Chun-Tao Yang

The multiplayer stochastic noncooperative tracking game (NTG) with conflicting target strategy and cooperative tracking game (CTG) with a common target strategy of the mean-field stochastic jump-diffusion (MFSJD) system with external disturbance is investigated in this study. Due to the mean (collective) behavior in the system dynamic and cost function, the designs of the NTG strategy and CTG strategy for target tracking of the MFSJD system are more difficult than the conventional stochastic system. By the proposed indirect method, the NTG and CTG strategy design problems are transformed into linear matrix inequalities (LMIs)-constrained multiobjective optimization problem (MOP) and LMIs-constrained single-objective optimization problem (SOP), respectively. The LMIs-constrained MOP could be solved effectively for all Nash equilibrium solutions of NTG at the Pareto front by the proposed LMIs-constrained multiobjective evolutionary algorithm (MOEA). Two simulation examples, including the share market allocation and network security strategies in cyber-social systems, are given to illustrate the design procedure and validate the effectiveness of the proposed LMI-constrained MOEA for all Nash equilibrium solutions of NTG strategies of the MFSJD system.

The financial market is a nonlinear stochastic system with continuous Wiener and discontinuous Poisson random fluctuations. Most managers or investors hope their investment policies to be with the not only high profit but also low risk. Managers and investors involved pursue their own interests which are partly conflicting with others. Stochastic game theory has been widely applied to multiperson noncooperative decision making problem of financial market. However, for the nonlinear stochastic financial system with random fluctuations, it still lacks an analytical or computational scheme to effectively solve the complex noncooperative game strategy design problem. In this paper, the stochastic multiperson noncooperative game strategy in cyber-financial systems is transformed to a multituple Hamilton-Jacobi-Isacc inequalities (HJIIs)-constrained multiobjective optimization problem (MOP). This HJIIs-constrained MOP solution is also found to be the Nash equilibrium solution of multiperson noncooperative game strategy in nonlinear stochastic financial systems. In order to simplify design procedure by the global linearization theory, a set of local linear systems are interpolated to approximate the nonlinear stochastic financial system so that the m-tuple HJIIs-constrained MOP for noncooperative game strategy of cyber-financial system could be converted to a linear matrix inequalities (LMIs)-constrained MOP. Finally, an LMIs-constrained multiobjective evolution algorithm is explored for effectively solving the multiperson noncooperative game strategy in cyber-financial systems. Two design examples are also given for the illustration of the design procedure and the performance validation of the proposed stochastic noncooperative investment strategy in the nonlinear stochastic financial systems.

Summary: Given a sparse‐splitting wavelength‐division multiplexing network with no wavelength converter, we study a group multicast problem that is how to transmit a number of multicast streams from the video server to multiple destinations simultaneously. To avoid the situation that the wavelengths are used up by the first few requests, one wavelength is available for each multicast request. Hence, some of destinations may not be included in the multicast trees because of the lack of wavelengths. Our goal is to construct a number of light trees with conflict‐free wavelengths for multiple requests so that the number of served clients is maximized. This problem is named as the revenue‐maximized and delay‐constrained group multicast routing problem. We first determine a set of multicast trees with the maximum number of served clients, then followed by the wavelength assignment to allocate the minimum number of wavelengths to the resulting trees. In this study, we propose two Integer Linear Programming ILP‐based algorithms for determining the optimal solutions for the light‐tree construction problem and the wavelength assignment problem, respectively. For large‐scale networks, two heuristics are introduced to solve the light‐tree construction problem approximately. A set of simulations are also provided for comparing performances of our algorithms against the other published methods. Copyright © 2016 John Wiley & Sons, Ltd.