bilevel optimization
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2022 ◽  
Vol 2022 ◽  
pp. 1-12
Kai Chen ◽  
Yilin Chen

The in-depth analysis of the strategies for the coordinated and continuous development of population, resources, environment, economy, and society based on the engineering management model is highly important for the sustainable development of the regional economy and society. In this article, a population-economy-resources-environment bilevel optimization model is established based on the economic and social development in a provincial region. The method of bilevel optimization is adopted to introduce the specific bilevel optimization model. The concept and objectives of the bilevel optimization are explained, and its corresponding technical applications are described. In this article, the development in coordinated economic and social development of population, resources, and environment is analyzed and compared based on the bilevel optimization model. In particular, the evolution and changes before and after the implementation of engineering management are studied. Through the results, it can be observed that after the implementation of project management, the coefficient of industry location has presented a downward trend, and the coordinated development of population, resources, environment, economy, and society has become more coordinated.

Christoph Buchheim ◽  
Dorothee Henke

AbstractWe consider a bilevel continuous knapsack problem where the leader controls the capacity of the knapsack and the follower chooses an optimal packing according to his own profits, which may differ from those of the leader. To this bilevel problem, we add uncertainty in a natural way, assuming that the leader does not have full knowledge about the follower’s problem. More precisely, adopting the robust optimization approach and assuming that the follower’s profits belong to a given uncertainty set, our aim is to compute a solution that optimizes the worst-case follower’s reaction from the leader’s perspective. By investigating the complexity of this problem with respect to different types of uncertainty sets, we make first steps towards better understanding the combination of bilevel optimization and robust combinatorial optimization. We show that the problem can be solved in polynomial time for both discrete and interval uncertainty, but that the same problem becomes NP-hard when each coefficient can independently assume only a finite number of values. In particular, this demonstrates that replacing uncertainty sets by their convex hulls may change the problem significantly, in contrast to the situation in classical single-level robust optimization. For general polytopal uncertainty, the problem again turns out to be NP-hard, and the same is true for ellipsoidal uncertainty even in the uncorrelated case. All presented hardness results already apply to the evaluation of the leader’s objective function.

Risheng Liu ◽  
Long Ma ◽  
Xiaoming Yuan ◽  
Shangzhi Zeng ◽  
Jin Zhang

2022 ◽  
pp. 210-234
Timothy Ganesan ◽  
Irraivan Elamvazuthi

Bilevel (BL) optimization of taxing strategies in consideration of carbon emissions was carried out in this work. The BL optimization problem was considered with two primary targets: (1) designing an optimal taxing strategy (imposed on power generation companies) and (2) developing optimal economic dispatch (ED) schema (by power generation companies) in response to tax rates. The resulting interaction was represented using Stackelberg game theory – where the novel fuzzy random matrix generators were used in tandem with the cuckoo search (CS) technique. Fuzzy random matrices were developed by modifying certain aspects of the original random matrix theory. The novel methodology was tailored for tackling complex optimization systems with intermediate complexity such as the application problem tackled in this work. Detailed performance and comparative analysis are also presented in this chapter.

2022 ◽  
Vol 412 ◽  
pp. 126577
Jesús-Adolfo Mejía-de-Dios ◽  
Efrén Mezura-Montes ◽  
Porfirio Toledo-Hernández

Péter Egri ◽  
Balázs Dávid ◽  
Tamás Kis ◽  
Miklós Krész

AbstractAs environmental awareness is becoming increasingly important, alternatives are needed for the traditional forward product flows of supply chains. The field of reverse logistics covers activities that aim to recover resources from their final destination, and acts as the foundation of the efficient backward flow of these materials. Designing the appropriate reverse logistics network for a given field is a crucial problem, as this provides the basis for all operations connected to the resource flow. This paper focuses on design questions in the supply network of waste wood, dealing with its collection and transportation to designated processing facilities. The facility location problem is studied for this use-case, and mathematical models are developed that consider economies of scale and the robustness of the problem. A novel approach based on bilevel optimization is used for computing the exact solutions of the robust problem on smaller instances. A local search and a tabu search method is also introduced for solving problems of realistic sizes. The developed models and methods are tested both on real-life and artificial instance sets in order to assess their performance.

2021 ◽  
Vol 147 (4) ◽  
pp. 04021052
Lingxuan Zhang ◽  
Monica Menendez ◽  
Minhao Xu ◽  
Bin Shuai

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