A neurodynamic approach for a class of pseudoconvex semivectorial bilevel optimization problem

The article proposes an exact approach to find the global solution of a nonconvex semivectorial bilevel optimization problem, where the objective functions at each level are pseudoconvex, and the constraints are quasiconvex. Due to its non-convexity, this problem is challenging, but it attracts more and more interest because of its practical applications. The algorithm is developed based on monotonic optimization combined with a recent neurodynamic approach, where the solution set of the lower-level problem is inner approximated by copolyblocks in outcome space. From that, the upper-level problem is solved using the branch-and-bound method. Finding the bounds is converted to pseudoconvex programming problems, which are solved using the neurodynamic method. The algorithm's convergence is proved, and computational experiments are implemented to demonstrate the accuracy of the proposed approach

A globally convergent neurodynamics optimization model for mathematical programming with equilibrium constraints

summary:This paper introduces a neurodynamics optimization model to compute the solution of mathematical programming with equilibrium constraints (MPEC). A smoothing method based on NPC-function is used to obtain a relaxed optimization problem. The optimal solution of the global optimization problem is estimated using a new neurodynamic system, which, in finite time, is convergent with its equilibrium point. Compared to existing models, the proposed model has a simple structure, with low complexity. The new dynamical system is investigated theoretically, and it is proved that the steady state of the proposed neural network is asymptotic stable and global convergence to the optimal solution of MPEC. Numerical simulations of several examples of MPEC are presented, all of which confirm the agreement between the theoretical and numerical aspects of the problem and show the effectiveness of the proposed model. Moreover, an application to resource allocation problem shows that the new method is a simple, but efficient, and practical algorithm for the solution of real-world MPEC problems

Pareto Adversarial Robustness: Balancing Spatial Robustness and Sensitivity-based Robustness

Adversarial robustness, which mainly contains sensitivity-based robustness and spatial robustness, plays an integral part in the robust generalization. In this paper, we endeavor to design strategies to achieve universal adversarial robustness. To hit this target, we firstly investigate the less-studied spatial robustness and then integrate existing spatial robustness methods by incorporating both local and global spatial vulnerability into one spatial attack and adversarial training. Based on this exploration, we further present a comprehensive relationship between natural accuracy, sensitivity-based and different spatial robustness, supported by the strong evidence from the perspective of robust representation. More importantly, in order to balance these mutual impacts of different robustness into one unified framework, we incorporate \textit{Pareto criterion} into the adversarial robustness analysis, yielding a novel strategy called \textit{Pareto Adversarial Training} towards universal robustness. The resulting Pareto front, the set of optimal solutions, provides the set of optimal balance among natural accuracy and different adversarial robustness, shedding light on solutions towards universal robustness in the future. To the best of our knowledge, we are the first to consider the universal adversarial robustness via multi-objective optimization

Capturing Transmission and Distribution Connected Wind Energy Variability

Although renewable energy provides a viable solution to address ongoing challenges of the economy and the environment in modern power systems, the variable generation of this technology results in major technical challenges for system operators. This issue is becoming more severe as the penetration of renewable generation is increasing. This dissertation addresses the variability challenge of renewable energy resources in transmission and distribution levels of modern power systems. For transmission level, this dissertation focuses on wind generation fluctuation. Three methods of reducing wind generation fluctuation are investigated from an economic perspective, including (a) dumping the wind generation, (b) using battery energy storage system (BESS) to capture excess wind generation, and (c) a hybrid method combining these two approaches. The economic viability of the hybrid method is investigated via a developed linear programming model with the objective of profit maximization, which in extreme cases will converge to one of the other methods. This dissertation further proposes a BESS planning model to minimize wind generation curtailment and accordingly maximize the deployment of this viable technology. For distribution level, this dissertation investigates the issue of microgrids net load variability stemmed from renewable generation. This is accomplished by investigating and comparing two options to control the microgrid net load variability resulted from high penetration of renewable generation. The proposed options include (a) Local management, which limits the microgrid net load variability in the distribution level by enforcing a cap constraint, and (b) Central management, which recommends on building a new fast response generation unit to limit aggregated microgrid net load variability in the distribution level. Moreover, the aggregated microgrid net load variability is studied in this dissertation by considering the distribution system operator (DSO). DSO would calculate the microgrids net load in day-ahead basis by receiving the aggregated demand bid curves. Accordingly, two models are proposed considering the DSO role in managing the grid operation and market clearing. The first one is security-constrained distribution system operation model which maximizes the system social welfare. The system security consists of distribution line outage as well as microgrid islanding. None of these two security events are in the control of the DSO, so associated uncertainties are considered in the problem modeling. The second one aims at reconfiguring the distribution grid, i.e., a grid topology control, using the smart switches in order to maximize the system social welfare and support grid reliability. The conducted numerical simulations demonstrate the effectiveness and the merits of the proposed models in identifying viable and economic options in capturing renewable generation variability

Evolutionary Computation 2020

Intelligent optimization is based on the mechanism of computational intelligence to refine a suitable feature model, design an effective optimization algorithm, and then to obtain an optimal or satisfactory solution to a complex problem. Intelligent algorithms are key tools to ensure global optimization quality, fast optimization efficiency and robust optimization performance. Intelligent optimization algorithms have been studied by many researchers, leading to improvements in the performance of algorithms such as the evolutionary algorithm, whale optimization algorithm, differential evolution algorithm, and particle swarm optimization. Studies in this arena have also resulted in breakthroughs in solving complex problems including the green shop scheduling problem, the severe nonlinear problem in one-dimensional geodesic electromagnetic inversion, error and bug finding problem in software, the 0-1 backpack problem, traveler problem, and logistics distribution center siting problem. The editors are confident that this book can open a new avenue for further improvement and discoveries in the area of intelligent algorithms. The book is a valuable resource for researchers interested in understanding the principles and design of intelligent algorithms