Bi-level programming model and KKT penalty function solution approach for reliable hub location problem

Korani, Ehsan; Eydi, Alireza

doi:10.1016/j.eswa.2021.115505

Cited by 23 publications

(6 citation statements)

References 58 publications

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“…It has aroused considerable interest among optimization community. Nonetheless, there are some methods available to solve these challenging problems, such as primal-dual algorithm [3], [4], Karush-Kahn-Tucker (KKT) conditional method [39], [25], and branch delimitation algorithm [9], [13]. In this paper, we will introduce a primal-dual algorithm based on complementary relaxation theorem to transform this bi-level programming problem into a standard programming problem.…”

Section: 5mentioning

confidence: 99%

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Bi-level programming for emergency blood transshipment-allocation considering substitution against public health events

Cheng,

Zhou,

Teo

2024

JIMO

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The emergence of major public health crises, such as the Covid-19 pandemic, has significantly impacted the blood supply chain. We developed a bi-level programming model for emergency blood transshipment-allocation under this scenario, based on a cross-regional blood transshipment allocation network with a hierarchical structure. Our model considers emergency allocation, blood acceptability limits, blood type substitution relationships, hierarchical relationships among scheduling networks, and cross-regional and multi-modal transportation. The upper-level objective of our model is to minimize the total system cost, which includes shortage and substitution penalties. The lowerlevel objective is to maximize blood allocation satisfaction while considering demand urgency and blood type substitution. A primal-dual algorithm based on complementary relaxation conditions is established to solve the transformed model. The efficacy of our proposed model and solution strategy is validated through numerical calculations.

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Section: 5mentioning

confidence: 99%

“…Similarly, by constraint (35) and constraint (36), we have y k jh ≥ 0 and z lk jh ≥ 0, and by constraint (20), constraint (24) and constraint (25), we have…”

Section: 5mentioning

confidence: 99%

Bi-level programming for emergency blood transshipment-allocation considering substitution against public health events

Cheng,

Zhou,

Teo

2024

JIMO

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“…2) The optimal scheduling problems of power system and natural gas system are modeled hierarchically in this paper. In comparison with the single-level model that directly sums the objective functions of two systems [22], the bi-level model can obviously reduce the operating cost of IEGS. 3) Compared with the traditional carbon trading mechanism [23], the ladder carbon trading mechanism in this paper has a more reasonable intensity of carbon emission rewards and penalties.…”

Section: Figure 3 Post-combustion Capture Flow Chartmentioning

confidence: 99%

Low-Carbon Economic Dispatch of Integrated Electricity-Gas Energy System Considering Carbon Capture, Utilization and Storage

Liu¹,

Li²,

Tian

et al. 2023

IEEE Access

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With the rapid development of modern industry, while improving people's living standards, the over-exploitation of coal, oil and natural gas has led to a shortage of fossil energy, global warming and an increasingly serious deterioration of the ecological environment. To mitigate the greenhouse effect caused by excessive carbon emissions, the vigorous development of integrated electricity-gas system (IEGS) dominated by clean energy is the future trend of sustainable development of energy systems. In this paper, a bi-level optimal scheduling model is proposed for an IEGS considering carbon capture, utilization and storage (CCUS), and the ladder carbon trading mechanism is introduced to convert carbon emissions into economic benefits. The upper model is an optimal distribution model of natural gas network, and the lower model is a day-ahead economic dispatch model of power system. Based on the Karush-Kuhn-Tucher (KKT) condition and strong duality theory of the lower model, the bi-level model is transformed into a mixed integer linear programming (MILP), which is solved by calling CPLEX through the Yalmip toolbox of the Matlab platform. Finally, the reasonableness and validity of the model are verified by three arithmetic simulations. The results show that the proposed bi-level model for low-carbon economic dispatch of IEGS considering CCUS can effectively reduce the operating costs and carbon emissions of the system.INDEX TERMS Low-carbon electricity, integrated electricity-gas system (IEGS), economic dispatch, carbon capture, utilization and storage (CCUS), mixed integer linear programming (MILP).

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“…However, for the inner level function in the second stage, the decision variables and uncertain parameters in the first stage are fixed, so the subproblem becomes a continuous linear optimization problem. KKT conditions can be used for reasonable equivalence (Korani and Eydi, 2021), that is, the lower-level objective function and constraint conditions are equivalent to KKT conditions, and then these KKT conditions are added to the upper-level model to form a complementary mathematical programming problem.…”

Section: Kkt Equivalencementioning

confidence: 99%

Two-stage robust optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage hybrid energy system

Zhou,

Lu,

Shen

et al. 2023

Front. Energy Res.

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The hybrid energy system of hydro-powers, pumped storages and renewable energies has become a new topic direction in modern power system developments. Consequently, it is essential to realize a rational and efficient allocation of different energy source capacities. Nevertheless, there is still a gap between the available studies and the requirement for further hybrid energy system development. This paper focuses on the optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage power system. In this direction, a bi-level programming model for the optimal capacity configuration of wind, photovoltaic, hydropower, pumped storage power system is derived. To model the operating mode of a pumped storage power station, two 0-1 variables are introduced. To handle the nonlinear and nonconvex lower level programing problem caused by the two 0-1 variables, it is proposed that the 0-1 variables are treated as some uncertain parameters. Also, by treating the 0-1 variables as some uncertain parameters, a two-stage robust optimization problem to decompose the original bi-level programing one into a master problem and a subproblem is finally introduced. The Karush-Kuhn-Tucker (KKT) conditions are then applied to simplify and linearize the min-max problem and nonlinear terms in the master problem. This results in both the master problem and the subproblem being formulated as mixed integer linear programming (MILP) problems. By utilizing the powerful Column-and-Constraint Generation (C&CG) algorithm, the two-stage robust optimization model is decomposed into an iterative procedure of solving the master problem and the subproblem sequentially. This approach eliminates the need for intricate optimization algorithms as commonly used in existing bi-level planning problems in hybrid energy systems. Finally, the effectiveness and advantages of the proposed model is verified by the numerical results on a case study.

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Bi-level programming model and KKT penalty function solution approach for reliable hub location problem

Cited by 23 publications

References 58 publications

Bi-level programming for emergency blood transshipment-allocation considering substitution against public health events

Bi-level programming for emergency blood transshipment-allocation considering substitution against public health events

Low-Carbon Economic Dispatch of Integrated Electricity-Gas Energy System Considering Carbon Capture, Utilization and Storage

Two-stage robust optimal capacity configuration of a wind, photovoltaic, hydropower, and pumped storage hybrid energy system

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