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Hybrid particle swarm optimization and differential evolution algorithm for bi-level programming problem and its application to pricing and lot-sizing decisions

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JOURNAL OF INTELLIGENT MANUFACTURING 2015年第3期26卷 471-483页

作者： Ma, Weimin Wang, Miaomiao Zhu, Xiaoxi Tongji Univ Sch Econ & Management Shanghai 200092 Peoples R China

This paper proposes a hierarchical hybrid particle swarm optimization (PSO) and differential evolution (DE) based algorithm (HHPSODE) to deal with bi-level programming problem (BLPP). To overcome the shortcomings of basic PSO and basic DE, this paper improves PSO and DE, respectively by using a velocity and position modulation method in PSO and a modified mutation strategy in DE. HHPSODE employs the modified PSO as a main program and the modified DE as a subprogram. According to the interactive iterations of modified PSO and DE, HHPSODE is independent of some restrictive conditions of BLPP. The results based on eight typical bi-level problems demonstrate that the proposed algorithm HHPSODE exhibits a better performance than other algorithms. HHPSODE is then adopted to solve a bi-level pricing and lot-sizing model proposed in this paper, and the data is used to analyze the features of the proposed bi-level model. Further tests based on the proposed bi-level model also exhibit good performance of HHPSODE in dealing with BLPP.

关键词： bi-level programming problem Hierarchical Particle swarm optimization Differential evolution Pricing and lot-sizing

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A novel multi-objective bi-level programming problem under intuitionistic fuzzy environment and its application in production planning problem

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COMPLEX & INTELLIGENT SYSTEMS 2022年第4期8卷 3263-3278页

作者： Singh, V. P. Sharma, Kirti Chakraborty, Debjani Ebrahimnejad, Ali Visvesvaraya Natl Inst Technol Nagpur Dept Math Nagpur 440010 Maharashtra India Indian Inst Technol Kharagpur Dept Math Kharagpur 721302 W Bengal India Islamic Azad Univ Dept Math Qaemshahr Branch Qaemshahr Iran

This paper presents an optimization method to solve a multi-objective model of a bi-level linear programming problem with intuitionistic fuzzy coefficients. The idea is based on TOPSIS (technique for order preference by similarity to ideal solution) method. TOPSIS method is a multiple criteria method that identifies a satisfactory solution from a given set of alternatives based on the minimization of distance from an ideal point and maximization of distance from the nadir point simultaneously. A new model of multi-objective bi-level programming problem in an intuitionistic fuzzy environment has been considered. The problem is first reduced to a conventional multi-objective bi-level linear programming problem using accuracy function. Then the modified TOPSIS method is proposed to solve the problem at both the leader and the follower level where various linear/non-linear membership functions are used to represent the flexibility in the approach of decision-makers (DMs). The problem is solved hierarchically, i.e., first the problem at the leader level is solved and then the feasible region is extended by relaxing the decision variables controlled by the leader. The feasible region is extended to obtain a satisfactory solution for the DMs at both levels. Finally, the application of the proposed approach in the production planning of a company has been presented. An illustrative numerical example is also given to explain the methodology defined in this paper.

关键词： Multi-objective optimization problem bi-level programming problem TOPSIS method Intuitionistic fuzzy number Fuzzy optimization

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A Double Layer Neural Network Based on Artificial Bee Colony Algorithm for Solving Quadratic bi-level programming problem 8th

A Double Layer Neural Network Based on Artificial Bee Colony...

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8th KES International Conference on Intelligent Decision Technologies (KES-IDT)

作者： Watada, Junzo Ding, Haochen Waseda Univ Grad Sch Informat Prod & Syst Wakamatsu Ku 2-7 Hibikino Kitakyushu Fukuoka 8080135 Japan

ISBN: (纸本)9783319396309;9783319396293

In this study, we formulate a double layer neural network based hybrid method to solve the quadratic bi-level programming problem. Our proposed algorithm comprises an improved artificial bee colony algorithm, a Hopfield network, and a Boltzmann machine in order to effectively and efficiently solve such problems. The improved artificial bee colony algorithm is developed for dealing with the upper level problem. The experiment results indicate that compared with other methods, the proposed double layer neural network based hybrid method is capable of achieving better optimal solutions for the quadratic bi-level programming problem.

关键词： bi-level programming problem Double layer neural networks Artificial bee colony algorithm

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Charging/Discharging strategy for electric vehicles based on bi-level programming problem: San Francisco case study 14

Charging/Discharging strategy for electric vehicles based on...

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14th IEEE International Conference on Compatibility, Power Electronics and Power Engineering (CPE-POWERENG)

作者： Tookanlou, M. Bagheri Marzband, M. Kyyra, J. Al Sumaiti, A. Al Hosani, K. Northumbria Univ Dep Math Phys & Elect Engn Newcastle Upon Tyne Tyne & Wear England Aalto Univ Dept Elect Engn & Automat Helsinki Finland Khalifa Univ Dept Elect Engn & Comp Sci Adv Power & Energy Ctr Dhabi U Arab Emirates

ISBN: (数字)9781728142180

ISBN: (纸本)9781728142180

The increasing market share of electric vehicles (EVs) leads to determine a proper strategy for charging/discharging EV batteries such that rewards of all agents including EV charging stations (EVCSs) and EV owners (EVOs) that participate in charging/discharging EV batteries are guaranteed. In this study, an economical and technical strategy is developed. It focuses on finding proper EVCSs by EVOs and determining optimal day-ahead electricity prices traded between all agents such that the rewards of EVCSs and EVOs are met simultaneously. This optimal charging/discharging decision making and optimal day-ahead electricity prices are determined by bi-level programming problem (BLPP). The outer level corresponds to the optimization problem of EVCSs and the inner level belongs to EVOs. Salp swarm optimization (SSO) algorithm is utilized to solve BLPP. Based on determination of minimum distance travelled by EVOs and optimal day-ahead electricity prices offered by EVCSs, the rewards of EVCSs and EVOs are analysed during charging/discharging period. For simulation purposes, a case study based on San Francisco in US is presented to visualize and validate the modelling results. Six EVCSs are installed in San Francisco for charging/discharging 247 EVs during 24 hours of a typical day. Simulation results show that under implementing the proposed charging/discharging strategy, the total cost of EVOs decreases by 17.8% and total revenue of EVCSs increases 18.2%, in comparison with not considering the proposed strategy.

关键词： bi-level programming problem charging/discharging decision electric vehicles electricity pricing

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A Hierarchical Wind Driven Optimization Method for Solving the bi-level programming problem

A Hierarchical Wind Driven Optimization Method for Solving t...

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International Conference on Logistics, Informatics and Service Sciences (LISS)

作者： Xu, Lan Teng, Wei Jiangsu Univ Sci & Technol Sch Econ & Management Zhenjiang Jiangsu Peoples R China

ISBN: (纸本)9781509011025

A hierarchical wind driven optimization (WDO) method is proposed to solve the bi-level programming problem. Firstly, the WDO method is used to optimize the lower level programming problem after the upper level variables are initialized, and the positions and velocities of air parcels in the lower level are updated. Then the solutions of the upper level are optimized by the WDO method with the constrained conditions. Finally, the solutions with the minimum sum of sequences of the two-level results are selected as the final solution from the solution set. The experimental results of the proposed algorithm show the effectiveness of the proposed hierarchical wind driven optimization for solving the bi-level programming problems.

关键词： Wind driven optimization bi-level programming problem Constrained optimization

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Determining a subsidy rate for Taiwan's recycling glass industry: an application of bi-level programming

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2012年第1期63卷 28-37页

作者： Shih, H-S Cheng, C-B Wen, U-P Huang, Y-C Peng, M-Y Tamkang Univ Dept Informat Management Taipei 25137 Taiwan Tamkang Univ Grad Inst Management Sci Taipei 25137 Taiwan Natl Tsing Hua Univ Hsinchu Taiwan

This study attempts to optimize the operations of the Recycling Fund Management Board (RFMB), founded by the Environmental Protection Administration of the R.O.C. Government (on Taiwan), through the decision of a subsidy rate for the domestic glass recycling industry. The hierarchical and interactive nature between the two parties is modelled by bi-level programming, where the RFMB plays the upper-level decision unit while the recycling industry is the lower-level counterpart. In order to solve the problem by optimization software, the bi-level formulation is transformed to a single-level problem via Karush-Kuhn-Tucker optimality conditions and is further transformed to a 0-1 mixed integer programming problem by variable substitution. The problem is solved with real-world data, and the obtained solutions are analysed and compared with the RFMB's current operations. The results suggest that the proposed approach can improve the operations of the RFMB. Journal of the Operational Research Society (2012) 63, 28-37. doi:10.1057/jors.2011.13 Published online 30 March 2011

关键词： bi-level programming problem glass recycling industry subsidy rate recycling and treatment fee 0-1 mixed integer programming KKT conditions

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Tri-level transmission expansion planning under intentional attacks: virtual attacker approach - part I: formulation

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IET GENERATION TRANSMISSION & DISTRIBUTION 2019年第3期13卷 390-398页

作者： Nemati, Hadi Latify, Mohammad Amin Yousefi, Gholam Reza Isfahan Univ Technol Dept Elect & Comp Engn Esfahan *** Iran

The first part of this two-part paper proposes tri-level transmission expansion planning (TTEP) under physical intentional attacks. In the first level, the network planner looks for an optimal transmission expansion plan to fortify the power network. In the second level, the attacker tries to maximise damages to the network. In the third level, the adverse effects of the attacks on the network operation are minimised by the network operator. Since the third level problem is a linear programming (LP) problem, the second and third levels are converted into a single-level model by using primal-dual transformation, and consequently, TTEP is converted into a bi-level programming problem. To achieve a single-level model, instead of assuming a unique attacker, a cooperative game of multiple virtual attackers (VAs) of which every VA is to maximise the damage by attacking one transmission line is introduced and modelled. The conditions that enforce Nash and Pareto equilibria of this game are derived as linear constraints which are lower level equivalent. By using this equivalence, the aforementioned bi-level TTEP model is converted into a single-level model that can be recast as a mixed integer LP problem. The numerical results are provided in the second part.

关键词： integer programming linear programming power transmission planning game theory physical attacks network operator network operation linear programming problem single-level model bi-level programming problem multiple virtual attackers virtual attacker approach tri-level transmission expansion planning model physical intentional attacks network planner problem optimal transmission expansion plan power network bi-level TTEP model Pareto equilibrium Nash equilibrium linear constraints

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Multimodal transit network design in a hub-and-spoke network framework

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TRANSPORTMETRICA A-TRANSPORT SCIENCE 2018年第8期14卷 706-735页

作者： Huang, Di Liu, Zhiyuan Fu, Xiao Blythe, Philip T. Southeast Univ Jiangsu Prov Collaborat Innovat Ctr Modern Urban Jiangsu Key Lab Urban ITS Nanjing 210096 Jiangsu Peoples R China Southeast Univ Sch Transportat Nanjing Jiangsu Peoples R China Newcastle Univ Sch Civil Engn & Geosci Transport Operat Res Grp Newcastle Upon Tyne Tyne & Wear England

This study focuses on the reconfiguration of bus services in an urban area with a newly constructed rail system. A hub-and-spoke network framework is introduced for the multimodal transit system. The rail services are taken as the backbone, and the bus services (main bus lines and feeder bus lines) are reconfigured to better integrate with rail services forming the core of a Mobility as a Service (MaaS). A cluster-based approach is used for selecting hubs from rail stations. Bus stops are taken as non-hub nodes. Main bus lines are designed based on a heuristic line generation approach and feeder bus lines are developed by solving a travelling salesman problem. A bi-level programming model is proposed to determine frequencies of each mode and addressed by the artificial bee colony algorithm. The effectiveness of the proposed methods is illustrated by numerical examples and applied to the Mandl's benchmark compared with existing studies.

关键词： Multimodal transit network design hub-and-spoke network cluster-based hub location problem bi-level programming problem

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Production-distribution network design of a global supply chain alliance from the key player's perspective

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2007年第2期45卷 245-265页

作者： Chen, H. -Y. S. Lin, C. -W. R. Yih, Y. Chaoyang Univ Technol Dept Informat Management Taichung Taiwan Natl Yunlin Univ Sci & Technol Dept Ind Management Yunlin Taiwan Purdue Univ Sch Ind Engn W Lafayette IN 47907 USA

A key player in a supply chain (SC) is the member who overlooks and leads others. Although it can compel its autonomous members to follow the planning of a production-distribution network (PDN), the key player has to create an environment in which the partnership with suppliers can also grow accordingly. Without the effective partnership, the efforts increase in managing and integrating the information and material flow across the PDN. Hence, while designing the PDN, the key player has to consider the constraint of the autonomous suppliers also seeking maximum profits as their business goals. In addition, to alleviate the impact of uncertainty on the PDN of a global SC, the strategy of alternative design features is incorporated in the PDN design model. In this paper, the problem for key player's PDN design with alternative design features (KPDN/ADF) is formulated as a bi-level programming problem. An extended genetic algorithm is proposed to solve the KPDN/ADF problem. The experiment results showed that the proposed algorithm can solve the problem satisfactorily. Furthermore, incorporating the product design strategy of alternative design features can make the key player's PDN have better profit under the uncertainty of the currency exchange rate. An illustrative global SC of personal computers/notebooks is also provided to demonstrate the applicability of the KPDN/ADF design model.

关键词： production and distribution network supply chain alternative design features bi-level programming problem genetic algorithm

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Subsidy rate decisions for the printer recycling industry by bi-level optimization techniques

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OPERATIONAL RESEARCH 2017年第3期17卷 901-919页

作者： Cheng, Chi-bin Shih, Hsu-Shih Chen, Boris Tamkang Univ Dept Informat Management New Taipei 25137 Taiwan Tamkang Univ Dept Management Sci New Taipei 25137 Taiwan

This study attempts to optimize the operations of the Recycling Fund Management Board (RFMB), founded by the Environmental Protection Administration of the ROC Government (in Taiwan), by using a subsidy rate decision for domestic printer recyclers. The hierarchical and interactive relation between the two parties is modeled by bi-level programming, where the RFMB serves as the upper-level decision unit, recyclers are the lower-level counterpart, and the consumer's action is embedded in the constraints of the lower level problem. The problem is solved by the Karush-Kuhn-Tucker transformation approach. Practical data including sales of printers per year, a survey of recycling intention, recycler cost structure, and resource recycling value are used to solve the problem. The resulting solution discovers the inefficiency of the current operations of RFMB, and suggests an appropriate recycling fee and subsidy rate that balance the interests of printer manufacturers, recyclers, and the RFMB.

关键词： bi-level programming problem Printer recyclers Subsidy rate Recycling rate KKT approach

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