evolutionary constrained multiobjective optimization has received extensive attention and research in the past two decades, and a lot of benchmarks have been proposed to test the effect of the constrained multiobjecti...
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evolutionary constrained multiobjective optimization has received extensive attention and research in the past two decades, and a lot of benchmarks have been proposed to test the effect of the constrainedmultiobjectiveevolutionary algorithms (CMOEAs). Especially, the constraint functions are highly correlated with the objective values, which makes the features of constraints too monotonic and differ from the properties of the real-world problems. Accordingly, previous CMOEAs cannot solve real-world problems well, which generally involve decision space constraints with multimodal/nonlinear features. Therefore, we propose a new benchmark framework and design a suite of new test functions with scalable high-dimensional decision space constraints. To be specific, different high-dimensional constraint functions and mixed linkages in variables are considered to be close to realistic features. In this framework, several parameter interfaces are provided, so that users can easily adjust the parameters to obtain the variant functions and test the generalization performance of the algorithms. Different types of existing CMOEAs are employed to test the use of the proposed test functions, and the results show that they are easy to fall into local feasible regions. Therefore, we improve one evolutionary multitasking-based CMOEA to better handle these problems, in which a new search algorithm is designed to enhance the search abilities of populations. Compared with the existing CMOEAs, the proposed CMOEA presents better performance.
multiobjective-based constraint-handling techniques are popular in evolutionaryconstrained single-objective optimization. However, most of these techniques run into troubles when dealing with constrained multiobjecti...
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multiobjective-based constraint-handling techniques are popular in evolutionaryconstrained single-objective optimization. However, most of these techniques run into troubles when dealing with constrainedmultiobjectiveoptimization problems (CMOPs). That is, they have difficulty optimizing too many objective functions, are ineffective in maintaining population diversity, or are challenged in establishing appropriate additional objective functions. As a remedy to these limitations, we propose a novel technique called NRC for handling CMOPs. The novelty of NRC lies in its three sorting procedures: 1) nondominated sorting;2) reversed nondominated sorting;and 3) constrained crowding distance sorting, which are performed in sequence to provide driving forces toward the Pareto front (PF) of a transformed unconstrainedmultiobjectiveoptimization problem (treating the overall constraint violation as an additional objective function), the boundary front, and the constrained PF, respectively. With the combination of these three different forces, NRC can conveniently approach the desired PF from diverse search directions. The effectiveness of NRC is experimentally verified. Also, we incorporate NRC into a two-archive mechanism and develop a novel constrainedmultiobjectiveevolutionary algorithm, called NRC2. Comprehensive experiments on 49 benchmark CMOPs and 21 real-world ones demonstrate that NRC2 is significantly superior or comparable to six state-of-the-art constrainedevolutionarymultiobjective optimizers on most test instances.
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