Surrogate-guided multi-objective optimization (SGMOO) using an efficient online sampling strategy

Three-objective optimization of micromixer with Cantor fractal structure based on Pareto genetic algorithm

This paper introduces the multi-objective optimization process of the micromixer with Cantor fractal baffle. The combination of fractal principle and multi-objective optimization is a main feature of this article. The three-dimensional Navier–Stokes equation is used to numerically analyze the fluid flow and mixing. The proxy modeling and Pareto genetic algorithm are used to optimize the shape of the Cantor fractal micromixer. We choose three parameters related to the geometry of the Cantor fractal baffle as design variables, and choose the mixing index, pressure drop and mixing sensitivity at the outlet of the micromixer as three objective functions. For the parameter study of the design space, the Latin hypercube sampling (LHS) method is used to select design points in the design space. We use response surface function (RSA) as a proxy modeling to approximate the objective function. A multi-objective genetic algorithm is used to find the Pareto optimal solution. K-means clustering is used to classify the optimal solution set, and then select representative design variables from it. The representative optimal design is analyzed by using numerical analysis method. The optimization results show that the Cantor fractal baffle is beneficial to promote faster mixing of the two fluids. At the same time, the suitable goal can be weighed in the Pareto optimal solution set. The mixing index and mixing sensitivity are increased by 13.55  and 3.91 %, respectively, compared with the reference design of the micromixer. And we have also proved that this multi-objective optimization method is applicable to any Reynolds numbers (Res).

A constrained multi-objective optimization algorithm using an efficient global diversity strategy

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.