for robust CMOP optimization in diverse problem landscapes.
Abstract
The effectiveness of Constrained Multi-Objective Evolutionary Algorithms (CMOEAs) depends on their ability to reach the different feasible regions during evolution, by exploiting the information present in infeasible solutions, in addition to optimizing the several conflicting objectives. Over the years, researchers have proposed several CMOEAs to handle Constrained Multi-objective Optimization Problems (CMOPs). However, most of the proposed CMOEAs with scalable performance are too complex because they are either multi-staged or multi-population-based algorithms. Consequently, to ensure the simplicity of CMOEAs, researchers have proposed different fitness-assignment-based CMOEAs by combining different fitness-assignment-based methods used to solve unconstrained multi-objective problems with information regarding the feasibility of each solution. The main performance drawback of such methods is that it is difficult to design a fitness assignment method that can account for constraint violation in addition to convergence and diversity. Hence in this paper, we propose an effective single-population fitness assignment-based CMOEA referred to as IcSDE+ that can explore different feasible regions in the search space. IcSDE+ is a fitness assignment-based algorithm, that is an efficient fusion of constraint violation (c), Shift-based Density Estimation (SDE), and sum of objectives (+). The performance of IcSDE+ is favorably compared against 9 state-of-the-art CMOEAs on 6 different benchmark suites with diverse characteristics.