This paper tackles the high-dimensional robust order scheduling problem. A multi-objective evolutionary algorithm called constrained nondominated sorting differential evolution based on decision variable classification is developed to search for robust order schedules. The decision variables are classified into highly and weakly robustness-related variables according to their contributions to the robustness of candidate solutions. The experimental results reveal that the performance of robust evolutionary optimization can be greatly improved via analyzing the properties of decision variables and then decomposing the high-dimensional robust optimization problem. It is also unveiled that the order scheduling is greatly affected by the uncertain daily production quantities. The robust order schedules are able to provide more information on earliness/tardiness of the orders, which enhances the flexibility of the production.

A distributed event-triggered protocol is proposed to deal with the time-varying formation control problem of Euler–Lagrange systems with uncertain model parameters in this research. By utilizing the small-gain theorem and matrix transformation, we show the input–output stability of the closed-loop cascade system with Euler–Lagrange dynamics. An event-triggered condition (ETC) is designed by only using the local information of each agent, which avoids the continuous communication in the event detection and excludes the Zeno behavior. Finally, the proposed methods are applied to the practical flight platform for quadrotors. The experiment using three quadrotors in the outdoor environment is demonstrated to test the effectiveness of the formation protocol.

Order scheduling is of vital importance in discrete manufacturing industries. This paper takes fashion industry as an example and discusses the robust order scheduling problem in the fashion industry. In the fashion industry, order scheduling focuses on the assignment of production orders to appropriate production lines. In reality, before a new order can be put into production, a series of activities known as preproduction events need to be completed. In addition, in real production process, owing to various uncertainties, the daily production quantity of each order is not always as expected. In this paper, by considering the preproduction events and the uncertainties in the daily production quantity, robust order scheduling problems in the fashion industry are investigated with the aid of a multiobjective evolutionary algorithm called nondominated sorting adaptive differential evolution (NSJADE). The experimental results illustrate that it is of paramount importance to consider preproduction events in order scheduling problems in the fashion industry. We also unveil that the existence of the uncertainties in the daily production quantity heavily affects the order scheduling.

With the rapid development of the scale of distributed energy resources, the implementation of distributed algorithms imposes ever-increasing requirements on communication resources. With the aim of reducing the communication burden required to solve the economic dispatch problem, we here consider three key aspects, namely the amount of information exchanged per broadcast, the broadcast frequency per iteration, and the number of iterations needed to achieve a certain accuracy. The proposed primal-dual based algorithm is integrated with a discrete dynamic event-triggered scheme and enjoys significant advantages in all three mentioned aspects. We prove that the proposed algorithm converges to the optimal point at a linear convergence rate for suitable operating parameters and for cost functions that are strongly convex and smooth. We confirm the effectiveness and demonstrate the advantages of our approach by means of a set of simulation experiments.