Search Results (21)

This paper proposes a robust bilevel mixed-integer profit maximization model for an independent distributed energy resource (DER) aggregator participating in the wholesale electricity market, considering the uncertain aggregation of electric vehicles (EVs) to the grid, as well as the discrete security check of the distribution system conducted by the non-market-participating distribution company. Regarding the uncertainty in EV–grid connectivity caused by stochastic transportation behavior, we characterize the robust connectivity at the lower level to ensure that the energy required for their daily transportation can be met. Solving the proposed bilevel mixed-integer profit maximization model is challenging due to the integer variables involved in the lower-level security check and robust connectivity problem, which makes the traditional strong duality and KKT method inapplicable. Thus, we propose using the total unimodularity property, multi-value-function approach, and strong duality method to transform the original bilevel model into an equivalent single-level model. Moreover, a sampling-based accelerated optimization algorithm is proposed to solve the equivalent single-level model efficiently. Case studies on a real-world transmission–distribution system verify that: (1) the proposed robust model outperforms deterministic models in profit by accommodating EV aggregation uncertainty; (2) the algorithm significantly reduces computational time compared to stochastic modeling approaches, while ensuring compliance with distribution network discrete security constraints. Full article

To address the limitations of existing power system low-carbon dispatching studies—such as over-reliance on generation-side carbon mitigation, price-oriented demand response (DR) failing to guide carbon reduction, and the low solution efficiency of traditional carbon emission flow (CEF)-based two-stage models—this paper proposes a data-driven CEF framework integrated with a bi-level economic and low-carbon dispatching model. First, a data-driven CEF calculation method is developed: It eliminates the need for complex power flow post-processing while maintaining calculation accuracy through multiple linear regression. On this basis, a bi-level optimization model is constructed: The upper level focuses on optimizing the economic and low-carbon objectives of power grid operation, while the lower level regulates industrial, commercial, and residential load aggregators (LAs) via carbon-intensity-oriented DR strategies and economic compensation mechanisms. Finally, a sample-based optimization algorithm combined with convex relaxation is proposed to solve the model, avoid the static setting of power flow and carbon intensity, and improve solution efficiency. Case studies demonstrate the following: the proposed method reduces the calculation time of node carbon intensity from 5 min to less than 100 ms, with the coefficient of determination (R²) ranging from 0.969 to 0.998; compared with the two-stage method, it achieves a 4.26% reduction in total scheduling cost, a 3.80% decrease in total carbon emissions, a 53.27% drop in carbon trading cost, and a 21.6% shortening in iteration time. These results verify that the proposed method can effectively enhance the source−load interaction and improve the accuracy and efficiency of low-carbon scheduling. This study provides a feasible technical path for the low-carbon transition of new-type power systems. Full article

Considering the global objective of carbon emission reduction, this paper focuses on optimizing the operational efficiency of grid-connected electric vehicles (EVs) and promoting sustainable energy integration and thus proposes a novel dual-incentive mechanism combining real-time pricing (RTP) and carbon quotas. A core of this study is the development of a bilevel programming model that effectively captures the strategic interaction between power suppliers (PS) and microgrid (MG) users. At the upper level, the model enables the PS to optimize electricity prices, achieving both revenue maximization and grid balance maintenance; at the lower level, it supports MGs in rational scheduling of EV charging/discharging, photovoltaic and wind energy (PWE) utilization, and load consumption, ensuring the fulfillment of user demands while maximizing MG profits. To address the non-convex factors in the model that hinder an efficient solution, another key is the design of a bilevel distributed genetic algorithm, which realizes efficient decentralized decision making and provides technical support for the practical application of the model. Through comprehensive simulations, the study verifies significant quantitative outcomes. The proposed algorithm converges after only 61 iterations, ensuring efficient solution performance. The average purchase price of electricity from the PS for the MG is USD 1.1, while the selling price of PWE sources from MG for the PS is USD 0.6. This effectively promotes the MG to prioritize the consumption of PWE sources and encourages the PS to repurchase the electricity generated by PWE sources. On average, carbon emissions decreased by approximately 300 g each time slot, and the average amount of carbon trading was around USD 8. Ultimately, this research delivers a practical and impactful solution for the development of MGs and the advancement of carbon reduction goals. Full article

Adversarial learning has been attracting more and more attention thanks to the fast development of machine learning and artificial intelligence. However, due to the complicated structure of most machine learning models, the mechanism of adversarial attacks is not well interpreted. How to measure the effect of attacks is still not quite clear. In this paper, we investigate the adversarial learning from the perturbation analysis point of view. We characterize the robustness of learning models through the calmness of the solution mapping. In the case of convex clustering models, we identify the conditions under which the clustering results remain the same under perturbations. When the noise level is large, it leads to an attack. Therefore, we propose two bilevel models for adversarial learning where the effect of adversarial learning is measured by some deviation function. Specifically, we systematically study the so-called $\delta$-measure and show that under certain conditions, it can be used as a deviation function in adversarial learning for convex clustering models. Finally, we conduct numerical tests to verify the above theoretical results as well as the efficiency of the two proposed bilevel models. Full article

This paper proposes a new accelerated fixed-point algorithm based on a double-inertial extrapolation technique for solving structured variational inclusion and convex bilevel optimization problems. The underlying framework leverages fixed-point theory and operator splitting methods to address inclusion problems of the form $0\in (A+B)(x)$, where A is a cocoercive operator and B is a maximally monotone operator defined on a real Hilbert space. The algorithm incorporates two inertial terms and a relaxation step via a contractive mapping, resulting in improved convergence properties and numerical stability. Under mild conditions of step sizes and inertial parameters, we establish strong convergence of the proposed algorithm to a point in the solution set that satisfies a variational inequality with respect to a contractive mapping. Beyond theoretical development, we demonstrate the practical effectiveness of the proposed algorithm by applying it to data classification tasks using Deep Extreme Learning Machines (DELMs). In particular, the training processes of Two-Hidden-Layer ELM (TELM) models is reformulated as convex regularized optimization problems, enabling robust learning without requiring direct matrix inversions. Experimental results on benchmark and real-world medical datasets, including breast cancer and hypertension prediction, confirm the superior performance of our approach in terms of evaluation metrics and convergence. This work unifies and extends existing inertial-type forward–backward schemes, offering a versatile and theoretically grounded optimization tool for both fundamental research and practical applications in machine learning and data science. Full article

The integration of high-penetration renewable energy sources (RESs) into transmission networks introduces profound uncertainty that challenges traditional infrastructure planning approaches. Existing transmission expansion planning (TEP) models either rely on static scenario sets or over-conservative worst-case assumptions, failing to capture the operational stress triggered by rare but structurally impactful renewable behaviors. This paper proposes a novel bi-level optimization framework for transmission planning under adversarial uncertainty, coupling a distributionally robust upper-level investment model with a lower-level operational response embedded with physics and market constraints. The uncertainty space was not exogenously fixed, but instead dynamically generated through a physics-informed spatiotemporal generative adversarial network (PI-ST-GAN), which synthesizes high-risk renewable and load scenarios designed to maximally challenge the system’s resilience. The generator was co-trained using a composite stress index—combining expected energy not served, loss-of-load probability, and marginal congestion cost—ensuring that each scenario reflects both physical plausibility and operational extremity. The resulting bi-level model was reformulated using strong duality, and it was decomposed into a tractable mixed-integer structure with embedded adversarial learning loops. The proposed framework was validated on a modified IEEE 118-bus system with high wind and solar penetration. Results demonstrate that the GAN-enhanced planner consistently outperforms deterministic and stochastic baselines, reducing renewable curtailment by up to 48.7% and load shedding by 62.4% under worst-case realization. Moreover, the stress investment frontier exhibits clear convexity, enabling planners to identify cost-efficient resilience strategies. Spatial congestion maps and scenario risk-density plots further illustrate the ability of adversarial learning to reveal latent structural bottlenecks not captured by conventional methods. This work offers a new methodological paradigm, in which optimization and generative AI co-evolve to produce robust, data-aware, and stress-responsive transmission infrastructure designs. Full article

Integrated sensing and communication (ISAC) has attracted extensive attention as a key technology to improve spectrum utilization and system performance for future wireless sensor networks. At the same time, active surveillance, as a legitimate means of surveillance, can improve the success rate of surveillance by sending interference signals to suspicious receivers, which is important for crime prevention and public safety. In this paper, we investigate the joint optimization of performance of both ISAC and active surveillance. Specifically, we formulate a bilevel optimization problem where the upper-level objective aims to maximize the probability of successful eavesdropping while the lower-level objective aims to optimize the localization performance of the radar on suspicious transmitters. By employing the Rayleigh quotient, introducing a decoupling strategy, and adding penalty terms, we propose an algorithm to solve the bilevel problem where the lower-level objective is convex. With the help of the proposed algorithm, we obtain the optimal solution of the analog transmit beamforming matrix and the digital beamforming vector. Performance analysis and discussion of key insights, such as the trade-off between eavesdropping success probability and radar localization accuracy, are also provided. Finally, comprehensive simulation results validate the effectiveness of our proposed algorithm in enhancing both the eavesdropping success probability and the accuracy of radar localization. Full article

Highway toll stations are equipped with electronic toll collection (ETC) lanes and manual toll collection (MTC) lanes. It is anticipated that connected autonomous vehicles (CAVs), MTC human-driven vehicles (MTC-HVs), and ETC human-driven vehicles (ETC-HVs) will coexist for a long time, sharing toll station infrastructure. To fully leverage the congestion reduction potential of ETC, this paper addresses the problem of ETC lane allocation at toll stations under heterogeneous traffic flows, modeling it as a mixed-integer nonlinear bilevel programming problem (MINLBP). The objective is to minimize total toll station travel time by optimizing the number of ETC lanes at station entrances and exits while considering ETC-HVs’ lane selection behavior based on the user equilibrium principle. As both upper-level and lower-level problems are convex, the bilevel problem is transformed into an equivalent single-level optimization using the Karush–Kuhn–Tucker (KKT) conditions of the lower-level problem, and numerical solutions are obtained using the commercial solver Gurobi. Based on surveillance video data from the Liulin toll station (Lianhuo Expressway) in Zhengzhou, China, numerical experiments were conducted. The results illustrate that the proposed method reduces total vehicle travel time by 90.44% compared to the current lane allocation scheme or the proportional lane allocation method. Increasing the proportion of CAVs or ETC-HVs helps accommodate high traffic demand. Dynamically adjusting lane allocation in response to variations in traffic arrival rates is proven to be a more effective supply strategy than static allocation. Moreover, regarding the interesting conclusion that all ETC-HVs choose the ETC lanes, we derived the relaxed analytical solution of MINLBP using a parameter iteration method. The analytical solution confirmed the validity of the numerical experiment results. The findings of this study can effectively and conveniently guide lane allocation at highway toll stations to improve traffic efficiency. Full article

Convex bilevel optimization problems (CBOPs) exhibit a vital impact on the decision-making process under the hierarchical setting when image restoration plays a key role in signal processing and computer vision. In this paper, a modified double inertial extragradient-like approach with a line search procedure is introduced to tackle the CBOP with constraints of the CFPP and VIP, where the CFPP and VIP represent a common fixed point problem and a variational inequality problem, respectively. The strong convergence analysis of the proposed algorithm is discussed under certain mild assumptions, where it constitutes both sections that possess a mutual symmetry structure to a certain extent. As an application, our proposed algorithm is exploited for treating the image restoration problem, i.e., the LASSO problem with the constraints of fractional programming and fixed-point problems. The illustrative instance highlights the specific advantages and potential infect of the our proposed algorithm over the existing algorithms in the literature, particularly in the domain of image restoration. Full article

To enhance the efficient utilization of space resources, it is critical to integrate information from various systems of the space station and formulate scientific and effective methods for planning cargo supplies. Considering the large-scale, multi-objective, complex nonlinear, non-convex, non-differentiable, and mixed-integer characteristics, this study decomposes the space station cargo supply planning problem into a bi-level optimization problem involving cargo manifest and loading layout iterations. A new CILPSO algorithm is proposed to solve this by integrating particle coding, reliability priority, and random generation mechanisms of population initialization, global and local versions of particle updating, and a local search strategy. The experimental results show that the CILPSO algorithm outperforms other algorithms regarding search performance and convergence efficiency. The proposed approach can effectively reduce the cargo supply cost of the space station and improve the output of space science and application achievements. It provides a decision-making basis for the responsible department to develop cargo supply schemes, for the cargo supply systems to submit cargo demands, and for the cargo spaceship system to design loading schemes. This study advances the logistics sustainability of the space station. Full article

This paper introduces a novel two-step inertial algorithm for locating a common fixed point of a countable family of nonexpansive mappings. We establish strong convergence properties of the proposed method under mild conditions and employ it to solve convex bilevel optimization problems. The method is further applied to the image recovery problem. Our numerical experiments show that the proposed method achieves faster convergence than other related methods in the literature. Full article

Fixed-point theory plays many important roles in real-world problems, such as image processing, classification problem, etc. This paper introduces and analyzes a new, accelerated common-fixed-point algorithm using the viscosity approximation method and then employs it to solve convex bilevel optimization problems. The proposed method was applied to data classification with the Diabetes, Heart Disease UCI and Iris datasets. According to the data classification experiment results, the proposed algorithm outperformed the others in the literature. Full article

This paper develops a two-stage robust optimization (TSRO) model for prosumers considering multiple uncertainties from the sustainable energy of wind power generation and load demand and extends the existing nested column-and-constraint generation (C&CG) algorithm to solve the corresponding optimization problem. First, considering the impact of these uncertainties on market trading strategies of prosumers, a box uncertainty set is introduced to characterize the multiple uncertainties; a TSRO model for prosumers considering multiple uncertainties is then constructed. Second, the existing nested C&CG algorithm is extended to solve the corresponding optimization problem of which the second-stage optimization is a bi-level one and the inner level is a non-convex optimization problem containing 0–1 decision variables. Finally, a case study is solved. The optimized final overall operating cost of prosumers under the proposed model is CNY 3201.03; the extended algorithm requires only four iterations to converge to the final solution. If a convergence accuracy of 10⁻⁶ is used, the final solution time of the extended algorithm is only 9.75 s. The case study result shows that prosumers dispatch the ESS to store surplus wind power generated during the nighttime period and release the stored electricity when the wind power generation is insufficient during the daytime period. It can contribute to promoting the local accommodation of renewable energy and improving the efficiency of renewable energy utilization. The market trading strategy and scheduling results of the energy storage system (ESS) are affected by multiple uncertainties. Moreover, the extended nested C&CG algorithm has a high convergence accuracy and a fast convergence speed. Full article

A new accelerated common fixed point algorithm is introduced and analyzed for a countable family of nonexpansive mappings and then we apply it to solve some convex bilevel optimization problems. Then, under some suitable conditions, we prove a strong convergence result of the proposed algorithm. As an application, we employ the proposed algorithm for regression and classification problems. Moreover, we compare the performance of our algorithm with others. By numerical experiments, we found that our algorithm has a better performance than the others. Full article

In the development of algorithms for convex optimization problems, symmetry plays a very important role in the approximation of solutions in various real-world problems. In this paper, based on a fixed point algorithm with the inertial technique, we proposed and study a new accelerated algorithm for solving a convex bilevel optimization problem for which the inner level is the sum of smooth and nonsmooth convex functions and the outer level is a minimization of a smooth and strongly convex function over the set of solutions of the inner level. Then, we prove its strong convergence theorem under some conditions. As an application, we apply our proposed algorithm as a machine learning algorithm for solving some data classification problems. We also present some numerical experiments showing that our proposed algorithm has a better performance than the five other algorithms in the literature, namely BiG-SAM, iBiG-SAM, aiBiG-SAM, miBiG-SAM and amiBiG-SAM. Full article