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

翻译：约束多目标进化算法（CMOEA）的有效性取决于其在进化过程中利用不可行解信息、优化多个冲突目标的同时，抵达不同可行区域的能力。多年来，研究者已提出多种CMOEA以处理约束多目标优化问题（CMOP）。然而，现有CMOEA大多基于分解或基于帕累托，针对基于指标的CMOEA研究较少。文献中多数基于指标的CMOEA采用以下策略：a) 使用求解无约束多目标问题的传统指标，通过目标值计算指标值并将其与总体约束违反度结合，将CMOP作为单目标约束问题求解；或b) 将每个约束或总体约束违反度作为附加目标与实际目标共同优化。本文提出一种有效的单种群基于指标的CMOEA——IcSDE+，能够探索搜索空间中的不同可行区域。IcSDE+是一种高效融合约束违反度（c）、基于偏移的密度估计（SDE）与目标求和（+）的指标。在6个具有不同特征的基准测试套件上，将采用IcSDE+的CMOEA与9种最先进的CMOEA进行性能对比，结果验证了其优越性。