As an essential data processing technology, cluster analysis has been widely used in various fields. In clustering, it is necessary to select appropriate measures to evaluate the similarity in the data. In this paper, firstly, a cluster center selection method based on the grey relational degree is proposed to solve the problem of sensitivity in initial cluster center selection. Secondly, combining the advantages of Euclidean distance, DTW distance, and SPDTW distance, a weighted distance measurement based on three kinds of reach is proposed. Then, it is applied to Fuzzy C-MeDOIDS and Fuzzy C-means hybrid clustering technology. Numerical experiments are carried out with the UCI datasets. The experimental results show that the accuracy of the clustering results is significantly improved by using the clustering method proposed in this paper. Besides, the method proposed in this paper is applied to the MUSIC INTO EMOTIONS and YEAST datasets. The clustering results show that the algorithm proposed in this paper can also achieve a better clustering effect when dealing with practical problems.

Improving transport efficiency is challenging for multimodal transport participants to improve cost-effectiveness. This paper proposes to select city nodes and establish a multi-objective fuzzy optimization model with mixed time window constraints to consider customer demand and transportation time uncertainty. T-rex Optimization algorithm (TROA) is used to solve the problem, which efficiently lowers transportation costs and carbon emissions and has higher precision and dependability than Particle Swarm Optimization (PSO) and Genetic Algorithm (GA). The efficacy of this method is proven using the example of the multimodal transportation network in China’s central-eastern economic zone. These findings provide potential solutions for multimodal transportation aimed at enhancing transportation efficiency.

In this paper, we consider a multistage feedback control strategy for producing 1,3‐propanediol in microbial continuous fermentation. Both the dilution rate and the concentration of glycerol in the input feed are used as control variables, and these variables are further assumed to be in the form of a linear combination of biomass and glycerol concentrations. Unlike the general form of linear feedback control, the coefficients of linear combination are continuous functions with respect to time. Inspired by the control parameterization method, we use the piecewise‐constant functions to approximate the coefficient functions; then we get the multistage feedback control law by solving nonlinear mathematical programming problems. Numerical results indicate the flexibility and effectiveness of our strategy.