IcSDE+ -- An Indicator for Constrained Multi-Objective Optimization

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 CMOPs. However, among the different CMOEAs proposed most of them are either decomposition-based or Pareto-based, with little focus on indicator-based CMOEAs. In literature, most indicator-based CMOEAs employ - a) traditional indicators used to solve unconstrained multi-objective problems to find the indicator values using objectives values and combine them with overall constraint violation to solve Constrained Multi-objective Optimization Problem (CMOP) as a single objective constraint problem, or b) consider each constraint or the overall constraint violation as objective(s) in addition to the actual objectives. In this paper, we propose an effective single-population indicator-based CMOEA referred to as IcSDE+ that can explore the different feasible regions in the search space. IcSDE+ is an (I)ndicator, that is an efficient fusion of constraint violation (c), shift-based density estimation (SDE) and sum of objectives (+). The performance of CMOEA with IcSDE+ is favorably compared against 9 state-of-the-art CMOEAs on 6 different benchmark suites with diverse characteristics