Distributed denial-of-service (DDoS) attacks pose a significant threat to network security by overwhelming systems with malicious traffic, leading to service disruptions and potential data breaches. The traditional centralized machine learning (ML) methods for detecting DDoS attacks in Internet of Things (IoT) environments raise privacy and security concerns due to their collection and distribution of data to a central entity that may not be trusted to perform model training. Federated learning (FL) offers a privacy-preserving solution that enables distributed collaboration by training a model only on local clients, without data exchanges, where the central entity only performs global model aggregation. However, the current practice of random client selection, combined with the statistical heterogeneity of client data and the device heterogeneity encountered in IoT environments, requires many training rounds to reach optimal accuracy, increasing the imposed computational overhead. To address these challenges, we propose a multiobjective optimization-based FL with adaptive client selection (FELACS) approach that maximizes client importance scores while satisfying resource, performance, and data diversity constraints. Experiments are carried out on the CIC-IDS2018, CIC-DDoS2019, BoT-IoT, and CIC-IoT2023 datasets, demonstrating that FELACS improves upon the accuracy of the existing approaches while exhibiting increased convergence speed when training a model in an FL scenario, hence reducing the number of communication rounds required to achieve the target accuracy, making it highly effective for performing IoT-based DDoS attack detection in FL scenarios.