Social Welfare Optimization Problem Research Articles

Composite Optimization With Coupling Constraints via Penalized Proximal Gradient Method in Asynchronous Networks

In this paper, we consider a composite optimization problem with linear coupling constraints in a multi-agent network. In this problem, the agents cooperatively optimize a strongly convex cost function which is the linear sum of individual cost functions composed of smooth and possibly non-smooth components. To solve this problem, we propose an asynchronous penalized proximal gradient (Asyn-PPG) algorithm, a variant of classical proximal gradient method, with the presence of the asynchronous updates of the agents and uniform communication delays in the network. Specifically, we consider a slot-based asynchronous network (SAN), where the whole time domain is split into sequential time slots and each agent is permitted to execute multiple updates during a slot by accessing the historical state information of the agents. By the Asyn-PPG algorithm, an explicit convergence rate can be guaranteed based on deterministic analysis. The feasibility of the proposed algorithm is verified by solving a consensus-based distributed regression problem and a social welfare optimization problem in the electricity market.

Experimental Design Networks: A Paradigm for Serving Heterogeneous Learners Under Networking Constraints

Significant advances in edge computing capabilities enable learning to occur at geographically diverse locations. In general, the training data needed in those learning tasks are not only heterogeneous but also not fully generated locally. In this paper, we propose an experimental design network paradigm, wherein learner nodes train possibly different Bayesian linear regression models via consuming data streams generated by data source nodes over a network. We formulate this problem as a social welfare optimization problem in which the global objective is defined as the sum of experimental design objectives of individual learners, and the decision variables are the data transmission strategies subject to network constraints. We first show that, assuming Poisson data streams in steady state, the global objective is a continuous DR-submodular function. We then propose a Frank-Wolfe type algorithm that outputs a solution within a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1-1/e$</tex-math> </inline-formula> factor from the optimal. Our algorithm contains a novel gradient estimation component which is carefully designed based on Poisson tail bounds and sampling. Finally, we complement our theoretical findings through extensive experiments. Our numerical evaluation shows that the proposed algorithm outperforms several baseline algorithms both in maximizing the global objective and in the quality of the trained models.

Uncertainty-Aware Management of Smart Grids Using Cloud-Based LSTM-Prediction Interval

This article introduces an uncertainty-aware cloud-fog-based framework for power management of smart grids using a multiagent-based system. The power management is a social welfare optimization problem. A multiagent-based algorithm is suggested to solve this problem, in which agents are defined as volunteering consumers and dispatchable generators. In the proposed method, every consumer can voluntarily put a price on its power demand at each interval of operation to benefit from the equal opportunity of contributing to the power management process provided for all generation and consumption units. In addition, the uncertainty analysis using a deep learning method is also applied in a distributive way with the local calculation of prediction intervals for sources with stochastic nature in the system, such as loads, small wind turbines (WTs), and rooftop photovoltaics (PVs). Using the predicted ranges of load demand and stochastic generation outputs, a range for power consumption/generation is also provided for each agent called "preparation range" to demonstrate the predicted boundary, where the accepted power consumption/generation of an agent might occur, considering the uncertain sources. Besides, fog computing is deployed as a critical infrastructure for fast calculation and providing local storage for reasonable pricing. Cloud services are also proposed for virtual applications as efficient databases and computation units. The performance of the proposed framework is examined on two smart grid test systems and compared with other well-known methods. The results prove the capability of the proposed method to obtain the optimal outcomes in a short time for any scale of grid.

Coded Distributed Computing With Predictive Heterogeneous User Demands: A Learning Auction Approach

Coded distributed computing(CDC) has shown great potentials to solve the unexpected delay caused by stragglers in distributed computing. In this paper, we focus on the auction design for efficient resource allocation in CDC. Specifically, we aim to design a learning auction mechanism to handle heterogeneous user demands and also to free users from the complexity of specifying valuations for resource combinations, which increases exponentially with the resource dimensions. The user demand type is heterogeneous according to different variation trends of the value with finish time and workload, which is modeled by deep learning. The platform would allocate resources according to the user value function. Then users do not need to consider the complex relationship between uncertain finish time and resource configuration in CDC. Due to the inference error of the learning model and the complexity of calculating uncertain finish time, the considered social welfare optimization problem is a non-linear and non-convex integer problem. Even worse, the typical VCG-based payment scheme cannot guarantee truthfulness with the inference error. In response to these difficulties, we transform the social welfare optimization problem into a mixed integer programming problem which already has efficient solutions. The social welfare gap caused by the inference error is analyzed theoretically. The relationship between the utility regret of reporting truthfully and the inference error is also analyzed. We prove that our mechanism satisfies incentive alignment and individual rationality. Extensive experiments show the superiority of our mechanism compared with existing ones.

A Game-Theoretical Approach for Secure Crowdsourcing-Based Indoor Navigation System With Reputation Mechanism

At present, the crowdsourcing-based indoor navigation system (CINS) has attracted extensive attention from both industry and academia owing to its low-cost and high-accuracy performance. Unfortunately, the system that relies on crowdsourced data is vulnerable to the collusion attack, which leads to severe security issues. To address the security issues in the CINS, we propose to utilize a fully trusted fog server platform to advocate secure transactions between service requesters and responders. First, we propose a novel reputation incentive mechanism based on the behaviors of responders. Then, we employ the offensive and defensive game to model the interactions between the fog server platform and the responders, whereby a social welfare optimization problem is formulated to maximize the social welfare of the system. Next, the game equilibriums are found by using the replicator dynamic equation while the game stability is discussed. Finally, the simulation results show that the proposed mechanism can effectively encourage responders to provide positive navigation services and obtain more social welfare of the system compared with the conventional mechanisms.

Composite optimization with coupling constraints via dual proximal gradient method with applications to asynchronous networks

AbstractIn this article, we consider solving a composite optimization problem with affine coupling constraints in a multi‐agent network based on proximal gradient method. In this problem, all the agents jointly minimize the sum of individual cost functions composed of smooth and possibly non‐smooth parts. To this end, we derive the dual problem by the concept of Fenchel conjugate, which gives rise to the dual proximal gradient (DPG) algorithm by allowing for the asymmetric individual interpretations of the coupling constraints. Then, an asynchronous DPG (Asyn‐DPG) algorithm is proposed for the asynchronous networks with heterogeneous step‐sizes and communication delays. For both the two algorithms, if the non‐smooth parts of the objective functions are simple‐structured, we only need to update dual variables by some simple operations, accounting for the reduction of the overall computational complexity. Analytical convergence rate of the proposed algorithms is derived and their efficacy is verified by solving a social welfare optimization problem of electricity market in the numerical simulation.

Evaluating the market power and coalition formation in double-sided power market: An analytical decomposition approach

In this paper, new indices of the market power are defined to recognize and prioritize the potentials of market power as well as the feasibility of forming a profitable coalition of electricity market players. To this aim, the social welfare optimization problem is formulated and solved in a double-sided power market environment. Then, by forming the Lagrange function, Karush Kuhn Tucker (KKT) conditions are analytically developed. Three major outputs of the above problem including the Locational Marginal Price (LMP), the generation power of each unit and the dispatched elastic load of each Load Service Entity (LSE) are decomposed into basic structural factors. These factors include supply, demand and line congestion effects. Using the coefficients obtained from the structural decomposition, four profit-based market power indices are formulated: (1) profit index of each generator, or GenCo, due to the change of generation units’ bids; (2) profit index of each generator, or GenCo, due to the change of LSEs’ offers; (3) benefit index of each LSE due to the change of generation units’ bids, and (4) benefit index of each LSE due to the change of their offers. The impact of changes in a player’s bidding/offering strategy on its own profits determines the market power of that player. In addition, these changes affect other players' profits. So, the possibility of forming a profitable coalition can be evaluated. The proposed method is simulated on the IEEE 24-bus test system and the proposed indices are calculated and analyzed. Assessment results provide valuable implications for market regulators to monitor the competition level of the power market.

Connections between mean-field game and social welfare optimization

This paper studies the connection between a class of mean-field games and a social welfare optimization problem. We consider a mean-field game in function spaces with a large population of agents, and each agent seeks to minimize an individual cost function. The cost functions of different agents are coupled through a mean-field term that depends on the mean of the population states. We show that although the mean-field game is not a potential game, under some mild condition the ϵ-Nash equilibrium of the mean-field game coincides with the optimal solution to a modified social welfare optimization problem. This enables us to study the mean-field equilibrium using standard optimization theory. Based on this connection, we derive new results on the existence and uniqueness of the mean-field equilibrium. We also show that the mean-field equilibrium can be computed by a decentralized primal–dual algorithm. Numerical results are presented to validate the solution, and examples are provided to show the applicability of the proposed approach.

Noncooperative Social Welfare Optimization With Resiliency Against Network Anomaly

This article presents a noncooperative game-theoretic framework to model the social welfare optimization (SWO) problem with load aggregators participating in integrated economic dispatch and demand response. In the proposed framework, distribution system operators interact with generation units and load aggregators to maximize the overall social welfare. The proposed SWO problem addresses practical system constraints and falls into the scope of mixed integer nonlinear programs, which cannot be well handled by existing distributed algorithms. The proposed SWO problem is formulated by a special noncooperative strategic game, known as the potential game, and solved by a revised version of the spatial adaptive play under network anomaly. It is shown that the proposed framework has guaranteed convergence to a Nash equilibrium that is also a global optimizer. Simulations on a 15-generator benchmark distribution network have been conducted to validate the proposed framework.

Secure and Efficient Vehicle-to-Grid Energy Trading in Cyber Physical Systems: Integration of Blockchain and Edge Computing

Smart grid has emerged as a successful application of cyber-physical systems in the energy sector. Among numerous key technologies of the smart grid, vehicle-to-grid (V2G) provides a promising solution to reduce the level of demand-supply mismatch by leveraging the bidirectional energy-trading capabilities of electric vehicles. In this paper, we propose a secure and efficient V2G energy trading framework by exploring blockchain, contract theory, and edge computing. First, we develop a consortium blockchain-based secure energy trading mechanism for V2G. Then, we consider the information asymmetry scenario, and propose an efficient incentive mechanism based on contract theory. The social welfare optimization problem falls into the category of difference of convex programming and is solved by using the iterative convex-concave procedure algorithm. Next, edge computing has been incorporated to improve the successful probability of block creation. The computational resource allocation problem is modeled as a two-stage: 1) Stackelberg leader-follower game and 2) the optimal strategies are obtained by using the backward induction approach. Finally, the performance of the proposed framework is validated via numerical results and theoretical analysis.

Secure Wireless Powered and Cooperative Jamming D2D Communications

This paper investigates a secure wireless-powered device-to-device (D2D) communication network in the presence of multiple eavesdroppers, where a hybrid base station (BS) in a cellular network not only provides power wirelessly for the D2D transmitter to guarantee power efficiency for the D2D network, but also serves as a cooperative jammer (CJ) to interfere with the eavesdroppers. The cellular and D2D networks can belong to different service providers, which means that the D2D transmitter would need to pay for the energy service released by the hybrid BS to guarantee secure D2D communication. In order to exploit the hierarchical interaction between the BS and the D2D transmitter, we first formulate a Stackelberg game based energy trading scheme, where the quadratic energy cost model is considered. Then, a non-energy trading based Stackelberg game is investigated to study the reversed roles of the BS and the D2D users. For comparison, we also formulate and resolve the social welfare optimization problem. We derive the closed-form Stackelberg equilibriums of the formulated games and the optimal solutions for the social welfare optimization problem. Simulation results are provided to validate our proposed schemes to highlight the importance of energy trading interaction between cellular and D2D networks.

Real-time electricity pricing of a comprehensive demand response model in smart grids

This paper proposes a real-time interactional pricing scheme to maximize the social welfare of players in real-time demand response program in smart grids. Lagrangian relaxation–based dual decomposition is used to separate the social welfare optimization problem into a retailer's problem along with many consumers' subproblems, and the gradient projection method is adopted to solve them. First, the consumers' subproblems are solved to determine the optimal demand responses to the price announced by the retailer. To obtain the optimal demand response, a comprehensive mathematical function is developed on the basis of a combination of 5 costumer's utility functions reported in literature (ie, linear, potential, logarithmic, exponential, and hyperbolic). Afterward, the retailer calculates a real-time price in response to the consumers' reactions to maximize its profit. In terms of practical implementation, the consumers and the retailer interact with each other via a limited number of control messages exchanges to find the optimal solution at each hour. The proposed method is evaluated considering the various retailer's cost functions and the consumers' behaviors. Also, the results of elasticity sensitivity analysis are presented from the retailer and consumer viewpoints.

A distributed continuous time consensus algorithm for maximize social welfare in micro grid

This paper considers a social maximize welfare problem in a micro grid. Firstly, to enhance capacity ability and the output stability of generators in a micro grid, a novel social welfare optimization problem is modeled using wavelet neural network and flywheel energy storage system. Based on augmented Lagrangian function, a continuous time distributed gradient algorithm is proposed for the novel model. In the framework of nonsmooth analysis and algebraic graph theory, we prove that with the algorithm, the optimal solution can always be found asymptotically. Simulation results on 14-bus and 100-bus systems are presented to substantiate the performance and characteristics of the proposed algorithm.

Distribution Locational Marginal Pricing for Optimal Electric Vehicle Charging Management

This paper presents an integrated distribution locational marginal pricing (DLMP) method designed to alleviate congestion induced by electric vehicle (EV) loads in future power systems. In the proposed approach, the distribution system operator (DSO) determines distribution locational marginal prices (DLMPs) by solving the social welfare optimization of the electric distribution system which considers EV aggregators as price takers in the local DSO market and demand price elasticity. Nonlinear optimization has been used to solve the social welfare optimization problem in order to obtain the DLMPs. The efficacy of the proposed approach was demonstrated by using the bus 4 distribution system of the Roy Billinton Test System (RBTS) and Danish driving data. The case study results show that the integrated DLMP methodology can successfully alleviate the congestion caused by EV loads. It is also shown that the socially optimal charging schedule can be implemented through a decentralized mechanism where loads respond autonomously to the posted DLMPs by maximizing their individual net surplus.

Social Welfare Maximization in Transmission Enhancement Considering Network Congestion

Transmission enhancement in a competitive electricity market is analyzed in terms of its impact on the social welfare. A formulation of social welfare and the utility functions are derived in this research. Variations of supply and demand during a year are considered in transmission enhancement decisions. The proposed social welfare optimization problem is solved to determine the transmission congestion status under the optimal condition of the existing system. Transmission enhancement options are compared quantitatively to demonstrate their ability to increase social welfare, which provides valuable information for long-term transmission. The proposed method provides a systematic and quantitative tool for social welfare evaluation that is not available in industry today.

Impact of the Transformer Tap-Ratio Control on the Electricity Market Equilibrium

In this paper, the primal-dual nonlinear interior point method has been used as a basis for the derivation of a novel supply function equilibrium (SFE) algorithm for modeling the strategic interactions in the electricity market, using the ac network model, which incorporates modeling of the transformer tap-ratio control. The algorithm is used to investigate the impact of transformer tap-ratio control on the electricity market equilibrium and the effect of the interactions between network constraints and transformer tap-ratio control. The interior point social welfare optimization problem is combined with the optimization problem for maximizing the profit of each strategic generating firm in the market. The final combined single-level SFE problem is solved iteratively based on solution techniques of the interior point method. Numerical examples illustrate the effect of network constraints and especially the impact of transformer tap-ratio control on market equilibrium.