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Integrating goal programming, Kuhn-Tucker conditions, and penalty function approaches to solve linear bi-level programming problems

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APPLIED MATHEMATICS AND COMPUTATION 2008年第2期195卷 585-590页

作者： Roghanian, E. Aryanezhad, M. B. Sadjadi, S. J. Iran Univ Sci & Technol Dept Ind Engn Tehran 16844 Iran

bi-level programming, a tool for modeling decentralized decisions, consists of the objective(s) of the leader at its first level and the follower(s) at the second level. Three level programming results when the second level itself is a bi-level programming which helps us develop the idea of bi-level programming to multi-level programs with any number of levels. There are many approaches for encountering with bi(multi)-level problems. The method introduced by Chenggen Shi et al. [Chenggen Shi, Jie Lu, Guangquan Zhang, An extended Kuhn-Tucker approach for linear bi-level programming, Applied Mathematics and Computation 162 (2005) 51-63] uses extended Kuhn-Tucker conditions to solve bi-level programming problems. In this paper, we integrate goal programming (GP), Kuhn-Tucker conditions (KKT) and Penalty Function approaches to solve linear bi-level programming problems. By using a numerical example we illustrate efficiency of our methodology. (c) 2007 Published by Elsevier Inc.

关键词： bi-level programming Kuhn-Tucker conditions goal programming penalty function

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A bi-level programming approach to design a sustainable supply chain network under uncertainty: a real-life case study

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CLEAN TECHNOLOGIES AND ENVIRONMENTAL POLICY 2024年 1-31页

作者： Fishani, Behzad Aghaei Mahmoodirad, Ali Niroomand, Sadegh Hajiaghaei-Keshteli, Mostafa Islamic Azad Univ Dept Ind Engn Cent Tehan Branch Tehran Iran Islamic Azad Univ Dept Math Babol Branch Babol Iran Shiraz Univ Technol Firouzabad Higher Educ Ctr Dept Ind Engn Shiraz Iran Tecnol Monterrey Sch Engn & Sci Monterrey Mexico

The purpose of this paper is to design a sustainable supply chain network in the presence of uncertainty. This network includes suppliers, manufacturers, distributors, and customers. In the network, some features, such as different levels of capacity, environmental effects of establishing distribution centers, and number of job opportunities created in the supply chain, are considered. Furthermore, in the case of sustainability, various production technologies and their effects on production speed and emission rates are studied. Various types of vehicles are considered for transportation of the products between the chain members. To model the problem, a bi-level mathematical model with a leader and a follower is introduced. In this chain, the government plays the role of leader and the private sector or industry owner plays the role of follower. The demand is from the parameters whose determination always creates a wide range of uncertainty in the input parameters. Determining the exact value of this parameter has a high computational complexity due to the wide range of customers. To cope with this uncertainty, a robust optimization scheme is adopted. As a result of the inherent uncertainty of the parameters, a realistic approach is developed to deal with the situation. A fuzzy-goal interactive approach is used to solve the proposed model, and its performance is tested using a case study in Iran. The calculation results indicate the appropriateness of the solution method used as well as the necessity to use appropriate uncertainty methods, such as robust planning.

关键词： Supply chain design Sustainability bi-level programming Uncertainty Fuzzy-goal interactive approach

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Surrogate-Based Constraint-Handling Technique for Multi-Area Combined Economic/Emission Dispatch Problems Within bi-level programming Framework

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IEEE TRANSACTIONS ON EMERGING TOPICS IN COMPUTATIONAL INTELLIGENCE 2024年

作者： Liang, Huijun Lin, Chenhao Pang, Aokang Hubei Minzu Univ Coll Intelligent Syst Sci & Engn Enshi 445000 Peoples R China

Due to long optimization time and limited dispatching cycle, multi-area combined economic/emission dispatch (MACEED) problems are converted into computationally expensive MACEED (CEMACEED) problems. Existing centralized and distributed method for CEMACEED problems include time-consuming and inaccurate disadvantages. The drawbacks, i.e., low convergence rate and unaffordable computing time may make scheduling cycles can hardly be met. In this paper, a novel surrogate-based bi-level programming framework is proposed. CEMACEED problem is decoupled to obtain completely independent sub-area dispatching problems. Then, a novel surrogate-based constraint-handling technique is proposed to handle tie line constraint while realizing decoupling. Original tie line constraint is replaced by improved polynomial regression surrogate models to save more than 75% of operating time. Finally, a novel meta-heuristic algorithm named emotional accumulation game evolutionary algorithm (EAGEA) is proposed to execute CEMACEED problems. The proposed method obtains the minimum cost, emission, and operating time over all simulation cases.

关键词： Dispatching Optimization Costs Metaheuristics programming Convergence Task analysis bi-level programming constraint-handling technique game theory multi-area combined economic/emission dispatch surrogate model

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A fuzzy bi-level programming approach to scarce drugs supply and ration planning problem under risk

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FUZZY SETS AND SYSTEMS 2022年 434卷 48-72页

作者： Aghababaei, Bahareh Pishvaee, Mir Saman Barzinpour, Farnaz

In this paper, a possibilistic bi-objective bi-level programming model is proposed to optimize the management of scarce drugs supply and rationing under difficult situations such as COVID-19 outbreak. Multiple followers and single leader exist in the proposed Stackelberg model in which the followers are divided into two groups, manufacturers and suppliers. The first group has priority over the latter. The competition between these two groups is addressed using a lexicographical procedure. Moreover, the interaction between the individuals in each group is incorporated through a normalized Nash equilibrium. To avoid the discriminative allocations, the disability-adjusted life years (DALY) index is employed to improve the rationing process. Due to the significance of uncertainty in such a problem, a novel risk-based possibilistic expected value approach is devised to control the mean and risk values of the objective functions. Finally, to validate the proposed solution method, the model is solved by applying Karush-Kuhn-Tucker (KKT) conditions and using the data extracted from a real case study. The results reveal the applicability and usefulness of the proposed possibilistic model compared to the conventional possibilistic approach (c) 2021 Elsevier B.V. All rights reserved.

关键词： Fuzzy mathematical programming Scarce resources allocation bi-level programming Pricing Possibilistic programming Multi-objective optimization COVID-19

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A bi-level programming model for sustainable supply chain network design that considers incentives for using cleaner technologies

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JOURNAL OF CLEANER PRODUCTION 2019年 213卷 1035-1050页

作者： Chalmardi, Mazyar Kaboli Camacho-Vallejo, Jose-Fernando Univ Kurdistan Dept Ind Engn Kurdistan Sanandaj Provin Iran Univ Autonoma Nuevo Leon Fac Ciencias Fis Matemat San Nicolas De Los Garza Mexico

Nowadays, the population growth leads environmental, legislative, and social concerns. As a consequence, government and companies started to be aware of the impact of supply chain operations in the environment and society. While most of research in Supply Chain Network Design (SCND) has focused on economic performance, recently some studies consider environmental and social aspects of the SCND. The majority of existing related papers deal with multi-objective optimization modelling approaches when considering sustainable aspects of the supply chain. In this study, the optimization of a hierarchized Sustainable Supply Chain Network Design (SSCND) is addressed. To model this situation, a bi-level programming approach is considered. In the proposed model, an Environmental Protection Agency from the government has the leader role and acts as the upper level decision maker. Also, the supply chain's manager assumes the follower role acting as the lower level decision maker. Leader's objective function considers environmental aspects, while follower's objective function considers economical aspects. In the modelled situation, the government tries to cause an impact in the SCND by offering financial incentives (subsidies) and by encouraging the supply chain's manager to use cleaner technologies. The resulting bi-level programming model is a mixed-integer linear program. Due to the structure of the lower level problem, the bi-level model cannot be reduced into an equivalent single-level one by using KKT conditions. Therefore, an algorithm based on the simulated annealing metaheuristic is proposed for solving the problem. The results show that an appropriate government's financial incentives strategy lead to significantly decrease the environmental impact of the SSCND. Moreover, a greater impact is achieved when the financial incentives do not depend on the total production obtained via the use of cleaner technologies (scenario 1) than assigning subsidies based on the product

关键词： Supply chain network design Sustainability bi-level programming

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Designing a hazardous materials transportation network by a bi-level programming based on toll policies

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 534卷 122324-000页

作者： Zhang, Lukai Feng, Xuesong Chen, Dalin Zhu, Nan Liu, Yi Beijing Jiaotong Univ Sch Traff & Transportat 3 Shangyuancun Beijing 100044 Peoples R China China Urban Construct Design & Res Inst Co LTD 36 Deshengmenwai St Beijing 100120 Peoples R China MCC Jingcheng Engn Technol Co LID 7 Jianan St Beijing 100176 Peoples R China

Hazardous materials (HAZMAT) are common in industry and agriculture, playing important roles in the development of society and economy. Meanwhile, in actual operation processes, because of the long distances between the producers and supply regions of HAZMAT, a mass of HAZMAT are always being transported, which bring risk within the corresponding areas. This study aims to design a feasible and practical HAZMAT transportation network, where the risk leading to incidents is mitigated. Adopting the congestion pricing principles for reference, link tolls are taken as the decision variables, and a bi-level programming optimization model with a variation inequality is established to interpret the problem. Moreover, a double-temperature simulated annealing algorithm inserted with a diagonalization algorithm is proposed to solve the model, and necessary computational experiments are executed. The calculated results and sensitivity analyses show that the newly proposed method is effective, which is able to be rational decision reference for relevant departments. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Hazardous materials Transportation network bi-level programming Toll policies Double-temperature simulated annealing algorithm

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Steady-state optimization of biochemical systems by bi-level programming

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COMPUTERS & CHEMICAL ENGINEERING 2017年 106卷 286-296页

作者： Xu, Gongxian Li, Yang Bohai Univ Dept Math Jinzhou 121013 Peoples R China

A new method is proposed for the steady-state optimization of biochemical systems described by Generalized Mass Action (GMA) models. In this method, a bi-level programming with a two-layer nested structure is established. In this bi-level problem, the upper-level objective is to maximize a flux or a metabolite concentration, and the lower-level objective is to minimize the total sum of metabolite concentrations of biochemical systems. The biological significance of the presented bi-level programming problem is to maximize the production rate or concentration of the desired product under a minimal metabolic cost to the biochemical system. To efficiently solve the above NP-hard, non-convex and nonlinear bi-level programming problem, we reformulate it into a single-level optimization problem by using appropriate transformation strategies. The proposed framework is applied to four case studies and has shown the tractability and effectiveness of the method. A comparison of our proposed method and other methods is also given. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Optimization bi-level programming Algorithm Generalized mass action biochemical systems

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Using bi-level programming to analyze the royalty for private-public partnership projects: the operational quantity-based model

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TRANSPORTATION PLANNING AND TECHNOLOGY 2010年第3期33卷 315-328页

作者： Kang, Chao-Chung Feng, Cheng-Min Kuo, Chiu-Yen Providence Univ Dept Business Adm Shalu 433 Taichung Hsien Taiwan Providence Univ Grad Inst Management Shalu 433 Taichung Hsien Taiwan Natl Chiao Tung Univ Inst Traff & Transportat Taipei 100 Taiwan

This paper develops a royalty negotiation model based on the operating quantity of Build, Operate, and Transfer (BOT) projects for both government and the private sector using a bi-level programming (BLP) approach. The royalty negotiation is one of many critical negotiation items of a concession contract. This study develops a royalty negotiation model to simulate the negotiation behavior of two parties, and derives the heuristic algorithm for the BLP problem. A number of factors are incorporated into this algorithm including the concession rate, the time value discount rate, the learning rate, and the number of negotiations. The paper includes a case study of the Taipei Port Container Logistic BOT Project. The results show that the two parties involved completed royalty negotiation at the sixth negotiation stage. The findings show that the government can receive a royalty from the concessionaire, calculated at 0.00386% of the operating quantity of this BOT project. Therefore, the royalty negotiation model developed here could be employed to explain negotiation behavior.

关键词： BOT project royalty negotiation bi-level programming

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A Highly Efficient Approach for bi-level programming Problems Based on Dominance Determination

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JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING 2022年第4期22卷 041006-041006页

作者： Wang, Guan Zou, Qiang Zhao, Chuke Liu, Yusheng Ye, Xiaoping Zhejiang Univ State Key Lab CAD & CG Hangzhou 310027 Peoples R China Huazhong Univ Sci & Technol Sch Elect & Elect Engn Wuhan 323000 Peoples R China Lishui Univ Key Lab Digital Design & Intelligent Mfg Creat Cu Lishui 323000 Peoples R China

bi-level programming, where one objective is nested within the other, is widely used in engineering design, e.g., structural optimization and electronic system design. One major issue of current solvers for these bi-level problems is their low computational efficiency, especially for complex nonlinear problems. The existing methods usually applied time-consuming nested computational structure, which requires an amount of function evaluations (FEs) since a lower-level (LL) optimization needs to be constructed for each upper-level (UL) solution. To solve this issue, a new method based on bi-level grey wolf optimizer (BLGWO) is proposed in this paper. The basic idea is to drop the conventional nested computational structure and instead use a simultaneous computational structure. The simultaneous structure is built on top of a dominance determination process for the grey wolf optimizer, so that the upper-level and lower-level problems can be optimized simultaneously, which greatly improves the efficiency of solving the bi-level problems. The effectiveness of this new method has been validated with ten benchmark functions and two engineering design examples, as well as comparisons with three important existing methods in the bi-level programming domain.

关键词： bi-level programming multi-objective grey wolf optimizer dominance prediction global optimization optimization efficiency

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A game theoretic analysis of knowledge sharing behavior of academics: bi-level programming application

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COMPUTERS & INDUSTRIAL ENGINEERING 2019年 131卷 13-27页

作者： Tabatabaei, Mohsen Afrazeh, Abbas Seifi, Abbas Amirkabir Univ Technol Dept Ind Engn & Management Syst Tehran Iran

Knowledge sharing amongst academics is a key process for universities to survive in the face of new changes in the education market. Despite the bulk of research on knowledge sharing, there are few studies on knowledge sharing analysis in higher education based on the game theory. Considering this gap, this paper aims to propose a nonlinear bi-level programming (BLP) model to analyze the knowledge sharing behavior of academics. The proposed model considers decisions made by Faculty Head (FH) and Faculty Members (FMs) at two separate but integrated levels. The upper-level problem is related to FH decisions about compensation rates, and the lower-level problem represents FM decisions in the motivation, opportunity and ability (MOA) framework. This modeling approach has several advantages including the consideration of both FHs and FMs decisions, and various factors influencing knowledge sharing using the MOA framework in a single model as well as the analysis of four different activities of FMs, including teaching, learning, sharing tacit knowledge and publishing codified knowledge in a single integrated model. The bi-level programming model was reduced to a single level nonlinear problem using KKT conditions. The resultant problem was solved for a set of randomly generated data. Results indicated that the optimal behavior of an FM varied relative to characteristics of other FMs. Also, the analysis of the solution at different levels of trust showed that its improvement might have a different effect on FMs. Extending the application of the model and developing efficient algorithms for its solution are suggested for future research.

关键词： bi-level programming Game theory Knowledge sharing behavior Academics Higher education Motivation-opportunity-ability framework

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