Abstract: This paper proposes a novel distributed neurodynamic optimization algorithm, designed by combining multi-agent theory and the penalty function method, which ensures fixed-time consensus for distributed nonconvex problems subject to local inequality constraints. The initial conditions of the algorithm can be chosen arbitrarily. By appropriately designing the penalty mechanism, it is guaranteed that the algorithm’s state variables enter the feasible region defined by the constraints within a finite time and remain therein thereafter. The consensus term of the algorithm combines a dynamic switching function with a sign function to achieve fixed-time consensus independent of initial conditions, thereby improving the efficiency and controllability of the optimization process. Based on Lyapunov theory, it is proven that, under appropriate assumptions, the algorithm’s state variables remain bounded, enter the feasible region of inequalities in finite time, achieve fixed-time consensus, and ultimately converge to the set of critical points of the nonconvex problem. Compared with existing distributed algorithms, the proposed algorithm adopts a single-layer differential inclusion framework and integrates a penalty mechanism that avoids complicated penalty-parameter tuning with an advanced fixed-time consensus control strategy. This design ensures highly controllable convergence time while preserving structural simplicity, low computational overhead, and flexibility in selecting initial points. The effectiveness and practicality of the algorithm are demonstrated through two simulation studies and an application to optimal facility location.

摘要： 针对一类带局部不等式约束的分布式非凸优化问题，本文结合多智能体理论与罚函数方法设计了一种新颖的具有固定时间一致的分布式神经动力学优化算法。该算法的初始条件能够任意选取，通过设计合适的惩罚机制保证了算法的状态变量能够在有限时间内进入约束条件可行域且永不离开。算法的一致项由动态开关函数和符号函数组合项共同构成，能够实现不依赖初始条件的固定时间一致性，使算法在解决优化问题时具备更高效可控的时间效率。基于李雅普诺夫理论，证明了在一定假设条件下，算法状态变量有界并能够在有限时间内进入不等式可行域和实现固定时间一致，最终收敛至非凸问题的临界点集。与现有分布式算法相比，所设计的算法采用单层的微分包含结构，使用了无需复杂计算罚因子的惩罚函数机制与先进的固定时间一致控制方法，具有结构简单、计算开销低、时间效率高、初始点任意选取的特点。最后，两个仿真实验和一个最优选址问题应用案例验证了所提算法的有效性与可行性。