Federated Fuzzy C-Means (FCM) clustering methods have demonstrated success in standard federated learning (FL) environments, but model heterogeneity presents a significant challenge. This heterogeneity hampers communication content selection and makes traditional aggregation methods, such as federated averaging (FedAvg), insufficient for diverse client models. Additionally, handling non-IID data distributions and learning robust feature representations remain unresolved in some existing approaches. To tackle these issues, we propose FFCMD, a federated FCM clustering framework designed to address model heterogeneity while enhancing feature learning and accommodating non-IID data. FFCMD integrates an autoencoder (AE) with a fuzzy C-Means network (FCMN), augmented by mutual knowledge distillation (mKD), to improve data feature learning, communication, and aggregation under heterogeneous conditions. The AE incorporates a clustering-oriented penalty term to learn discriminative features, boosting performance on complex datasets. Rather than direct parameter aggregation, mKD updates the global model using local devices' soft assignments, naturally handling structural variations across client models. Moreover, FFCMD employs discrepancy-aware weighting mechanisms to dynamically align local and global category distributions during soft assignment embedding, effectively addressing the challenges posed by non-IID data. Extensive experiments on multiple public datasets show that FFCMD outperforms state-of-the-art methods, particularly in non-IID scenarios, and excels even in the presence of model heterogeneity.

Federated Fuzzy C-Means (FCM) has received considerable attention due to the increasing need for privacy-conscious data analysis across diverse domains and sources in many real-world applications. Recent developments in federated FCM, however, are still in their infancy and largely unexplored. These methods struggle to handle nonindependent and identically distributed (non-iid) data. Moreover, critical hyperparameters, such as the number of iterations for local updates, are typically set manually, which can significantly affect the performance of federated clustering. To address these challenges, we introduce an Adaptive Federated FCM with an auxiliary model, named AF-FCM. In this approach, prior information from the auxiliary model, along with a proximal term in the local objective, mitigates the effects of the non-iid environment, enhancing both model robustness and effectiveness. Critical hyperparameters are adaptively adjusted using a proposed adaptive particle swarm optimization (APSO) algorithm, guided by a carefully designed fitness function. Within APSO, a nonlinear regression function adjusts the inertia weight, reducing the risk of convergence to local optima. In AF-FCM, global prototypes are refined using momentum gradient descent (MGD). Numerical experiments highlight the effectiveness and generalization performance of AF-FCM across various conditions, including heterogeneity variations, the number of clients, and the number of clusters. Comparative analysis against state-of-the-art federated clustering baseline methods validates the competitive performance of AF-FCM.

This paper investigates Earth observation scheduling of agile satellite constellation based on evolutionary multiobjective optimization (EMO). The mission planning of agile Earth observation satellite (AEOS) is to select and specify the observation activities to acquire images on the earth surface. This should be done in accordance with operational constraints and in order to maximize certain objectives. In this paper three objectives are considered, i. e. profit, quality and timeliness. Preference-based EMO methods are introduced to generate solutions preferable for the decision maker, whose preference is expressed by a reference point. An improved algorithm based on R-NSGA-II, which is named CD-NSGA-II, is proposed and compared with other algorithms in various scheduling scenarios. Results show that the chosen preference modeling paradigm allows to focus search on the interesting part of the Pareto front. Moreover, the tested algorithms behave differently with the change of reference point and degree of conflicts, among them CD-NSGA-II has the best overall performance. Suggestions on applying these algorithms in practice are also given in this paper.

In this paper, a target region based multiobjective evolutionary algorithm framework is proposed to incorporate preference into the optimization process. It aims at finding a more fine-grained resolution of a target region without exploring the whole set of Pareto optimal solutions. It can guide the search towards the regions on the Pareto Front which are of real interest to the decision maker. The algorithm framework has been combined with SMS-EMOA, R2-EMOA, NSGA-II to form three target region based multiobjective evolutionary algorithms: T-SMS-EMOA, T-R2-EMOA and T-NSGA-II. In these algorithms, three ranking criteria are applied to achieve a well-converged and well-distributed set of Pareto optimal solutions in the target region. The three criteria are: 1. Non-dominated sorting; 2. indicators (hypervolume or R2 indicator) or crowding distance in the new coordinate space (i.e. target region) after coordinate transformation; 3. the Chebyshev distance to the target region. Rectangular and spherical target regions have been tested on some benchmark problems, including continuous problems and discrete problems. Experimental results show that new algorithms can handle the preference information very well and find an adequate set of Pareto-optimal solutions in the preferred regions quickly. Moreover, the proposed algorithms have been enhanced to support multiple target regions and preference information based on a target point or multiple target points. Some results of enhanced algorithms are presented.