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When solving constrained multi-objective optimization problems (CMOPs), multiple conflicting objectives and multiple constraints need to be considered simultaneously, which are challenging to handle. Although some recent constrained multi-objective evolutionary algorithms (CMOEAs) have been developed to solve CMOPs and have worked well on most CMOPs. However, for CMOPs with small feasible regions and complex constraints, the performance of most algorithms needs to be further improved, especially when the feasible region is composed of multiple disjoint parts or the search space is narrow. To address this issue, an efficient global diversity CMOEA (EGDCMO) is proposed in this paper to solve CMOPs, where a certain number of infeasible solutions with well-distributed feature are maintained in the evolutionary process. To this end, a set of weight vectors are used to specify several subregions in the objective space, and infeasible solutions are selected from each subregion. Furthermore, a new fitness function is used in this proposed algorithm to evaluate infeasible solutions, which can balance the importance of constraints and objectives. In addition, the infeasible solutions are ranked higher than the feasible solutions to focus on the search in the undeveloped areas for better diversity. After the comparison tests on three benchmark cases and an actual engineering application, EGDCMO has more impressive performance compared with other constrained evolutionary multi-objective algorithms.

Aiming at the constrained optimization problem where function evaluation is time-consuming, this paper proposed a novel algorithm called data-driven Harris Hawks constrained optimization (DHHCO). In DHHCO, Kriging models are utilized to prospect potentially optimal areas by leveraging computationally expensive historical data during optimization. Three powerful strategies are, respectively, embedded into different phases of conventional Harris Hawks optimization (HHO) to generate diverse candidate sample data for exploiting around the existing sample data and exploring uncharted region. Moreover, a Kriging-based data-driven strategy composed of data-driven population construction and individual selection strategy is presented, which fully mines and utilizes the potential available information in the existing sample data. DHHCO inherits and develops HHO's offspring updating mechanism, and meanwhile exerts the prediction ability of Kriging, reduces the number of expensive function evaluations, and provides new ideas for data-driven constraint optimization. Comprehensive experiments have been conducted on 13 benchmark functions and a real-world expensive optimization problem. The experimental results suggest that the proposed DHHCO can achieve quite competitive performance compared with six representative algorithms and can find the near global optimum with 200 function evaluations for most examples. Moreover, DHHCO is applied to the structural optimization of the internal components of the real underwater vehicle, and the final satisfactory weight reduction effect is more than 18%.

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