scholarly journals Distributed Adaptive Optimization for Generalized Linear Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-10
Author(s):  
Shuxin Liu ◽  
Haijun Jiang ◽  
Liwei Zhang ◽  
Xuehui Mei
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Adaptive Algorithms ◽  
Adaptive Optimization ◽  
Damping Term ◽  
Convex Optimization Problem ◽  
Adaptive Law ◽  
General Linear Dynamics ◽  
Edge Based ◽  
The Cost

In this paper, the edge-based and node-based adaptive algorithms are established, respectively, to solve the distribution convex optimization problem. The algorithms are based on multiagent systems with general linear dynamics; each agent uses only local information and cooperatively reaches the minimizer. Compared with existing results, a damping term in the adaptive law is introduced for the adaptive algorithms, which makes the algorithms more robust. Under some sufficient conditions, all agents asymptotically converge to the consensus value which minimizes the cost function. An example is provided for the effectiveness of the proposed algorithms.

Inventory optimization considering the vehicle capacity and specifics of cash flows at rental storage sites

2020 ◽  
pp. 77-90
Author(s):  
V.D. Gerami ◽  
I.G. Shidlovskii
Keyword(s):  
Supply Chain ◽  
Inventory Management ◽  
Sufficient Conditions ◽  
Cash Flows ◽  
Management Systems ◽  
Cargo Capacity ◽  
Special Modification ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Vehicle Capacity

The article presents a special modification of the EOQ formula and its application to the accounting of the cargo capacity factor for the relevant procedures for optimizing deliveries when renting storage facilities. The specified development will allow managers to take into account the following process specifics in the format of a simulated supply chain when managing inventory. First of all, it will allow considering the most important factor of cargo capacity when optimizing stocks. Moreover, this formula will make it possible to find the optimal strategy for the supply of goods if, also, it is necessary to take into account the combined effect of several factors necessary for practice, which will undoubtedly affect decision-making procedures. Here we are talking about the need for additional consideration of the following essential attributes of the simulated cash flow of the supply chain: 1) time value of money; 2) deferral of payment of the cost of the order; 3) pre-agreed allowable delays in the receipt of revenue from goods sold. Developed analysis and optimization procedures have been implemented to models of this type that are interesting and important for a business. This — inventory management systems, the format of which is related to the special concept of efficient supply. We are talking about models where the presence of the specified delays for the outgoing cash flows allows you to pay for the order and the corresponding costs of the supply chain from the corresponding revenue on the re-order interval. Accordingly, the necessary and sufficient conditions are established based on which managers will be able to identify models of the specified type. The purpose of the article is to draw the attention of managers to real opportunities to improve the efficiency of inventory management systems by taking into account these factors for a simulated supply chain.

scholarly journals An Adaptive Optimization Method Based on Learning Rate Schedule for Neural Networks

2021 ◽  
Vol 11 (2) ◽  
pp. 850
Author(s):  
Dokkyun Yi ◽  
Sangmin Ji ◽  
Jieun Park
Keyword(s):  
Artificial Intelligence ◽  
Cost Function ◽  
Numerical Experiments ◽  
Global Minimum ◽  
Optimization Method ◽  
Learning Method ◽  
Adaptive Optimization ◽  
The Cost ◽  
Proof Of Convergence ◽  
Learning Data

Artificial intelligence (AI) is achieved by optimizing the cost function constructed from learning data. Changing the parameters in the cost function is an AI learning process (or AI learning for convenience). If AI learning is well performed, then the value of the cost function is the global minimum. In order to obtain the well-learned AI learning, the parameter should be no change in the value of the cost function at the global minimum. One useful optimization method is the momentum method; however, the momentum method has difficulty stopping the parameter when the value of the cost function satisfies the global minimum (non-stop problem). The proposed method is based on the momentum method. In order to solve the non-stop problem of the momentum method, we use the value of the cost function to our method. Therefore, as the learning method processes, the mechanism in our method reduces the amount of change in the parameter by the effect of the value of the cost function. We verified the method through proof of convergence and numerical experiments with existing methods to ensure that the learning works well.

Optimal actuator placement in adaptive optics systems

2021 ◽  
pp. 107754632110324
Author(s):  
Berk Altıner ◽  
Bilal Erol ◽  
Akın Delibaşı
Keyword(s):  
Cost Function ◽  
Adaptive Optics ◽  
Disturbance Attenuation ◽  
Linear Quadratic ◽  
Placement Problem ◽  
Convex Optimization Problem ◽  
Wavefront Aberrations ◽  
The Cost ◽  
Actuator Placement ◽  
Quadratic Cost Function

Adaptive optics systems are powerful tools that are implemented to degrade the effects of wavefront aberrations. In this article, the optimal actuator placement problem is addressed for the improvement of disturbance attenuation capability of adaptive optics systems due to the fact that actuator placement is directly related to the enhancement of system performance. For this purpose, the linear-quadratic cost function is chosen, so that optimized actuator layouts can be specialized according to the type of wavefront aberrations. It is then considered as a convex optimization problem, and the cost function is formulated for the disturbance attenuation case. The success of the presented method is demonstrated by simulation results.

scholarly journals Bipartite Consensus of High-Order Edge Dynamics on Coopetition Multiagent Systems

2019 ◽  
Vol 2019 ◽  
pp. 1-12 ◽  
Author(s):  
Yilong Yang ◽  
Zhijian Ji ◽  
Lei Tian ◽  
Huizi Ma ◽  
Qingyuan Qi
Keyword(s):  
Multiagent Systems ◽  
Line Graph ◽  
Sufficient Conditions ◽  
High Order ◽  
Third Order ◽  
Positive Weight ◽  
The Third ◽  
Initial Graph ◽  
Strongly Connected ◽  
Bipartite Consensus

The bipartite consensus of high-order edge dynamics is investigated for coopetition multiagent systems, in which the cooperative and competitive relationships among agents are characterized by positive weight and negative weight, respectively. By mapping the initial graph to a line graph, the distributed control protocol is proposed for the strongly connected, digon sign-symmetric structurally balanced line graph; and then we give sufficient conditions for the third-order multi-gent system to achieve both the bipartite consensus of edge dynamics and the final value of bipartite consensus. By transforming the coefficients of characteristic polynomial from complex domain to real number domain, the sufficient conditions for the bipartite consensus of high-order edge dynamics are also proposed, and the final values of the high-order edge dynamics on multiagent systems are obtained.

scholarly journals Integrated Offline and Online Decision Making under Uncertainty

2021 ◽  
Vol 70 ◽  
pp. 77-117
Author(s):  
Allegra De Filippo ◽  
Michele Lombardi ◽  
Michela Milano
Keyword(s):  
Optimization Problems ◽  
Greedy Heuristic ◽  
Management Problem ◽  
Quality Improvements ◽  
Solution Quality ◽  
Convex Optimization Problem ◽  
Routing Problem ◽  
Multi Stage ◽  
The Cost ◽  
Parametric Convex Optimization

This paper considers multi-stage optimization problems under uncertainty that involve distinct offline and online phases. In particular it addresses the issue of integrating these phases to show how the two are often interrelated in real-world applications. Our methods are applicable under two (fairly general) conditions: 1) the uncertainty is exogenous; 2) it is possible to define a greedy heuristic for the online phase that can be modeled as a parametric convex optimization problem. We start with a baseline composed by a two-stage offline approach paired with the online greedy heuristic. We then propose multiple methods to tighten the offline/online integration, leading to significant quality improvements, at the cost of an increased computation effort either in the offline or the online phase. Overall, our methods provide multiple options to balance the solution quality/time trade-off, suiting a variety of practical application scenarios. To test our methods, we ground our approaches on two real cases studies with both offline and online decisions: an energy management problem with uncertain renewable generation and demand, and a vehicle routing problem with uncertain travel times. The application domains feature respectively continuous and discrete decisions. An extensive analysis of the experimental results shows that indeed offline/online integration may lead to substantial benefits.

scholarly journals First and second order optimality conditions for the control of Fokker-Planck equations

2021 ◽  
Vol 27 ◽  
pp. 15
Author(s):  
M. Soledad Aronna ◽  
Fredi Tröltzsch
Keyword(s):  
Control Variable ◽  
Sufficient Conditions ◽  
Planck Equation ◽  
Second Order ◽  
Optimal Controls ◽  
Main Emphasis ◽  
The Cost ◽  
Necessary And Sufficient ◽  
Fokker Planck Equations ◽  
Fokker Planck

In this article we study an optimal control problem subject to the Fokker-Planck equation ∂tρ − ν∆ρ − div(ρB[u]) = 0 The control variable u is time-dependent and possibly multidimensional, and the function B depends on the space variable and the control. The cost functional is of tracking type and includes a quadratic regularization term on the control. For this problem, we prove existence of optimal controls and first order necessary conditions. Main emphasis is placed on second order necessary and sufficient conditions.

Minimum Span Frequency Assignment Based on a Multiagent Evolutionary Algorithm

2011 ◽  
Vol 2 (3) ◽  
pp. 29-42
Author(s):  
Jing Liu ◽  
Jinshu Li ◽  
Weicai Zhong ◽  
Li Zhang ◽  
Ruochen Liu
Keyword(s):  
Evolutionary Algorithms ◽  
Evolutionary Algorithm ◽  
Frequency Spectrum ◽  
Multiagent Systems ◽  
Experimental Results ◽  
Frequency Assignment ◽  
Assignment Problems ◽  
The Cost ◽  
Very High

In frequency assignment problems (FAPs), separation of the frequencies assigned to the transmitters is necessary to avoid the interference. However, unnecessary separation causes an excess requirement of spectrum, the cost of which may be very high. Since FAPs are closely related to T-coloring problems (TCP), multiagent systems and evolutionary algorithms are combined to form a new algorithm for minimum span FAPs on the basis of the model of TCP, which is named as Multiagent Evolutionary Algorithm for Minimum Span FAPs (MAEA-MSFAPs). The objective of MAEA-MSFAPs is to minimize the frequency spectrum required for a given level of reception quality over the network. In MAEA-MSFAPs, all agents live in a latticelike environment. Making use of the designed behaviors, MAEA-MSFAPs realizes the ability of agents to sense and act on the environment in which they live. During the process of interacting with the environment and other agents, each agent increases the energy as much as possible so that MAEA-MSFAPs can find the optima. Experimental results on TCP with different sizes and Philadelphia benchmark for FAPs show that MAEA-MSFAPs have a good performance and outperform the compared methods.

scholarly journals Multiconsensus of Nonlinear Multiagent Systems with Intermittent Communication

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jie Chen ◽  
Guang-Hui Xu ◽  
Liang Geng
Keyword(s):  
Nonlinear Dynamics ◽  
Lyapunov Function ◽  
Multiagent Systems ◽  
Closed Loop ◽  
Sufficient Conditions ◽  
Control Parameters ◽  
Numerical Examples ◽  
Relative Information ◽  
Loop Dynamics ◽  
Intermittent Communication

Compared with single consensus, the multiconsensus of multiagent systems with nonlinear dynamics can reflect some real-world cases. This paper proposes a novel distributed law based only on intermittent relative information to achieve the multiconsensus. By constructing an appropriate Lyapunov function, sufficient conditions on control parameters are derived to undertake the reliability of closed-loop dynamics. Ultimately, the availability of results is completely validated by these numerical examples.

scholarly journals Adaptive Guaranteed-Performance Consensus Control for Multi-Agent Systems with an Adjustable Convergence Speed

2019 ◽  
Vol 2019 ◽  
pp. 1-9 ◽  
Author(s):  
Haiying Ma ◽  
Xiao Jia ◽  
Ning Cai ◽  
Jianxiang Xi
Keyword(s):  
Multiagent Systems ◽  
Sufficient Conditions ◽  
Convergence Speed ◽  
Multi Agent Systems ◽  
Consensus Protocol ◽  
Consensus Control ◽  
Control Gain ◽  
Multi Agent ◽  
The Stability ◽  
Theoretical Results

In this paper, adaptive guaranteed-performance consensus control problems for multiagent systems with an adjustable convergence speed are investigated. A novel adaptive guaranteed-performance consensus protocol is proposed, where the communication weights can be adaptively regulated. By the state space decomposition method and the stability theory, sufficient conditions for guaranteed-performance consensus are obtained and the guaranteed-performance cost is determined. Moreover, the lower bound of the convergence coefficient for multiagent systems is deduced, which is linearly adjustable approximately by changing the adaptive control gain. Finally, simulation examples are introduced to demonstrate theoretical results.

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