Multi-agent Optimization Method Research Articles

Distributed Quasi-Newton Method for Multi-Agent Optimization

Distributed Quasi-Newton Method for Multi-Agent Optimization

Optimal scheduling of distributed hydrogen refueling stations for fuel supply and reserve demand service with evolutionary transfer multi-agent reinforcement learning

With the extensive utilization of fossil fuels, environmental concerns have been growing. Hydrogen-powered vehicles (HPVs) as well as hydrogen refueling stations (HRSs) are expected to proliferate to alleviate the pollution. In order to promote the economic valibity of HRSs, this paper proposes an optimal scheduling model for distributed HRSs to maximize HRSs’ revenue during a day. HRSs serves both the mobility sector with fuel individually and the power system with reserve demand response collaboratively. The elaborated operating of electrolysers and relaxed control of hydrogen storage are involved to enhance practicability and flexibility of the scheduling. Considering that this model has multiple variables, intractable high-dimension nonlinear constraints, a transfer multi-agent reinforcement learning algorithm is developed. The algorithm consists of two parts: the one is the multi-agent optimization method by transforming multi-decision optimization into a multi-agent optimization; the other is to transfer the empirical knowledge of the source task to reinforcement learning according to the similarity between the source task and the target task, making it cut down the blindness of exploration and accelerate convergence. Numerical studies reveal that participating in the reserve services market collaboratively increases overall revenues of HRSs by up to 32.90%, and the computation time is sharply shortened by approximately 34 times compared to the basic reinforcement learning.

Cooperative multiagent optimization method for wind farm power delivery maximization

Reducing wake losses and improving the overall power output of wind farms have become a research focus in attempts to optimize wind farm power generation. A cooperative multiagent optimization method (CMAOM) for wind farm power delivery maximization has been proposed in this paper. In the CMAOM, a wind farm wake distribution calculation model, based on the Jensen wake model, was constructed, and each turbine was then assigned as an agent; the CMAOM was used to reduce wake losses and improve the overall wind farm power output. The agent, multiagent objective function and grid environment were defined in this study using wind turbine characteristics, and the CMAOM, including the neighborhood competition operator, mutation operator, and self-learning operator, were calibrated using wind turbine aerodynamic correlation characteristics. The Danish Horns Rev wind farm was selected as a case study, and the CMAOM and particle swarm optimization (PSO) algorithm were used to conduct analyses there. The results showed that the CMAOM proposed in this paper was more effective than the PSO algorithm and that the wind farm overall power output was increased by 7.51% for a 270° incoming wind direction and an incoming wind speed of 8.5 m/s.

A unitary distributed subgradient method for multi-agent optimization with different coupling sources

Distributed optimization techniques offer high quality solutions to various engineering problems, such as resource allocation and distributed estimation and control. In this work, we first consider distributed convex constrained optimization problems where the objective function is encoded by multiple local and possibly nonsmooth objectives privately held by a group of agents, and propose a distributed subgradient method with double averaging (abbreviated as DSA2) that only requires peer-to-peer communication and local computation to solve the global problem. The algorithmic framework builds on dual methods and dynamic average consensus; the sequence of test points is formed by iteratively minimizing a local dual model of the overall objective where the coefficients, i.e., approximated subgradients of the objective, are supplied by the dynamic average consensus scheme. We theoretically show that DSA2 enjoys non-ergodic convergence properties, i.e., the local minimizing sequence itself is convergent, a distinct feature that cannot be found in existing results. Specifically, we establish a convergence rate of O(1t) in terms of objective function error. Then, extensions are made to tackle distributed optimization problems with coupled functional constraints by combining DSA2 and dual decomposition. This is made possible by Lagrangian relaxation that transforms the coupling in constraints of the primal problem into that in cost functions of the dual, thus allowing us to solve the dual problem via DSA2. Both the dual objective error and the quadratic penalty for the coupled constraint are proved to converge at a rate of O(1t), and the primal objective error asymptotically vanishes. Numerical experiments and comparisons are conducted to illustrate the advantage of the proposed algorithms and validate our theoretical findings.

A Multi-Agent Optimization Method for Preemptive Resource-Constrained Project Scheduling

A multi-agent optimization method is proposed to solve the preemptive resource-constrained project scheduling problem in which activities are allowed to be preempted no more than once. The proposed method involves a multi-agent system, a negotiation process, and two types of agents (activity agents and schedule agent). The activity agents and the schedule agent negotiate with each other to allocate resources and optimize the project schedule. Computational experiments were conducted using the standard project scheduling problem sets. Compared with prior studies, results of the proposed method are competitive in terms of project makespan. The method can be extended to other preemptive resource-constrained project scheduling problems.

Heterogeneous multi-agent optimization framework with application to synthesizing optimal nuclear waste blends

Multi-agent optimization method is a nature-inspired framework that supports the cooperative search of an optimal solution of an optimization problem by a group of algorithmic agents connected through an environment with certain predefined information sharing protocol. In this work, we propose a novel heterogeneous multi-agent optimization (HTMAO) framework. The proposed framework is validated using a set of benchmark problems a real-world synthesizing radioactive waste blending problem. The optimal radioactive waste blending problem is formulated as a mixed integer nonlinear programming. The total frit used for vitrification process is minimized subject to thermodynamic properties and process model constraints. The model simultaneously determines the optimal decisions that include the combination of the waste tanks that form each waste blend and the amount of frit needed for the vitrification of each waste blend. In developing the HTMAO framework, efficient ant colony optimization algorithms; efficient simulated annealing; efficient genetic algorithm; and sequential quadratic programming solver are considered as algorithmic agents. We illustrate this approach through a real-world case study of the optimal radioactive waste blending of Hanford site in Southern Washington where nuclear waste is stored.

Distributed mirror descent method for multi-agent optimization with delay

This paper investigates a distributed optimization problem associated a time-varying multi-agent network with the presence of delays, where each agent has local access to its convex objective function, and cooperatively minimizes a sum of convex objective functions of the agents over the network. Based on the mirror descent method, we develop a distributed algorithm to solve this problem by exploring the delayed gradient information. Furthermore, we analyze the effects of delayed gradients on the convergence of the algorithm and provide an explicit bound on the convergence rate as a function of the delay parameter, the network size and topology. Our results show that the delays are asymptotically negligible for smooth problems. The proposed algorithm can be viewed as a generalization of the distributed gradient-based projection methods since it utilizes a customized Bregman divergence instead of the usual Euclidean squared distance. Finally, some simulation results on a logistic regression problem are presented to demonstrate the effectiveness of the algorithm.

Randomized gradient-free method for multiagent optimization over time-varying networks.

In this brief, we consider the multiagent optimization over a network where multiple agents try to minimize a sum of nonsmooth but Lipschitz continuous functions, subject to a convex state constraint set. The underlying network topology is modeled as time varying. We propose a randomized derivative-free method, where in each update, the random gradient-free oracles are utilized instead of the subgradients (SGs). In contrast to the existing work, we do not require that agents are able to compute the SGs of their objective functions. We establish the convergence of the method to an approximate solution of the multiagent optimization problem within the error level depending on the smoothing parameter and the Lipschitz constant of each agent's objective function. Finally, a numerical example is provided to demonstrate the effectiveness of the method.

Robust Control, Optimization, and Applications to Markovian Jumping Systems

Robust Control, Optimization, and Applications to Markovian Jumping Systems

Distributed dual averaging method for multi-agent optimization with quantized communication

In this paper we propose a distributed dual averaging method for solving the constrained multi-agent optimization problem, in which multiple agents try to cooperatively optimize the sum of their local convex objective functions subject to a global convex constraint set over a network. We consider two cases: (i) The communications among agents are perfect, and (ii) The communications among agents are deterministically or probabilistically quantized. In the first case, we provide a way to control the convergence performance of the proposed method through adjusting the number of consensus iterations we run in the subgradient step. In the second case, we consider two kinds of quantizers, and provide bounds on their convergence rates to highlight the dependence on the quantization resolutions respectively. Finally, we provide a numerical example to show the effectiveness of the proposed methods.

Distributed Primal–Dual Subgradient Method for Multiagent Optimization via Consensus Algorithms

This paper studies the problem of optimizing the sum of multiple agents' local convex objective functions, subject to global convex inequality constraints and a convex state constraint set over a network. Through characterizing the primal and dual optimal solutions as the saddle points of the Lagrangian function associated with the problem, we propose a distributed algorithm, named the distributed primal-dual subgradient method, to provide approximate saddle points of the Lagrangian function, based on the distributed average consensus algorithms. Under Slater's condition, we obtain bounds on the convergence properties of the proposed method for a constant step size. Simulation examples are provided to demonstrate the effectiveness of the proposed method.