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Demand and Response in Smart Grid
Published in F. Richard Yu, Xi Zhang, Victor C. M. Leung, Green Communications and Networking, 2016
Qifen* Dong, Li* Yu, WenZhan+ Song
In the energy market model above, the decision variables are PGib, PDjk and ρn(i). As mentioned previously, LMPs relate to Lagrange multipliers corresponding to power flow balance constraints in ISO model, pn(i) can be viewed as fixed values in both generation and consumption modeling. So the three models are linear programming problems. Therefore, the three sets of Karush-Kuhn-Tucker (KKT) optimality conditions are both necessary and sufficient for describing overall market equilibrium. In addition, the three KKT sets result in a Mixed Linear Complementarity Problem (MLCP).
A compact MLCP-based projection recurrent neural network model to solve shortest path problem
Published in Journal of Experimental & Theoretical Artificial Intelligence, 2022
Mohammad Eshaghnezhad, Sohrab Effati, Amin Mansoori
The motivation of the paper is based on the above explanations. In this paper, we are going to present a compact (mixed linear complementarity problem) MLCP-based single-layer structure RNN model to solve the SPP. As we investigate the published papers, there is no attempt to solve the SPP by projection RNN models. As mentioned above, there are several RNN models for solving the SPP. The aim of the present paper is to investigate the existing projection RNN model to solve the SPP. We show the applicability of the paper and the method by adding a case study. The contributions of this paper are as follows:
A symplectic pseudospectral method for constrained time-delayed optimal control problems and its application to biological control problems
Published in Optimization, 2021
Xinwei Wang, Jie Liu, Xianzhou Dong, Chongwei Li, Yong Zhang
It is seen that the set of linear algebraic equations in Eq. (76) together with the LCP in Eq. (88) comprise a mixed linear complementarity problem (MLCP). An efficient way to solve such an MLCP is to express and as linear functions of by solving Eq. (76), and then substitute them into Eq. (88) to construct a standard LCP with respect to [36]. The detailed solving procedure is given as follows.
Managing morning commute congestion with a tradable credit scheme under commuter heterogeneity and market loss aversion behavior
Published in Transportmetrica B: Transport Dynamics, 2019
Mohammad Miralinaghi, Srinivas Peeta, Xiaozheng He, Satish V. Ukkusuri
In this context, the credit outcome is considered as gain by commuters if they sell excess credits in the market. Otherwise, it is considered as a loss. Thereby, the reference point for a group is the initial credit endowment for a commuter of that group. Then, the corresponding credit consumption disutility, , of a commuter of group departing in time interval is as follows: where parameter denotes the ‘loss aversion’ coefficient, indicating that commuters are more sensitive to loss than gain. Let denote the gain of a commuter of group departing in time interval by selling excess credits in the market when credit charge is less than initial endowment. The monetary gain of selling excess credits can be obtained as follows: where if , and 0 otherwise. Equation (6) can be written as: Using this notation, Equation (5) can be rewritten as: Under the TCS, commuters choose their departure times based on the total travel disutilities, which include three components: (1) queuing delay cost, (2) schedule delay cost, and (3) credit consumption disutility. The travel disutility, , of a commuter of group departing in time interval is as follows: Since the credit consumption disutility can be negative, the travel disutility of a commuter of group departing in time interval can be either negative or positive. A negative travel disutility implies that the monetary gain of a commuter by selling his/her excess credits in the market is higher than the summation of the experienced queuing delay costs and schedule delay costs. The mixed-linear complementarity problem (MLCP) for the equilibrium problem with TCS is as follows: