A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> G. CONSTRAINT HANDLING TECHNIQUES <s> This paper modifies the replacement and update scheme in MOEA/D-DE developed in [1] for dealing with constraints in multiobjective optimization problems. The modified scheme introduces a penalty function to penalize infeasible solutions. The penalty function uses a threshold to control the amount of penalty to infeasible solutions. Experimental results have shown that this penalty method is very promising. <s> BIB001 </s> A Survey of Multiobjective Evolutionary Algorithms Based on Decomposition: Variants, Challenges and Future Directions <s> G. CONSTRAINT HANDLING TECHNIQUES <s> This paper proposes an improved epsilon constraint handling method embedded in the multi-objective evolutionary algorithm based on decomposition (MOEA/D) to solve constrained multi-objective optimization problems (CMOPs). More specifically, it dynamically adjusts the epsilon level, which is a critical parameter in the epsilon constraint method, according to the feasible ratio of solutions in the current population. In order to verify the effect of the improved epsilon constraint handling method, three algorithms - MOEA/D-CDP, MOEA/D-Epsilon, and MOEA/D-IEpsilon (MOEA/D with the improved epsilon constraint handling mechanism) are tested on nine CMOPs (CMOP1-CMOP9). The comprehensive experimental results indicate that the proposed epsilon constraint handling method is very effective on the performance of both convergence and diversity. <s> BIB002
Various constraint handling techniques have been well integrated into MOEA/D to solve CMOPs. The penalty function method BIB001 is simple to operate, but it remains difficult to select the appropriate penalty factor for a specific problem. The mechanism that treats objectives and constraints separately BIB002 does not require any parameters, and thus it is more efficient and universal than the penalty function method. The repair algorithm  is another way to convert infeasible solutions into feasible ones, which can effectively avoid the search falling into the local optimum. However, each algorithm is always suitable for the specific problem only. Therefore, it is necessary to design suitable constraint handling techniques for different problems, which requires a comprehensive consideration of the characteristics of practical problems and algorithm implementation difficulty.