Bilevel Optimization Approach Research Articles

A bilevel learning approach for nonlocal image deblurring with variable weights parameter

This paper introduces an innovative bilevel optimization approach to elevate the deblurring process. By integrating a weights variable nonlocal model with a spatially varying attached term, the methodology aims to achieve enhanced restoration outcomes. Theoretical scrutiny is dedicated to unraveling the solution of the model, paving the way for the development of an efficient algorithm meticulously crafted to compute the clean image. This algorithm excels in learning both the weights parameter and the balanced L2-L1 attached parameter concurrently, thereby ensuring optimal performance. Through careful parameter selection, the proposed nonlocal deblurring model showcases superior effectiveness, surpassing existing models in terms of both performance and efficacy.

Enhancing Neural Radiance Fields with Adaptive Multi-Exposure Fusion: A Bilevel Optimization Approach for Novel View Synthesis

Neural Radiance Fields (NeRF) have made significant strides in the modeling and rendering of 3D scenes. However, due to the complexity of luminance information, existing NeRF methods often struggle to produce satisfactory renderings when dealing with high and low exposure images. To address this issue, we propose an innovative approach capable of effectively modeling and rendering images under multiple exposure conditions. Our method adaptively learns the characteristics of images under different exposure conditions through an unsupervised evaluator-simulator structure for HDR (High Dynamic Range) fusion. This approach enhances NeRF's comprehension and handling of light variations, leading to the generation of images with appropriate brightness. Simultaneously, we present a bilevel optimization method tailored for novel view synthesis, aiming to harmonize the luminance information of input images while preserving their structural and content consistency. This approach facilitates the concurrent optimization of multi-exposure correction and novel view synthesis, in an unsupervised manner. Through comprehensive experiments conducted on the LOM and LOL datasets, our approach surpasses existing methods, markedly enhancing the task of novel view synthesis for multi-exposure environments and attaining state-of-the-art results. The source code can be found at https://github.com/Archer-204/AME-NeRF.

Design of chiller system with thermal and battery storage for enhanced integration with on-site PV

Space-cooling is dominating building energy use in warm regions. Integrating on-site PV generation with cooling systems is a potential building-scale decarbonization solution. However, designing the system to ensure cost-effectiveness and reliability is challenging since it requires solving a highly non-linear design and dispatch problem. This paper proposes a solution strategy to the design problem of an integrated multi-chillers system with PV, and ice thermal and battery storage to reduce emissions and annual system costs. The proposed strategy adopts a bi-level optimization approach eliminating the need for simplistic models. The upper level employs particle swarm optimization to determine storage and chillers' capacities and types, while the lower level solves the dispatch problem using mixed-integer linear programming. To validate the proposed strategy and decarbonization solution, the model was applied to a generic residential building in Qatar and was exposed to a varying range of carbon pricing. The results highlight the potential for deep decarbonization in regions with abundant solar resources and high cooling needs. In Qatar, the model suggests a moderate carbon pricing range of $75–125/ton of CO2 for deep decarbonization. The developed model demanded reasonable computational resources with an execution time of less than 1 h and exhibited stability with consistent convergence.

Market design for ancillary service provisions of inertia and frequency response via virtual power plants: A non-convex bi-level optimisation approach

The Great Britain (GB) government is paving the path to decarbonisation by actively promoting the integration of wind power into its generation mix. This sharp transition to renewable energy, however, introduces specific challenges. The characteristics of non-synchronous wind turbines have the potential to impact grid stability and frequency security due to the reduction in system inertia. In response to these challenges, the deployment of virtual power plants (VPPs) is envisioned in deregulated power systems, which allow for the aggregation and coordinated control of diverse distributed energy resources, enhancing grid flexibility, reliability, and efficiency. Moreover, VPPs offer the provision of system inertia and frequency response services at the national level. This study drops this assumption and leverages the localised flexibility inherent in VPPs to meet the ancillary service requirements of the low-carbon power system. The formulated problem is constructed as a non-convex bi-level optimisation problem, where the upper-level problem represents the operation of a frequency-constrained unit commitment model, and the lower-level problem embodies the energy dispatches and frequency responses of a group of VPPs, guided by the dual price signals of cleared energy and ancillary services. To address the non-convex nature of the unit commitment problem, a two-fold approach is employed. First, binary commitment status decision variables are relaxed to continuous versions. Subsequently, the duality gap between the original non-convex unit commitment problem and its relaxed dual form is minimised, yielding a solution closely approximating the optimal solution of the original problem. Second, the relaxed bi-level optimisation problem is transformed into a single-level mathematical programs with equilibrium constraints by replacing the lower-level VPP problems with their equivalent Karush-Kuhn–Tucker optimality conditions. The case studies conducted in this work encompass a comprehensive scope. Initially, the study evaluates the effectiveness of VPPs in delivering ancillary services within the projected context of the GB power system for 2030. The findings reveal a substantial 28.28% decrease in system operation costs when compared to the benchmark case lacking VPP flexibility. Additionally, the integration of VPPs leads to significantly lower price signals for inertia, primary frequency response, and enhanced frequency response, reduced by 81.21%, 79.13%, and 86.27%, respectively, in contrast to the benchmark case. The analysis then delves into a sensitivity exploration, investigating the inherent flexibility of VPPs. The profit of local VPPs is expected to increase with VPP flexibility. Finally, the study illustrates how VPPs can adapt to and derive benefits from an increasing level of wind power penetration by providing a higher amount of frequency response.

Green product family design with low-carbon postponement fulfilment: A bilevel interactive optimization approach

In the globalization process, postponement is still an effective strategy for enterprises to reduce supply chain risks and uncertainties. The enterprises must additionally consider low-carbon issues in product development process with the increasing environmental concerns. The inherent coupling of product design and postponement fulfillment that considers environmental concerns necessitates joint optimization of green product family (GPF) design and low-carbon postponement (LCP) fulfillment. However, existing literature tends to aggregate the postponement and environmental concerns into a single-level and all-in-one optimization problem based on the assumption that a (fixed) GPF architecture is pre-determined at the outset. Different from existing modes, this article proposes a bilevel interactive optimization (BIO) approach to reveal the hierarchical interactions and complex decisions involved in GPF design and LCP fulfillment. Based on bilevel programming theory, a non-linear BIO model consisting of an upper-level GPF design problem and two lower-level LCP fulfillment problems is established. A nested genetic algorithm is developed to solve the proposed BIO model. A case study of LCP manufacturing of a green electric vehicle product family is adopted to verify the feasibility and superiority of the BIO approach for the GPF design and the LCP fulfillment. Some important managerial insights are derived from the comparison experiments and the sensitivity analysis on the proposed demand postponement parameter.

An Analytical Polytope Approximation Aggregation of Electric Vehicles Considering Uncertainty for the Day-Ahead Distribution Network Dispatching

The integration of large-scale heterogeneous electric vehicles (EVs) into the distribution network increases the system management complexity significantly. Due to the flexible charging/discharging operation and shiftable energy consumption during the parking time, EVs possess a great dispatching potential for the distribution network. This paper develops an analytical polytope approximation (APA) aggregation model to efficiently depict the dispatchable regions of large-scale EVs with uncertainties and proposes a bilevel cooperative optimization approach for EV aggregators to participate in the distribution network day-ahead optimal scheduling. Uncertainties of EVs are modeled by chance constraints with different confidence levels to accommodate various regulatory requirements. The proposed approach can obtain large-scale EVs dispatchable capabilities with minimum flexibility loss and realize the regulation command disaggregation without violations. Numerical case studies are conducted on IEEE 33-bus and 141-bus distribution networks based on real data sets, which show that the proposed approach outperforms other state-of-art methods in terms of low operation flexibility conservatism, high system economics, and computational efficiency.

Modeling the power trading strategies of a retailer with multi-microgrids: a robust bi-level optimization approach

ABSTRACT The primary contribution of this paper lies in the development of a bi-level optimization framework designed to model a retailer’s power trading strategies within the context of multi-microgrids. Another noteworthy aspect of this research is managing the risk associated with the retailer’s decision-making process, achieved by addressing the unpredictability of market prices through a robust bi-level structure. In this model, the upper-level problem focuses on the retailer’s decision-making, while the lower-level problem addresses microgrid considerations. Furthermore, a load-shifting strategy is integrated into the microgrid problem to enhance the profitability-to-cost ratio for both the retailer and the microgrids. The results demonstrate a 3% increase in the retailer’s profits and a significant 30% reduction in the microgrids’ costs using the load-shifting strategy. In the most unfavorable scenario, the retailer experiences a profit reduction of 21.67%, while the maximum increase in the microgrids’ costs reaches 238.3%.

Bilevel optimal parameter learning for a high-order nonlocal multiframe super-resolution problem

This work elaborated an improved method to multiframe super-resolution (SR), which involves a nonlocal first-order regularization combined with a nonlocal p-Laplacian term. The nonlocal TV term excels at edge preserving, whilst the nonlocal p-Laplacian is commonly used to perfectly reconstruct image textures. Firstly, we discuss the existence and uniqueness of a solution to our new model in a well posed framework. Then, we derive a modified Primal-dual iteration to compute the super-resolved solution. Furthermore, we introduce a new bilevel optimization approach to learn two regularization parameters. The included tests validate that the introduced optimization procedure performs favorably compared to numerous SR approaches in terms of efficiency and accuracy.

FedCSS: Joint Client-and-Sample Selection for Hard Sample-Aware Noise-Robust Federated Learning

Federated Learning (FL) enables a large number of data owners (a.k.a. FL clients) to jointly train a machine learning model without disclosing private local data. The importance of local data samples to the FL model vary widely. This is exacerbated by the presence of noisy data, which exhibit large losses similar to important (hard) samples. Currently, there lacks an FL approach that can effectively distinguish hard samples (which are beneficial) from noisy samples (which are harmful). To bridge this gap, we propose the Federated Client and Sample Selection (FedCSS) approach. It is a bilevel optimization approach for FL client-and-sample selection to achieve hard sample-aware noise-robust learning in a privacy preserving manner. It performs meta-learning based online approximation to iteratively update global FL models, select the most positively influential samples and deal with training data noise. Theoretical analysis shows that it is guaranteed to converge in an efficient manner. Experimental comparison against six state-of-the-art baselines on five real-world datasets in the presence of data noise and heterogeneity shows that it achieves up to 26.4% higher test accuracy, while saving communication and computation costs by at least 41.5% and 1.2%, respectively.

Bi-level multi-objective optimization of the structure and attitude for space solar power station

To utilize space solar energy efficiently, this study focuses on the optimization of multi-rotary joints space solar power satellite (MR-SSPS), which is designed to efficiently collect and transmit solar energy to Earth. A constraint multi-objective optimization model is proposed for the MR-SSPS, which encompasses three objectives: truss mass, structural stiffness, and attitude control energy. A bi-level optimization method is proposed, considering the characteristics of the structure and attitude control models. The first-level optimizes the structure of the solar array system and truss, while the second-level optimizes the attitude controller. The mass and certain structural parameters serve as correlation variables linking the two levels. To enhance efficiency, a database and parallel computing are employed. Compared to the traditional multi-objective optimization approach, the proposed bi-level method achieves better solutions in both accuracy and efficiency. The optimized MR-SSPS structure meets attitude control accuracy constraints while reducing mass and energy consumption. This research provides insights into the design of MR-SSPS and demonstrates the effectiveness of the bi-level optimization approach for complex engineering problems.

Capacity optimization and performance analysis of wind power-photovoltaic-concentrating solar power generation system integrating different S-CO2 Brayton cycle layouts

This study investigates a wind power-photovoltaic-concentrated solar power (WP-PV-CSP) system that incorporates different supercritical CO2 (S-CO2) Brayton cycle layouts to address grid-connected safety issues associated with solar and wind energy. Additionally, it aims to enhance the system's techno-economic performance. Notably, prior research has not explored the optimal capacity configuration of the WP-PV-CSP system or identified the most effective S-CO2 Brayton cycle layout for system optimization. Reasonable capacity allocation can guarantee the system's reliability and feasibility, while an appropriate operation schedule can better handle the problem of mismatch between output and demand, and capacity and operation interact with each other. Consequently, this paper proposes a bi-level capacity-operation collaborative optimization approach to optimize the system's main components' capacity and operation scheduling with the optimization objectives of levelized cost of energy (LCOE) and CO2 emissions. Moreover, it seeks to pinpoint the most advantageous S-CO2 Brayton cycle layout. The results demonstrate that employing the S-CO2 intercooling Brayton cycle as the CSP system's power cycle yields the WP-PV-CSP system's best techno-economic performance. Compared with the WP-PV-CSP system integrating the steam Rankine cycle, the LCOE, CO2 emissions, and power discard are reduced by 13.81%, 40.36%, and 37.06%, respectively, and the system efficiency experiences a noteworthy 36.36% increase. These findings comprehensively highlight the substantial techno-economic and environmental advantages of adopting the S-CO2 Brayton cycle. In summary, this research contributes valuable insights into optimizing WP-PV-CSP systems, explicitly addressing capacity and operational challenges, and underscores the potential benefits of selecting the S-CO2 Brayton cycle in advancing renewable energy solutions.

A bi-level optimization approach for joint rack sequencing and storage assignment in robotic mobile fulfillment systems

A bi-level optimization approach for joint rack sequencing and storage assignment in robotic mobile fulfillment systems

A gradient-based bilevel optimization approach for tuning regularization hyperparameters

A gradient-based bilevel optimization approach for tuning regularization hyperparameters

Energy management of multi-microgrids with renewables and electric vehicles considering price-elasticity based demand response: A bi-level hybrid optimization approach

This article develops an energy management scheme for multi-microgrid systems involving the scheduling strategy of distributed resources, renewables and plug-in electric vehicles penetration to enhance the economic-environmental benefits of the system. The proposed framework also integrates the price elasticity-based augmented demand response program into the energy management (EM) problem to investigate the influence of dynamic energy pricing and incentives provided to consumers. The local power trading between adjacent microgrids and external trading with the primary grid through each microgrid's generation resources scheduling facilitates the microgrids’ cost reduction while maintaining supply-demand balance in the system. But, the ubiquitous intermittent nature of renewables, load demands, and vehicle charging imply complexities in the system. Hence, this work formulates the EM problem incorporating the uncertainties of renewables and load demands by the worst-case realization and employs a bi-level hybrid grey wolf-whale optimization; the first level is optimized from the microgrid's standpoint to obtain the dynamic pricing, and the load demands modification, whereas the operational cost of the multi-microgrid system and the utility profit are optimized in the second level. The proposed approach is studied on a test system consisting of residential, commercial and industrial microgrids; substantial simulation results are presented to validate the effectiveness.

Interpretable model learning in variational imaging: a bilevel optimization approach

Abstract In this paper, we investigate the use of bilevel optimization for model learning in variational imaging problems. Bilevel learning is an alternative approach to deep learning methods, which leads to fully interpretable models. However, it requires a detailed analytical insight into the underlying mathematical model. We focus on the bilevel learning problem for total variation models with spatially- and patch-dependent parameters. Our study encompasses the directional differentiability of the solution mapping, the derivation of optimality conditions, and the characterization of the Bouligand subdifferential of the solution operator. We also propose a two-phase trust-region algorithm for solving the problem and present numerical tests using the CelebA dataset.

Joint Terminal Pairing and Multi-Dimensional Resource Allocation for Cooperative Computation in a WP-MEC System

The combination of multi-access edge computing (MEC) and wireless power transfer (WPT) can potentially improve system performance and prolong terminals’ battery lifetime. In this paper, we study cooperative computation in a wireless powered multi-access edge computing (WP-MEC) system. In this system, there are an access point (AP) deployed with an MEC server and multiple cellular terminals that are powered by harvested energy from a power station. The computational task of each terminal is partially completed locally and partially offloaded to the AP and an nearby idle terminal. In order to minimize energy consumption in the system, we jointly optimize terminal pairing and multi-dimensional resource (i.e., computing power and communication resource) allocation. A non-convex mixed-integer non-linear programming (MINLP) problem is formulated in this paper. To solve this challenging problem, we propose a bilevel optimization approach, in which the multi-dimensional resource allocation scheme is designed under given terminal pairing relationships in the inner level, and then the pairing relationships between terminals are obtained in the outer level based on the obtained multi-dimensional resource allocation scheme. Extensive numerical results show that the proposed bilevel optimization scheme can reduce energy consumption considerably compared to some baseline schemes.

Bilevel optimization approach to fast charging station planning in electrified transportation networks

Unplanned en-route charging of electric vehicles (EVs) can unexpectedly cripple traffic conditions. As less-effective location of fast charging station (FCS) may exacerbate this issue, the effects of FCS on EVs' charging behaviors should be incorporated at the system planning stage. This paper proposes a strategic-charging-behavior awared model in the context of electrified transportation network environment. This model is formulated into a bilevel mixed-integer programming problem. A newly designed network equilibrium model targets on the low-level problem, which is to model the drivers' charging reaction to a certain FCS layout. In considering the EV self-serving routing and charging behaviors as well as power network constraints, the upper-level problem is formulated for location and sizing decision-makings, of which the objective is to minimize the overall traffic time and investment cost. To handle the proposed bilevel problem, a descent algorithm is further developed. To examine the effectiveness of the proposed approach, extensive numerical experiments are conducted, through which the obtained results demonstrate that the EV charging demand can perfectly be met while traffic congestions can be alleviated to a great extent.

Modelling a bi-level multi-objective post-disaster humanitarian relief logistics network design problem under uncertainty

Post-disaster humanitarian relief logistics focuses on managing the supply and shipment of relief items. Owing to the complexity arising from the hierarchical decision relationship and the uncertainties of demand and transportation, it is challenging to develop an effective humanitarian relief logistics network (HRLN). A globalized robust bi-level multi-objective HRLN model involving uncertainties in transportation time, transportation cost and demand is developed to address this problem, in which an upper-level decision-maker focuses on the allocation problem and a lower-level decision-maker considers the supply problem. For tractability, the goal programming approach is employed to trade off conflicting timeliness, satisfaction and operational cost objectives. The proposed globalized robust bi-level HRLN model is reformulated as its globalized robust counterpart formulations under two different perturbation structures. The primal–dual approach is adopted to transform the bi-level models into equivalent mixed-integer conic programs. A case study concerning an Iranian earthquake is conducted to prove the performance of the proposed model. Globalized robust models are more flexible and able to immunize against uncertainty by comparison with traditional robust optimization and deterministic solutions. The managerial insights of using the globalized robust bi-level optimization approach are reported for disaster response management. The design of an emergency aviation network to circumvent the effects of COVID-19 could be considered in future research.

Mobile energy storage systems with spatial–temporal flexibility for post-disaster recovery of power distribution systems: A bilevel optimization approach

In recent years, the damage to power distribution systems caused by the frequent occurrence of extreme disasters in the world cannot be ignored. In the face of the customer’s demand for high power supply reliability and high power quality, it is urgent to establish a resilient distribution network that can not only resist extreme disasters and quickly recover the power distribution system loads, but also ensure a high voltage quality of the distribution system during recovery process. Therefore, mobile energy storage systems with adequate spatial–temporal flexibility are added, and work in coordination with resources in an active distribution network and repair teams to establish a bilevel optimization model. The objective of the upper-level optimization model is minimum the total load curtailment of the distribution system after the disaster. And the objective of the lower-level optimization model is minimum the voltage offset of power supply buses during the recovery stage. A modified IEEE 33-bus distribution test system is used to verify this model. The simulation results show that the bilevel optimization strategy proposed in this research can effectively reduce the voltage offset during the recovery process of distribution systems, and ensure the minimum total load curtailment simultaneously.

Smart camera placement for building surveillance using OpenBIM and an efficient Bi-level optimization approach

Cameras have been widely used in buildings for safety and efficiency surveillance. Especially with the integration of artificial intelligence and building information modeling (BIM), many intelligent applications have emerged. However, optimizing the camera plan in buildings with various geometric and semantic properties remains challenging. This study proposes a smart camera placement framework that can be generally applied in different building scenarios to solve this problem. Firstly, a camera-integrated BIM is constructed based on a systematic literature review (SLR) and Industry Foundation Classes (IFC) schema, followed by a sample-based voxelization method to convert BIM models to semantic voxels. Secondly, a realistic camera coverage analysis method is developed to consider the object's properties, based on which a bi-level formulation is proposed. Finally, an efficient bi-level genetic algorithm (EBGA) is proposed to ensure both optimization accuracy and efficiency. The performance of the proposed placement framework is validated in a study of a multi-purpose laboratory and office floor. The validation demonstrated that EBGA obtained full coverage of essential objects and 21.4% more coverage values over the experience-based method. Compared with two benchmark GAs, EBGA saved 65.2% and 49.7% of computation time correspondingly in the experiment.