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• A fast hypervolume approximation algorithm is proposed that accelerates the hypervolume calculation with a steady accuracy error, through a segmentation strategy and the Monte Carlo simulation. The proposed algorithm achieves ten times faster than other compared algorithms in experiments. • Base on above the fast approximation method, an incremental version algorithm is proposed to solve many objective optimization problem and promotes the performance of hypervolume based algorithms. Hypervolume indicator based evolutionary algorithms have been reported to be very promising in many-objective optimization, but the high computational complexity of hypervolume calculation in high dimensions restrains its further applications and developments. In this paper, we develop a fast hypervolume approximation method with both improved speed and accuracy than the previous approximation methods via a new segmentation strategy. The proposed approach consists of two crucial process: segmentation and approximation. The segmentation process recursively finds areas easy to be measured and quantified from the original geometric figure as many as possible, and then divides the measurement of the rest areas into several subproblems. In the approximation process, an improved Monte Carlo simulation is developed to estimate these subproblems. Those two processes are mutually complementary to simultaneously improve the accuracy and the speed of hypervolume approximation. To validate its effectiveness, experimental studies on four widely-used instances are conducted and the simulation results show that the proposed method is ten times faster than other comparison algorithms with a same measurement error. Furthermore, we integrate an incremental version of this method into the framework of SMS-EMOA, and the performance of the integrated algorithm is also very competitive among the experimental algorithms. [ABSTRACT FROM AUTHOR]

To improve the utilization of infrastructure resources and reduce the cost of operators in the future 6G network construction, a 6G shared base stations optimization model is proposed in this paper, which is a bi-level multiobjective optimization problem (BLMOP). In such a BLMOP, the tower company is responsible for the construction of base stations at the upper level, while operators share the base station resources of the tower company at the lower level. In addition, we also propose two strategies to solve the optimization efficiently. First, we use surrogate models to fit lower-level Pareto fronts (PF), then the degree of lower-level optimality constraint violation is converted to distance between the candidate solutions and the approximate lower level PF. So the BLMOP is transformed to a single-level constrained multi-objective optimization problem. Second, to accelerate the current lower-level optimization, we migrate the modified population from the adjacent lower-level optimization tasks. These two strategies effectively reduce the computational overhead. Compared with three existing works, the proposed method has achieved the best or comparable results on 7 benchmark problems and 5 generated test instances with less computation overhead, whose efficiency has been confirmed. [ABSTRACT FROM AUTHOR]