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Night deliveries are increasingly used by motor carriers to cut costs, but many carriers struggle to secure night truck drivers because many drivers dislike night driving. Monetary incentives are offered to drivers to accept night loads, but the incentive system currently used in practice is inefficient, as it not only pays more incentives than necessary but also does not incentivize the right drivers, both of which increase costs. This paper develops a new incentive system that allows carriers to secure night drivers at lower costs. Based on the interviews conducted with seven motor carriers, as well as the analysis of large night delivery data, we propose a bi-level programming approach that (1) generates a unique incentive for each driver based on his/her night driving performance, and (2) implicitly aligns the incentive paid to each driver with his/her reservation price. Simulation experiments conducted with real-world data showed that by using our approach carriers can not only avoid over-incentivizing drivers, but also (1) incentive only the right set of drivers who can bring cost savings and (2) encourage other drivers to improve night driving. Results also showed that our approach may give cost savings of up to 2.5% over the current system. [ABSTRACT FROM AUTHOR]

Adverse selection is a version of the principal-agent problem that includes monopolist nonlinear pricing, where a monopolist with known costs seeks a profit-maximizing price menu facing a population of potential consumers whose preferences are known only in the aggregate. For multidimensional spaces of agents and products, Rochet and Choné (Econometrica, 1998) reformulated this problem as a concave maximization over the set of convex functions, by assuming agent preferences combine bilinearity in the product and agent parameters with a quasilinear sensitivity to prices. We characterize solutions to this problem by identifying a dual minimization problem. This duality allows us to reduce the solution of the square example of Rochet–Choné to a novel free boundary problem, giving the first analytical description of an overlooked market segment. [ABSTRACT FROM AUTHOR]

This study proposed a method for optimizing a multi-period freight network design problem with industrial relocation (MPNDP-IR). Firstly, a land-use transport interaction (LUTI) model is developed to quantitatively describe the intricate interactions between industrial relocation behavior and freight network upgrades. Then, the proposed LUTI model is integrated into a bilevel programming framework to effectively optimize the multi-period network investment strategies and maximize benefits from relocated industries and freight transshipment. Finally, taking the Yangtze River Economic Belt (YREB) as a case study, the study results indicate that the sensitivity to location utility significantly affects the scope of the beneficial impacts of freight network investment policies, thereby affecting the industrial relocation pattern. Among manufacturing activities, the raw material and chemical industry is most responsive to such network investment policies along an important railway corridor. Under the low-sensitivity scenario, the relocation pattern of such an industry aligns with a gradient relocation mode; while, under the high-sensitivity scenario, it tends to choose a "fly-in" mode. This study provides a decision support method tailored for the MPNDP-IR. It not only simulates the coevolution of different industrial activities and freight network upgrades but also evaluates the spatiotemporal impact of multi-period network investment policies in the context of industrial relocation. • Identify the trend of industrial relocation and regional attractiveness for relocated industries. • Extend the application of the LUTI model for multiperiod transportation policy. • Provide a spatial econometric method for analyzing for coevolution of industrial activities and transportation networks. • Optimize multiperiod freight network policies balancing the diverse interests of different stakeholders. [ABSTRACT FROM AUTHOR]

We introduce a Bi-level OPTimization (BiOPT) framework for minimizing the sum of two convex functions, where one of them is smooth enough. The BiOPT framework offers three levels of freedom: (i) choosing the order p of the proximal term; (ii) designing an inexact pth-order proximal-point method in the upper level; (iii) solving the auxiliary problem with a lower-level non-Euclidean method in the lower level. We here regularize the objective by a (p + 1) th-order proximal term (for arbitrary integer p ≥ 1 ) and then develop the generic inexact high-order proximal-point scheme and its acceleration using the standard estimating sequence technique at the upper level. This follows at the lower level with solving the corresponding pth-order proximal auxiliary problem inexactly either by one iteration of the pth-order tensor method or by a lower-order non-Euclidean composite gradient scheme. Ultimately, it is shown that applying the accelerated inexact pth-order proximal-point method at the upper level and handling the auxiliary problem by the non-Euclidean composite gradient scheme lead to a 2q-order method with the convergence rate O (k - (p + 1)) (for q = ⌊ p / 2 ⌋ and the iteration counter k), which can result to a superfast method for some specific class of problems. [ABSTRACT FROM AUTHOR]

In group decision making, the decision participants may exhibit various interaction behaviors, some of them are efficient at facilitating the efficiency of consensus reaching process. Motivated by the view of this, a bi-level consensus model with maximum return and minimum cost considering interaction and transaction behaviors (MRMC-IT) is proposed in the way of adopting the Choquet integral. The bi-level feedback mechanism based on the adjustment of opinions guarantees the interaction between the moderator in the upper level and the decision makers in the lower level. Meanwhile, a transaction mechanism of discourse weights is elicited to present the trading behaviors between the pairwise decision makers. Additionally, in order to solve the complex proposal, a bi-level interactive approach based on satisfactory degree is applied to obtain a satisfactory solution for all decision participants. Finally, an application of sewage discharge rights trading is conducted to demonstrate the validity and the rationality of the proposal. [ABSTRACT FROM AUTHOR]

The power-to-gas (P2G) technology transforms the unidirectional coupling of power network and natural gas network into bidirectional coupling, and its operational characteristics provide an effective way for wind and solar energy accommodation. The paper proposes a bi-level optimal dispatch model for the integrated energy system with carbon capture system and P2G facility. The upper model is an optimal allocation model for coal-fired units, and the lower model is an economic dispatch model for the integrated energy system. Moreover, the upper model is solved by transforming the model into a mixed-integer linear programming problem and calling CPLEX, and the lower model is a multi-objective planning problem, which is solved by improving the small-habitat particle swarm algorithm. Finally, the simulation is validated by the MATLAB platform, and the results show that the simultaneous consideration of carbon capture system and P2G facility improves the economics of the integrated energy system and the capacity of wind and solar energy accommodation. [ABSTRACT FROM AUTHOR]

This paper proposes a multi‐objective evolutionary algorithm based on bilayered decomposition (MOEA/BLD) for solving constrained multi‐objective optimization problems. MOEA/D is an effective method for solving unconstrained multi‐objective optimization problems. It decomposes the objective space using weight vectors and simultaneously searches for solutions for the subproblems. However, real‐world applications impose many constraints, and these constraints must be handled appropriately when searching for good feasible solutions. The proposed MOEA/BLD treats such constraints as an additional objective function. Furthermore, in addition to the conventional weight vector, an augmented weight vector is introduced that decomposes the objective space and constraint violation space hierarchically. In the first stage, the objective space is decomposed by conventional weight vectors. In the next stage, the bi‐objective space consisting of the scalarizing function and constraint violation is decomposed by augmented weight vectors. The augmented weights are adjusted so that they decrease linearly in the search process as the search gradually moves from infeasible regions to feasible regions. The proposed algorithm is compared to several state‐of‐the‐art constrained MOEA/Ds using multi‐ and many‐objective problems. The results show that the proposed method outperforms existing methods, in terms of search performance, under various conditions. © 2024 Institute of Electrical Engineers of Japan and Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Hazardous materials pose significant dangers during transportation due to their flammable and explosive properties. The consequences of accidents involving such materials are often severe and irreparable. A well‐designed hazardous materials transportation network can mitigate these risks. However, designing such a network presents two major challenges: quantifying the risk associated with hazardous materials transportation and addressing the hierarchical relationship between government and companies. To address these challenges, we enhance the accuracy of accident probability estimates and the comprehensiveness of accident consequence assessments, incorporating the uncertainty of accident outcomes. We propose a comprehensive risk assessment model and develop a bilevel programming model to reflect the hierarchical relationship. In this model, the government at the upper level aims to minimize the total risk, while companies at the lower level seek to minimize their total costs. The model is transformed using chance‐constrained programming and solved using heuristic algorithms. We apply the model to the highway network in Anhui province, China, to verify its validity. The results demonstrate that the model effectively manages the hierarchical relationship between government and companies, reduces the risk of hazardous materials transportation, and enhances the stability and safety of the transportation network. [ABSTRACT FROM AUTHOR]

The multi-leader–multi-follower game (MLMFG) involves two or more leaders and followers and serves as a generalization of the Stackelberg game and the single-leader–multi-follower game. Although MLMFG covers wide range of real-world applications, its research is still sparse. Notably, fundamental solution methods for this class of problems remain insufficiently established. A prevailing approach is to recast the MLMFG as an equilibrium problem with equilibrium constraints (EPEC) and solve it using a solver. Meanwhile, interpreting the solution to the EPEC in the context of MLMFG may be complex due to shared decision variables among all leaders, followers' strategies that each leader can unilaterally change, but the variables are essentially controlled by followers. To address this issue, we introduce a response function of followers' noncooperative game that is a function with leaders' strategies as a variable. Employing this approach allows the MLMFG to be solved as a single-level differentiable variational inequality using a smoothing scheme for the followers' response function. We also demonstrate that the sequence of solutions to the smoothed variational inequality converges to a stationary equilibrium of the MLMFG. Finally, we illustrate the behavior of the smoothing method by numerical experiments. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

With the burgeoning of remote sensing and space technology, multi-satellite collaborative mission planning, which is the key to achieving efficient Earth observation, has become increasingly intricate due to the expanding complexity and volume of observation missions. Addressing the multi-satellite collaborative mission planning problem, which is characterized by its two-stage decision-making process involving mission assignment and resource scheduling, this study investigates a comprehensive joint decision making that encompasses both mission assignment and resource scheduling and comprehensively optimizes the mission completion rate, the mission profit rate, and the satellite resource utilization rate. Considering the interaction of these decisions, we formulate the problem as a bilevel programming model from a game-theoretic perspective and propose a nested bilevel improved genetic algorithm (NBIGA) for its solution. Simulation experiments substantiate the applicability of the bilevel programming model in joint decision making for the stages of mission assignment and resource scheduling in multi-satellite collaborative mission planning, as well as the robustness of the NBIGA. A comparative analysis with the nested bilevel genetic algorithm (NBGA) confirms that the algorithm proposed in this study can achieve superior optimization outcomes and higher solving efficiency. [ABSTRACT FROM AUTHOR]

Under the background of the Energy Internet and the shared economy, it is of great significance to explore the collaborative planning strategies of multi-energy microgrids (MEMGs) and a shared energy storage operator (SESO) supported by shared energy storage resources. In this context, a joint planning method of SESO and MEMG alliances based on a dynamic game with perfect information is proposed in this paper. First, an upper-level model for energy storage capacity configuration and pricing strategy planning of SESO is proposed to maximize the total planning and operational income of SESO. Then, a lower-level model for the optimal configuration of MEMGs' alliance considering SES is proposed to minimize the total planning and operational costs of the MEMG alliance. On this basis, a solving algorithm based on the dynamic game theory with perfect information and the backward induction method is proposed to obtain the Nash equilibrium solution of the proposed bi-level optimization models. Finally, a case study with one SESO and an alliance consisting of five MEMGs is conducted, and the simulation results show that the proposed bi-level optimization method can increase SESO's net income by 1.47%, reduce the average planning costs for each MEMG at least by 1.7%, and reduce model solving time by 62.9% compared with other counterpart planning methods. [ABSTRACT FROM AUTHOR]

This paper introduces a deterministic algorithm to solve the discrete network design problem (DNDP) efficiently. This non‐convex bilevel optimization problem is well‐known as an non deterministic polynomial (NP)‐hard problem in strategic transportation planning. The proposed algorithm optimizes budget allocation for large‐scale network improvements deterministically and with computational efficiency. It integrates disjunctive programming with an improved partial linearized subgradient method to enhance performance without significantly affecting solution quality. We evaluated our algorithm on the mid‐scale Sioux Falls and large‐scale Chicago networks. We assess the proposed algorithm's accuracy by examining the objective function's value, specifically the total travel time within the network. When tested on the mid‐scale Sioux Falls network, the algorithm achieved an average 46% improvement in computational efficiency, compared to the best‐performing method discussed in this paper, albeit with a 4.17% higher total travel time than the most accurate one, as the value of the objective function. In the application to the large‐scale Chicago network, the efficiency improved by an average of 99.48% while the total travel time experienced a 4.34% increase. These findings indicate that the deterministic algorithm proposed in this research improves the computational speed while presenting a limited trade‐off with solution precision. This deterministic approach offers a structured, predictable, and repeatable method for solving DNDP, which can advance transportation planning, particularly for large‐scale network applications where computational efficiency is paramount. [ABSTRACT FROM AUTHOR]

This article proposes a unilateral Adaptive update strategy based Interval Prediction (AIP) model for short‐term load prediction, which is developed based on lower and upper bound estimation (LUBE) architecture. In traditional LUBE interval prediction model, the model training is usually trained by heuristic algorithms. In this article, the model training is formulated as a bi‐level optimization problem with the help of proposed unilateral adaptive update strategy and cost function. In lower‐level problem, a simplified biased convex cost function is developed to supervise the learning direction of basic prediction engines. The basic prediction engine utilizes Gated Recurrent Unit (GRU) to extract features and Full connected Neural Network (FNN) to generate interval boundary. In upper‐level problem, a unilateral adaptive update strategy with unilateral coverage rate is put forward. It iteratively tunes hyper‐parameters of cost function during training process. Comprehensive experiments based on residential load data are implemented and the proposed interval prediction model outperforms the tested state‐of‐the‐art algorithms, achieving a 15% reduction in prediction error and a 20% decrease in computational time. [ABSTRACT FROM AUTHOR]

This paper is concerned with the value function approach to multiobjective bilevel optimization which exploits a lower-level frontier-type mapping in order to replace the hierarchical model of two interdependent multiobjective optimization problems by a single-level multiobjective optimization problem. As a starting point, different value-function-type reformulations are suggested and their relations are discussed. Here, we focus on the situations where the lower-level problem is solved up to efficiency or weak efficiency, and an intermediate solution concept is suggested as well. We study the graph-closedness of the associated efficiency-type and frontier-type mappings. These findings are then used for two purposes. First, we investigate existence results in multiobjective bilevel optimization. Second, for the derivation of necessary optimality conditions via the value function approach, it is inherent to differentiate frontier-type mappings in a generalized way. Here, we are concerned with the computation of upper coderivative estimates for the frontier-type mapping associated with the setting where the lower-level problem is solved up to weak efficiency. We proceed in two ways, relying, on the one hand, on a weak domination property and, on the other hand, on a scalarization approach. Illustrative examples visualize our findings and some flaws in the related literature. [ABSTRACT FROM AUTHOR]

Most implicit sentiment sentences in aspect level implicit sentiment analysis lack emotional words, but there are still potential emotional clues. Current research mainly utilizes contextual information and external knowledge of text for semantic enhancement, thereby improving implicit sentiment analysis. However, in these models, the semantic correlation between words decays as the distance between the two increases, leading to weak and difficult to capture emotional cues at long distances, presenting ambiguity in emotional polarity and reducing the performance of sentiment analysis. To solve this problem, in this paper, we propose aspect-level implicit sentiment analysis model based on semantic wave and knowledge enhancement. Firstly, the semantic wave-based aspect word context information enhancement method uses the fluctuation property of semantic wave to perform weight adaptive enhancement of semantically related long-distance context information. This method essentially utilizes a sine wave function to significantly reduce the weight of words that are close but semantically unrelated, thereby allowing the weight of words that are close and semantically similar to be relatively reflected, in order to solve the problem of hiding emotional clues at long distances. Then, the implicit sentiment analysis method based on supervised contrastive pre-training is used to capture potential sentiment cues from context information and embed them into the sentence vector by weak feature learning of implicit sentiment. Finally, multi-feature interaction-based knowledge enhancement method is used to focus on the context content of sentences that are more related to background knowledge in a feature interaction way, and the information scaling factor is combined to enhance the dependency between aspect words and sentiment cues, thereby solving the problem of weak features in long-distance emotional clues and accurately identifying the emotional polarity of aspect words. The experiment shows that the model proposed in this paper has made significant improvements on the Restaurant and Laptop datasets in SemEval 2014 Task 4, with an accuracy increase of 3.38% and 4.57% in implicit emotions, respectively, achieving the best performance so far. At the same time, generalization and robustness testing experiments were conducted on the model, achieving preferable performance improvement. [ABSTRACT FROM AUTHOR]

This study focuses on solving the problem of metro first/last mile, studying the method for designing microcirculation bus routes and coordinating schedules considering the impact of shared bicycles. First, we propose a bilevel mixed-integer programming model for designing microcirculation bus routes and coordinating schedules considering the impact of shared bicycles. The upper-level model minimizes the weighted sum of the travel time cost of passengers and the operating cost of public transport enterprises, and the lower-level model maximizes the number of passengers served by microcirculation bus routes. Then, an improved genetic algorithm is developed to solve the model, called the Monte Carlo adaptive genetic algorithm (M-GAI). Finally, the proposed model and algorithm are evaluated using the case study in the area near the Fubao metro station of Shenzhen Metro Line 3. Results show that if the impact of shared bicycles is not considered, the passenger demand will be greater than the actual value, and the operating cost of public transport enterprises will be increased by 36%. Compared with GAI, the average number of iterations of M-GAI is reduced by 31%, and the objective function value is decreased by 4%. In addition, when the number of routes increases, the average waiting time of passengers is shortened, the average attendance rate of microcirculation buses increases, and the average empty distance of each vehicle is shortened. However, the operating cost of public transport enterprises will increase with the number of routes. Finally, when weight factors α and β are 0.6 and 0.4, respectively, and the sum of the travel time cost of passengers and the operating cost of public transport enterprises reach optimal. [ABSTRACT FROM AUTHOR]

Current unsupervised domain adaptation methods for intelligent fault diagnosis focus on learning domain-invariant representations under covariate shift assumption. However, the covariate shift assumption is usually unsatisfied when each fault class in different domains consists of multiple modes with skewed proportions, which is common in industrial scenarios. Imbalanced data from multiple modes cause the presence of within-domain class imbalance and between-domain label distributional shift. This paper introduces a novel subpopulation shift that further considers the domain shift from a subpopulation perspective, i.e., that covariate shift and label distributional shift across domains are caused by shifts in the multiple modes. To address this issue, a label propagation-based unsupervised domain adaptation is proposed based on a realistic expansion assumption. We apply the theoretical analysis of the proposed method with a bi-level optimization strategy adapted from meta-learning. Using joint optimization of a teacher model and a student model, the label propagation-based model-agnostic meta-learning (LPMAML) not only propagates supervision information from the source to the target but also adjusts the teacher's strategy throughout the student's learning process. To alleviate the noise caused by label distributional shift, we integrate a sampling-based alignment method that aligns the empirical label distributions across the two domains into LPMAML. Experimental results on three bearing datasets show that the proposed method has impressive generalization ability under covariate, label distributional, and subpopulation shifts. The proposed method offers consistent improvements to unsupervised domain adaptation (UDA) methods. Compared with the vanilla UDA methods, the average diagnosis accuracies of the proposed method on the label distributional shift benchmark and subpopulation shift benchmark are improved by 8.21% and 7.63%, respectively. [ABSTRACT FROM AUTHOR]

The increasing energy crisis and environmental problems promote the development of distributed energy systems (DESs) that utilize combined heat and power technology, renewable energy technology, and waste heat recovery technology to meet various load requirements. Although there is existing work and research on a variety of DESs, most previous studies tend to focus on energy production with little consideration of a distributed energy network and its energy loss, which results in large errors in energy-efficiency calculations and performance analyses. In this paper, a new DES model is proposed with full consideration of an energy network and the full use of solar energy, terrestrial heat, and exhaust gases. At the same time, an effective bi-level optimization method is also proposed for the daily operation of the DES in order to improve the system performance and benefits in the energy, the economy, and the environment. Specifically, the co-generation energy station and water heating network in the DES are optimized separately with two different optimization models. The first-level optimization model is used to seek the optimal values of water mass flow rate and water temperature of the water heating network, and the second-level optimization model is built to determine the optimal energy purchasing strategy and the optimal energy outputs of the co-generation energy station. In order to verify the advantages and effectiveness of the proposed system and method, a contrastive simulation study is undertaken to provide a comparison of the global optimization method. Simulation results show that energy loss, energy cost, and energy consumption of the DES using the bi-level optimization operation strategy only account for 22.51%, 33.42%, and 51.31% of the quantities of the global optimization method, respectively. The hourly curves of the optimal operating variables also demonstrate that the proposed bi-level optimization method can improve the operating stability of the DES better than the global optimization method. [ABSTRACT FROM AUTHOR]

This article introduces a class of Nash games among Stackelberg players (NASPs), namely, a class of simultaneous noncooperative games where the players solve sequential Stackelberg games. Specifically, each player solves a Stackelberg game where a leader optimizes a (parametrized) linear objective function subject to linear constraints, whereas its followers solve convex quadratic problems subject to the standard optimistic assumption. Although we prove that deciding if a NASP instance admits a Nash equilibrium is generally a Σ2p -hard decision problem, we devise two exact and computationally efficient algorithms to compute and select Nash equilibria or certify that no equilibrium exists. We use NASPs to model the hierarchical interactions of international energy markets where climate change aware regulators oversee the operations of profit-driven energy producers. By combining real-world data with our models, we find that Nash equilibria provide informative, and often counterintuitive, managerial insights for market regulators. This paper was accepted by Chung Piaw Teo, optimization. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.03418. [ABSTRACT FROM AUTHOR]

The primary objective of this paper is to minimize the overall travel costs for passengers while simultaneously maximizing the operational revenue for the transportation company. This is achieved through the optimization and adjustment of various factors, such as the intervals between regular bus and subway services, the duration of vehicle stops at each station, and the pricing structure for subway and shared bicycle usage. By enhancing the efficiency of passenger travel, we have successfully bolstered the company's operational profits. In contrast to prior research, this paper comprehensively considers the dual uncertainties associated with both bus operations and shared bicycle operations within a cooperative system. By establishing a coordinated dual‐level optimization model for regular bus, subway, and bike‐sharing networks under dual uncertainty conditions, we employed convex combination techniques to unify the dual uncertain variables into a single objective, which was then incorporated into a chance‐constrained bilevel programming model. Ultimately, we utilized KKT conditions to transform the model from a bilevel to a single level for resolution. This paper centers its research on the collaborative system comprising the Nanchang Metro Line 1, Bus Route 520, Bus Route 211, and the adjacent region hosting a cluster of shared bicycles. By leveraging Python programming, optimization models, empirical data on traffic flow and stoppage times, and OD data, we conducted an optimization analysis to solve the problem at hand. According to the optimization results, passenger waiting time, passenger transfer time, and passenger on board time are effectively reduced by 6.81%, 18.29%, and 23.92%. At a confidence level of 95%, the resulting time level results in a 12.44% reduction in total travel time. The average subway fare increased by 18.12%, the average shared bicycle fare decreased by 19.12%, and the total cost of travel expenses increased by 16.68%. The final total cost of travel was reduced by 4.06%, and the business operating income was increased by 13.10%. The comprehensive optimization results have effectively fulfilled the objectives of the bilevel optimization model, thereby confirming the rationality and practicality of the optimization approach. The research outcomes hold significant practical implications for facilitating the efficient and cooperative development of urban transportation networks, ultimately enhancing the convenience of residents' travel experiences. [ABSTRACT FROM AUTHOR]

This article discusses research on time-of-use compensation pricing strategies for load aggregators based on user demand response. The study aims to address the issue of mismatch between purchased electricity and market bid volume, which results in punitive costs for companies. The researchers propose a tiered pricing strategy to adjust power distribution and establish a Stackelberg leader-follower game model to promote a mutually beneficial relationship between load aggregators and controllable load users. Through case studies, the paper examines the operational profits of load aggregators and the power adjustment behaviors of controllable load users under tiered and fixed compensation pricing schemes. The results indicate that tiered compensation pricing significantly reduces punitive costs and enhances user participation in demand response. The article also discusses a dynamic compensation pricing model for controllable load power adjustment in power systems, including interactions between load aggregators and controllable load users. A case study is presented to validate the model's effectiveness, and future work will explore the integration of artificial intelligence and machine learning technologies to further optimize demand response strategies. [Extracted from the article]

An optimal credit term decision in supply chain finance often needs to be made in a dynamic way considering the varying market demand among other factors. We study the dynamic credit term optimization problem (DCTOP), where a supplier determines the credit term in conjunction with its production and inventory decision, while anticipating a buyer's order quantity in a leader-follower game setting. The DCTOP is first approached to using a continuous time optimal control model, with analytical results characterizing the structural properties of the optimal solution. To complement the structural properties, we then develop a discrete time bilevel programming model to provide computationally tractable and implementable numerical solutions. A comprehensive computational study shows significant advantage of our optimal solutions over the heuristic credit term rules in practice, and provides managerial insights regarding the impacts of key problem parameters on the optimal solutions and coordination scheme. [ABSTRACT FROM AUTHOR]

In this paper, we propose two bilevel models to cope with problems concerning waste management. The first formulation stems from a multi-objective version of the problem present in the literature, while the second one improves upon the first by taking into account a theoretical result associated with the first formulation. For both models, we provide the optimistic and the pessimistic versions. We validate these formulations in a case study in the Pathum Thani province in Thailand. Moreover, we compare the results obtained by the bilevel formulation to those obtained by a multi-objective version of the problem. Finally, we provide our thoughts on future applications in this field. [ABSTRACT FROM AUTHOR]

We show how to solve a maximum clique problem on a given graph by an equivalent problem on an auxiliary graph. The transformation has interesting consequences in the bilevel setting. In fact, it allows to map a clique interdiction problem with edge interdiction into a clique interdiction problem with node interdiction. As a byproduct of the mapping, we can generalize to the edge interdiction problem complexity and algorithmic results that hold for the node interdiction problem. [ABSTRACT FROM AUTHOR]

This paper focuses on developing effective algorithms for solving a bilevel program. The most popular approach is to replace the lower-level problem with its Karush-Kuhn-Tucker conditions to generate a mathematical program with complementarity constraints (MPCC). However, MPCC does not satisfy the Mangasarian-Fromovitz constraint qualification (MFCQ) at any feasible point. In this paper, inspired by a recent work using the lower-level Wolfe duality (WDP), we apply the lower-level Mond-Weir duality to present a new reformulation, called MDP, for bilevel program. It is shown that, under mild assumptions, they are equivalent in globally or locally optimal sense. An example is given to show that, different from MPCC, MDP may satisfy the MFCQ at its feasible points. Relations among MDP, WDP, and MPCC are investigated. On this basis, we extend the MDP reformulation to present another new reformulation (called eMDP), which has similar properties to MDP. Furthermore, to compare two new reformulations with the MPCC and WDP approaches, we design a procedure to generate 150 tested problems randomly and comprehensive numerical experiments show that MDP has quite evident advantages over MPCC and WDP in terms of feasibility to the original bilevel programs, success efficiency, and average CPU time, whereas eMDP is far superior to all other three reformulations. History: Accepted by Pascal Van Hentenryck, Area Editor for Computational Modeling: Methods & Analysis. Funding: This work was supported by the National Natural Science Foundation of China [Grants 12071280 and 11901380]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information (https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0108) as well as from the IJOC GitHub software repository (https://github.com/INFORMSJoC/2023.0108). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/. [ABSTRACT FROM AUTHOR]

Supply or service networks are vulnerable to hazards that can stem from both unintentional and intentional human actions, as well as natural calamities. To ensure vital infrastructure resilience in these networks, address the interdiction facility location problem. Currently, diverse groups of attackers target supply and service systems to cause maximum disruption. Collaboration among attackers improves system vulnerability detection accuracy and realism. This research examines the challenges of interdiction location with different defense systems and heterogeneous attackers. To address this challenge, a mixed-integer non-linear bi-level programming model was considered. Heuristic optimization methods including variable neighborhood search, simulated annealing, and hybrid variable neighborhood search are used to efficiently solve the suggested model. The outcomes of our investigation suggest that implementing various protective methods leads to an escalation in system damage when attackers collaborate. Furthermore, the findings illustrate the efficacy of the suggested algorithms in resolving interdiction location issues within supply or service networks. [ABSTRACT FROM AUTHOR]

In last-mile delivery logistics, peer-to-peer logistic platforms play an important role in connecting senders, customers, and independent carriers to fulfill delivery requests. As the carriers are not under the platform's control, the platform has to anticipate their reactions while deciding how to allocate the delivery operations. Indeed, carriers' decisions largely affect the platform's revenue. In this paper, we model this problem using bilevel programming. At the upper level, the platform decides how to assign the orders to the carriers; at the lower level, each carrier solves a profitable tour problem to determine which offered requests to accept, based on her own profit maximization. Possibly, the platform can influence carriers' decisions by determining also the compensation paid for each accepted request. The two considered settings result in two different formulations: the bilevel profitable tour problem with fixed compensation margins and with margin decisions, respectively. For each of them, we propose single-level reformulations and alternative formulations where the lower-level routing variables are projected out. A branch-and-cut algorithm is proposed to solve the bilevel models, with a tailored warm-start heuristic used to speed up the solution process. Extensive computational tests are performed to compare the proposed formulations and analyze solution characteristics. Funding: The research of E. Fernandez was partially funded through the Spanish Ministerio de Ciencia y Tecnología and European Regional Development Funds (ERDF) [Grant MTM2019-105824GB-I00]. The research of C. Archetti, M. Cerulli, and I. Ljubić was partially funded by CY Initiative of Excellence, France [Grant "Investissements d'Avenir ANR-16-IDEX-0008"]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/trsc.2023.0129. [ABSTRACT FROM AUTHOR]

The problem considered in this paper is a sequence of two optimization problems in which the feasible region of the upper-level optimization problem is determined implicitly by the solution set of the lower-level optimization problem. Using the optimal value reformulation, together with the partial calmness property, we give necessary optimality conditions in terms of tangential subdifferentials. An example that illustrates our finding is also given. [ABSTRACT FROM AUTHOR]

In this research, we study convex bi-level optimization problems for which the inner level consists of the sum of two proper, convex, and lower semi-continuous functions. We propose and analyze a new accelerated forward-backward algorithm using linesearch and inertial techniques for solving a solution of convex bi-level optimization. We then establish a strong convergence theorem of the proposed method under some suitable conditions. As an application, we apply our algorithm to solving data classifications of some non-communicable diseases. We conduct a comparative analysis with existing algorithms to show the effectiveness of our algorithm. Our numerical experiments confirm that our proposed algorithm outperforms other methods in the literature. [ABSTRACT FROM AUTHOR]

Developing cooperative relationships between neighboring ports has emerged as an effective strategy for enhancing overall productivity. Two key factors to consider in such collaborations are: cooperative motivation (which drives the decision to cooperate between ports) and cooperation type (which defines the business scope of collaborative activities). Cooperative motivation can be categorized into regional welfare and competition, while cooperation type encompasses activities related to hinterland access and terminal management. This study aims to determine the most optimal types of cooperation based on different motivations. To achieve this, a bi-level optimization model was developed to analyze the relationship between shippers and ports, specifically focusing on the cooperation between the Kobe and Osaka ports. Competition with the Busan port was examined as a case study to provide a comprehensive understanding of the dynamics involved. The findings revealed that cooperation plays a crucial role in enhancing regional welfare for both North American and Southeast Asian cargo, particularly when cooperation levels are relatively low. Furthermore, it was observed that an effective cooperative strategy for competition in the Kobe and Osaka ports is contingent upon specific conditions. Hence, for successful competition-based cooperation, careful consideration of market dynamics and prevailing circumstances is essential. [ABSTRACT FROM AUTHOR]

A location‐allocation problem faced by a company that aims to locate warehouses to supply products to a set of customers is addressed in this paper. The company's objective is to minimize the total cost of locating the warehouses and the cost due to inventory policies. However, these inventory decisions are made by a different decision‐maker. In other words, once the company makes the location decisions, the decision‐maker associated with each warehouse must determine its own order quantity. Warehouses are allowed to have a certain maximum number of backorders, which represents an extra cost for them. This situation can be modeled as a bilevel programming problem, where the upper level is associated with the company that needs to minimize the costs related to location‐allocation and the total orders of each warehouse. Each warehouse is associated with an independent lower level, in which a warehouse manager aims to minimize the total inventory cost. The bilevel problem results in a single‐objective upper‐level problem with non‐linear, multiple independent lower‐level problems, making it generally challenging to find an optimal solution. A population‐based metaheuristic under the Brain Storm Optimization algorithm scheme is proposed. To solve each non‐linear problem associated with the lower level, the Lagrangian method is applied. Both decision levels are solved in a nested manner, leading to obtaining bilevel feasible solutions. To validate the effectiveness of the proposed algorithm, an enumerative algorithm is implemented. A set of benchmark instances has been considered to conduct computational experiments. Results show that optimality is achieved by the proposed algorithm for small‐sized instances. In the case of larger‐sized instances, the proposed algorithm demonstrates the same efficiency and consistent results. Finally, interesting managerial insights deduced from the computational experimentation and some proposals for future research directions are included. [ABSTRACT FROM AUTHOR]

In this paper, we propose an adaptive algorithm with multi-step inertia for solving a convex bilevel optimization problem. Under suitable parameter conditions, we prove that our algorithm converges strongly to some solution of the problem, which is the unique solution to some variational inequality problem. The effectiveness of the proposed algorithm is verified by numerical experiments and compared with other algorithms. [ABSTRACT FROM AUTHOR]

This study concentrates on the pricing issue in a low-carbon dual-channel (DC) supply chain, where the upper-level manufacturer is regulated by the cap-and-trade (CAT) mechanisms. Market demand is a key factor affecting pricing decision and demand uncertainty complicates the pricing problem. To deal with the challenge that only partial demand distribution information is available, this paper proposes a novel ambiguity distribution set to depict the uncertain demand. Under the proposed ambiguity distribution set, a robust fuzzy bi-level optimization pricing model is developed for the low-carbon DC supply chain. Three CAT regulation mechanisms, no CAT regulation, grandfathering (GF) mechanism and benchmarking (BM) mechanism, are considered to address the manufacturer's CAT regulation. The analytically tractable counterpart of the proposed model is derived and the corresponding robust equilibrium solutions are obtained under three CAT mechanisms. Numerical analyses are carried out to explore the impact of the demand uncertainty on the manufacturer's selection of the CAT regulation mechanism. The numerical results indicate that the uncertainty degree can change the manufacturer's selection of the regulated mechanisms. Specifically, when the uncertainty degree is smaller, the BM mechanism is beneficial for the manufacturer comparing with the GF mechanism; when the uncertainty degree is bigger, the manufacturer prefers to GF mechanism rather than BM mechanism. [ABSTRACT FROM AUTHOR]

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Estimating individual treatment effects in networked observational data is a crucial and increasingly recognized problem. One major challenge of this problem is violating the stable unit treatment value assumption (SUTVA), which posits that a unit's outcome is independent of others' treatment assignments. However, in network data, a unit's outcome is influenced not only by its treatment (i.e., direct effect) but also by the treatments of others (i.e., spillover effect) since the presence of interference. Moreover, the interference from other units is always heterogeneous (e.g., friends with similar interests have a different influence than those with different interests). In this article, we focus on the problem of estimating individual treatment effects (including direct effect and spillover effect) under heterogeneous interference in networks. To address this problem, we propose a novel dual weighting regression (DWR) algorithm by simultaneously learning attention weights to capture the heterogeneous interference from neighbors and sample weights to eliminate the complex confounding bias in networks. We formulate the learning process as a bi-level optimization problem. Theoretically, we give a generalization error bound for the expected estimation error of the individual treatment effects. Extensive experiments on four benchmark datasets demonstrate that the proposed DWR algorithm outperforms the state-of-the-art methods in estimating individual treatment effects under heterogeneous network interference. [ABSTRACT FROM AUTHOR]

Constraint‐based optimization of microbial strains and model‐based bioprocess design have been used extensively to enhance yields in biotechnological processes. However, strain and process optimization are usually carried out in sequential steps, causing underperformance of the biotechnological process when scaling up to industrial fermentation conditions. Herein, we propose the optimization formulation SimulKnock that combines the optimization of a fermentation process with metabolic network design in a bilevel optimization program. The upper level maximizes space‐time yield and includes mass balances of a continuous fermentation, while the lower level is based on flux balance analysis. SimulKnock predicts optimal gene deletions and finds the optimal trade‐off between growth rate and product yield. Results of a case study with a genome‐scale metabolic model of Escherichia coli indicate higher space‐time yields than a sequential approach using OptKnock for almost all target products considered. By leveraging SimulKnock, we reduce the gap between strain and process optimization. [ABSTRACT FROM AUTHOR]

This study delves into the application of min-max fuzzy relation systems, specifically focusing on equality and inequality, in the examination of educational institution networks and their resource-sharing dynamics, akin to a P2P network structure. Expanding upon this framework, this article intricately explores a mathematical system featuring three or more terminals within an education resource system, each comprising distinct sharing capabilities. The terminals exchange information on various educational facets, encompassing variations and expenditures per share data, within the framework of a programming-type fuzzy objective function, constrained by the parameters of an educational information system. In these scenarios, the transfer of resources from one terminal to another is interlinked, introducing complexities that warrant a comprehensive examination. Notably, the consideration of greater downloading resources in specific cases is proposed for enhanced practicality. The primary objective of this article is to minimize network congestion within different educational networks, given fixed priority grades assigned to the terminals. To achieve this, the concept of a Lexicographic minimum solution is introduced to address max-min fuzzy relation inequalities, aligning with the defined objectives. The article presents a detailed and effective scenario for implementing the Lexicographic minimal solution. For validation purposes, the proposed scenario is supported by illustrative examples, offering tangible insights into its applicability and efficacy [ABSTRACT FROM AUTHOR]

This paper develops a bilevel problem to address the interdiction and fortification of the healthcare network in Golestan province, Iran. We explore a bilevel hierarchical covering interdiction/fortification problem (BHCIFP) to analyze the dynamics between interdiction and fortification operations, referral systems for healthcare services, capacitated health facilities, and budgetary constraints for both defense and offense. The defender (leader) aims to minimize the establishment cost of protective equipment and subsequent healthcare costs post-interdiction while maximizing patient coverage. Conversely, the attacker (follower) aims to disrupt the healthcare network by interdicting facilities, thereby increasing the total travel distance for patients. To solve this NP-hard problem, we employ a hybrid approach that integrates the tabu search algorithm (TS) for the leader’s problem with an exact method for the follower’s problem. A case study of Golestan’s healthcare network is presented to validate the model and hybrid approach. The model effectively minimizes travel distances by strategically locating defense bases, considering both the leader’s and attacker’s decisions. Comparative evaluations of the proposed hybrid TS and two other metaheuristic approaches are conducted on different case study instances and random instances. Numerical results demonstrate that the novel bilevel TS approach provides superior quality solutions in a reasonable time, establishing it as a competitive method for the proposed model. [ABSTRACT FROM AUTHOR]

Bilevel optimization problems embed the optimality of a subproblem as a constraint of another optimization problem. We introduce the concept of near-optimality robustness for bilevel optimization, protecting the upper-level solution feasibility from limited deviations from the optimal solution at the lower level. General properties and necessary conditions for the existence of solutions are derived for near-optimal robust versions of general bilevel optimization problems. A duality-based solution method is defined when the lower level is convex, leveraging the methodology from the robust and bilevel literature. Numerical results assess the efficiency of exact and heuristic methods and the impact of valid inequalities on the solution time. [ABSTRACT FROM AUTHOR]

Interactive users' preferences and waiting time together have great impact on charging station network design of electric vehicles (EVs), but only waiting time was considered in previous studies. To fill this research gap, this paper addresses a location planning problem for EV charging stations, which considers users' preferences and waiting time simultaneously. The problem is formulated as a multi-objective bi-level programming model, the upper level model determines locations and capacity options of charging stations with the objectives of minimising total cost and minimising total service tardiness, and the lower level model determines the allocation of users to stations with the objective of minimising total travel time. A hybrid non-dominated sorting genetic algorithm II (HNSGA-II) with embedded level determination algorithm (LDA) and a partial enumeration algorithm (PEA) are proposed, respectively, to solve the model. Furthermore, managerial analysis is implemented to verify the advantages of considering users' preferences in reducing charging service tardiness and saving cost compared with the mode of no considering users' preferences. And sensitivity analysis is also performed to provide managerial insights for EV charging station location practice. Finally, a real-world case study is conducted to verify the applicability of the proposed approach in solving practical location planning problems. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to establish necessary and sufficient optimality conditions and some duality results for weakly efficient solutions of a constrained bilevel multiobjective fractional programming problem (P) with an extremal-value function. Using parametric approach, the problem (P) is first equivalently transformed into a parametric problem (P µ) with µ ∈ Rp, for which we construct then a dual problem. This is achieved in terms of conjugate duality theory. Under appropriate assumptions, the weak and strong duality results for (Pµ) are presented. These results permit us to give dual characterizations for the weakly efficient solutions of the problem (P).

In recent years, as the energy market continues to change, an emerging business model is gradually emerging as an energy provider (EP). The participation of EP as an independent entity in the distribution network investment model not only helps realize a win–win situation for multiple stakeholders but also promotes the innovation and sustainable development of the energy industry. However, in the energy system, EPs, grids, microenergy grids (MEGs), and shared energy storage service providers usually belong to different stakeholders, and their respective pursuit of profit maximization can easily lead to uncontrolled competition, which greatly reduces market efficiency. To address the varying ownership structures within the energy system, a refined bilevel coordinated optimization operation model is introduced, rooted in the master–slave game theory. In this model, the EP assumes the role of the master, while the MEG operator and the shared energy storage operator (SESO) act as slaves. A peer‐to‐peer energy‐sharing mechanism between MEGs and an energy trading mechanism between MEGs and shared energy storage is used to further increase the local consumption rate of new energy. Simulation results demonstrate that the proposed method not only boosts the revenues of an EP, SESO, and MEG operators but also effectively accounts for the MEG's energy storage needs and SESOs' profitability. [ABSTRACT FROM AUTHOR]

Developing a self‐sufficient renewable power (RP) road transport (SRPRT) system is an important future direction for transport–energy integration. More well‐developed studies must be conducted on the coordinated planning of transport, power supply, and power generation networks. This paper carries out the joint operation and planning of highway charging networks with the wind‐photovoltaic‐energy storage (HCN‐WPE) system. Under multi‐network integration and the interaction among multiple entities, a nested bi‐level optimization model is proposed to optimize the users' charging and travel behavior, charging network's deployment, and power generation system's (PGS) configuration. An H‐M‐L algorithm structure is developed, combining the heuristic algorithm, multi‐agent‐based simulation technology, and linear programming algorithm. Its convergence and applicability are verified on the Nguyen‐Dupius network. An empirical case in the Hu‐Bao‐Wu city agglomeration in China is employed to explore and discuss the managerial insights for the HCN‐WPE system. The study finds that multi‐network coordinated planning can improve the benefits of multiple entities, where the net present value, RP supply rate, and RP consumption rate increase by 12.0%, 3.2%, and 10.5%, compared to independent planning. Network‐level planning can play a management and induction role in balancing the station's load pressure. In addition, the PGS co‐configuration can leverage the complementary power supply of multiple RP generators and the peak cutting and valley filling of energy storage systems, which is essential for achieving the SRPRT goal. [ABSTRACT FROM AUTHOR]

The rapid expansion of energy storage integration has not provided sufficient time to strengthen and expand the transmission and distribution network. This issue can lead to PCC congestion in green multi-microgrid (MMG) systems. In these systems, microgrids operate independently and connect to the grid at a point of common coupling (PCC) without sharing operational data with neighboring microgrids. To address this issue, this paper proposes a bi-level optimization model designed to reschedule hydrogen storage systems. The first level allows each microgrid to optimize its energy transactions with the grid and communicates any unbalanced energy to the second level, where a hydrogen management system (HMS) is introduced. The HMS optimizes virtual hydrogen prices to address the PCC congestion and maximize the MMG's profit. These virtual prices are then sent to the first level, allowing the microgrids to reschedule the hydrogen storage systems based on these virtual prices. Finally, the MMG's profit is fairly allocated among the microgrids using the Shapley value method. The proposed method's effectiveness is demonstrated using simulations, which show a six percent increase in MMG profit compared to scenarios that only share PCC capacity while maintaining the data privacy of all the involved microgrids. [ABSTRACT FROM AUTHOR]

With the integration of large-scale wind power clusters into the power system, wind farms play a crucial role in grid reactive power regulation. However, the range of its reactive power remains uncertain, posing challenges in formulating a viable program for regulating reactive power to ensure the safe and cost-effective operation of the power system. Based on this, this paper develops a bi-level reactive power optimization for wind clusters integrating the power grid while considering the reactive capability. Firstly, this paper carries out a refined analysis of the wind power clusters, taking into account the characteristics of different areas to estimate the exact value of the reactive power capability in wind power clusters. Secondly, a bi-level reactive power optimization model is established. The upper-layer optimization aims to minimize active losses and voltage deviation in power system operation, while the lower-layer optimization focuses on maximizing reactive power margin utilization in wind farms. To solve this bi-level optimization model, an improved artificial fish swarm algorithm (AFSA) is employed, which decouples real variables and integer variables to enhance the optimization ability of the algorithm. Finally, the effectiveness of our proposed optimization strategy and algorithm is validated through the simulation results. [ABSTRACT FROM AUTHOR]

Background and aim: Cancer related fatigue significantly impairs the ability to undertake sustained physical activity across the domains of daily living, work and recreation. The purpose of this study is to monitor cancer related fatigue and the factors affected or caused by it for 12 months in head and neck cancer patients following their diagnosis. Their perceptions of how fatigue might affect their activity levels in addition to identifying avenues to improve engagement with physical activity will be also explored. Methods: A single centre longitudinal mixed-methods study will be conducted. Forty head and neck cancer patients will be recruited over 6 months following the confirmation of their treatment plan, after which fatigue and physical activity will be assessed at four time points over 12 months. Additionally, other factors which influence fatigue such as body composition, blood counts, systemic inflammation levels, haemoglobin concentration, thyroid function, sleep quality, cardiorespiratory fitness and upper and lower extremity strength will be measured to understand how the multifactorial problem of fatigue may evolve over time and influence physical activity levels. Semi-structured interviews will be conducted after treatment completion and at end of twelve months which will analyse the participants fatigue experiences, understand how their perceived fatigue may have impacted physical activity and report the factors which may improve engagement with physical activity during cancer. Quantitative data will be analysed and reported using standard descriptive statistics and post-hoc pairwise comparisons. The changes in outcome measures across time will be analysed using the MIXED procedure in SPSS software. Statistical significance will be accepted at p<0.05. Qualitative data will be analysed using the Interpretative Phenomenological Approach using the NVivo software. Discussion: The results from this study may help inform the planning and delivery of appropriately timed interventions for the management of cancer related fatigue. [ABSTRACT FROM AUTHOR]

Multi-teacher knowledge distillation is a powerful technique that leverages diverse information sources from multiple pre-trained teachers to enhance student model performance. However, existing methods often overlook the challenge of effectively transferring knowledge to weaker student models. To address this limitation, we propose BOMD (Bi-level Optimization for Multi-teacher Distillation), a novel approach that combines bi-level optimization with multiple orthogonal projections. Our method employs orthogonal projections to align teacher feature representations with the student's feature space while preserving structural properties. This alignment is further reinforced through a dedicated feature alignment loss. Additionally, we utilize bi-level optimization to learn optimal weighting factors for combining knowledge from heterogeneous teachers, treating the weights as upper-level variables and the student's parameters as lower-level variables. Extensive experiments on multiple benchmark datasets demonstrate the effectiveness and flexibility of BOMD. Our method achieves state-of-the-art performance on the CIFAR-100 benchmark for multi-teacher knowledge distillation across diverse scenarios, consistently outperforming existing approaches. BOMD shows significant improvements for both homogeneous and heterogeneous teacher ensembles, even when distilling to compact student models. [ABSTRACT FROM AUTHOR]