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When the leader's objective function of a nonlinear bilevel programming problem is nondifferentiable and the follower's problem of it is nonconvex, the existing algorithms cannot solve the problem. In this paper, a new effective evolutionary algorithm is proposed for this class of nonlinear bilevel programming problems. First, based on the leader's objective function, a new fitness function is proposed that can be easily used to evaluate the quality of different types of potential solutions. Then, based on Latin squares, an efficient crossover operator is constructed that has the ability of local search. Furthermore, a new mutation operator is designed by using some good search directions so that the offspring can approach a global optimal solution quickly. To solve the follower's problem efficiently, we apply some efficient deterministic optimization algorithms in the MATLAB Toolbox to search for its solutions. The asymptotically global convergence of the algorithm is proved. Numerical experiments on 25 test problems show that the proposed algorithm has a better performance than the compared algorithms on most of the test problems and is effective and efficient.

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Clustering ensemble has drawn much attention in recent years due to its ability to generate a high quality and robust partition result. Weighted clustering ensemble and selective clustering ensemble are two general ways to further improve the performance of a clustering ensemble method. Existing weighted clustering ensemble methods assign the same weight to each cluster in a partition of the ensemble. Since the qualities of the clusters in a partition are different, the clusters should be weighted differently. To address this issue, this article proposes a new measure to calculate the similarity between a cluster and a partition. Theoretically, this measure is effective in handling two problems in measuring the quality of a cluster, which are defined as the symmetric problem and the context meaning problem. In addition, some properties of the proposed measure are analyzed. This measure can be easily expanded to a clustering performance measure that calculates the similarity between two partitions. As a result of this measure, we propose a novel selective clustering ensemble framework, which considers the differences between the objective of the ensemble selection stage and the object of the ensemble integration stage in the selective clustering ensemble. To verify the performance of the new measure, we compare the performance of the measure with the two existing measures in weighting clusters. The experiments show that the proposed measure is more effective. To verify the performance of the novel framework, four existing state-of-the-art selective clustering ensemble frameworks are employed as references. The experiments show that the proposed framework is statistically better than the others on 17 UCI benchmark datasets, 8 document datasets, and the Olivetti Face Database.

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