Y. Zheng, Q. Liu, A review of distributed optimization: Problems, models and algorithms, Neurocomputing, in press.

Abstract: With the development of big data and artificial intelligence, distributed optimization has emerged as an indispensable tool for solving large-scale problems. In particular, the multi-agent system based on distributed information processing can be elaborately designed for distributed optimization, in which the agents collaboratively minimize a global objective function made up of a sum of local objective cost functions subject to some local and/or global constraints. Inspired by the applications involving resource allocation, machine learning, power systems, sensor networks and cloud computing, a variety of distributed optimization models and algorithms have been investigated and developed. The optimization models include unconstrained and constrained problems in continuous and discontinuous systems with undirected and directed communication topology graphs. The constraints include bounded constraint, separable and inseparable equality and inequality constraints. Meanwhile, in distributed algorithms, every agent executes its local computation and updating on basis of its own data information and that exchanging with its neighboring agents by means of the underlying communication networks, in order to deal with the optimization problems in a distributed way. This paper is designed to provide a comprehensive overview of extant distributed models and algorithms for distributed optimization.

C. Xu, Q. Liu, An inertial neural network approach for robust time-of-arrival localization considering clock asynchronization, Neural Networks, 146: 98-106, 2022.

Abstract: This paper presents an inertial neural network to solve the source localization optimization problem with l1-norm objective function based on the time of arrival (TOA) localization technique. The convergence and stability of the inertial neural network are analyzed by the Lyapunov function method. An inertial neural network iterative approach is further used to find a better solution among the solutions with different inertial parameters. Furthermore, the clock asynchronization is considered in the TOA l1-norm model for more general real applications, and the corresponding inertial neural network iterative approach is addressed. The numerical simulations and real data are both considered in the experiments. In the simulation experiments, the noise contains uncorrelated zero-mean Gaussian noise and uniform distributed outliers. In the real experiments, the data is obtained by using the ultra wide band (UWB) technology hardware modules. Whether or not there is clock asynchronization, the results show that the proposed approach always can find a more accurate source position compared with some of the existing algorithms, which implies that the proposed approach is more effective than the compared ones.

M. Wang, Q. Liu, Y. Zheng, A curvature-segmentation-based minimum time algorithm for autonomous vehicle velocity planning, Information Sciences, 565: 248-261, 2021.

Abstract: Velocity planning serves as an important issue in motion planning for autonomous vehicles. The presented paper proposes a novel velocity planning method with minimum moving time on the basis of path curvature which is accomplished in three steps. First, the assigned path is divided into some elementary parts based on the path curvature. Second, the velocity planning is transformed into an unconstrained optimization problem by assuming the velocity of vehicle to be a specific cubic polynomial on every elementary part to avoid a sudden acceleration in path switching. Finally, we use a modified projection particle swarm optimization (PPSO) algorithm to obtain the time-optimal velocity profile. The proposed method can generate a smooth time-optimal velocity profile while considering all possible relevant constraints. Three examples are provided on different types of path to demonstrate that the final velocity profile is efficient to avoid the sudden acceleration change. Furthermore, the modified PPSO algorithm in this paper is used to solve the optimization problem with high dimensional variables when its upper bound is known, which can not be achieved by the general PPSO algorithm.

Q. Liu, M. Wang, A projection-based algorithm for optimal formation and optimal matching of multi-robot system, Nonlinear Dynamics, 104: 439-450, 2021.

Abstract: In this paper, the optimal formation and optimal matching of a multi-robot system are investigated with a projection-based algorithm designed to get the optimal formation moving in real time. The formation-related optimization problem is proposed under the consideration of two cases: the free formation and the formation with anchor(s). For the latter, equality constraints are formulated for the anchor, and the objective of the optimal formation is to minimize the total distance to the initial formation of the multirobot system. Here, the objective function with mixed norm is considered to get a compact formation. Sufficient conditions on the design parameter for global convergence of the proposed algorithm are provided in the theoretical results. Furthermore, the projection particle swarm optimizer is investigated for getting the optimal matching between the initial/intermediate formation and the optimal formation. Finally, simulations on several numerical examples are presented to validate the effectiveness of the proposed method.

Q. Liu, X. Le, K. Li, A distributed optimization algorithm based on multiagent network for economic dispatch with region partitioning, IEEE Transactions on Cybernetics, 51(5): 2466-2475, 2021.

Abstract: In this article, a discrete-time distributed optimization algorithm is proposed for solving the economic dispatch (ED) problem with some groups of generator units to communicate over a connected graph, which is independent of the power system. The ED problem is converted to a distributed optimization problem with an objective of the sum of individual convex functions and constraints of local generators. Based on the optimal conditions, a class of distributed algorithms is designed to find the solution to the ED problem. The distributed algorithm can be realized as a multiagent system with a connected graph, whose convergence can be proved using the dynamic analysis method. Moreover, experiments with simulations are presented to demonstrate the performance of the proposed algorithm.