Reduction of Dimension of the Upper Level Problem in a Bilevel Programming Model Part 2

2011 ◽  
pp. 265-272 ◽  
Author(s):  
Vyacheslav V. Kalashnikov ◽  
Stephan Dempe ◽  
Gerardo A. Pérez-Valdés ◽  
Nataliya I. Kalashnykova
Keyword(s):  
Bilevel Programming ◽  
Programming Model ◽  
Level Problem ◽  
Reduction Of Dimension ◽  
Upper Level ◽  
Bilevel Programming Model

scholarly journals The Shrinking of Beijing and the Rising of Xiong’an: Optimize Population Migration in terms of Transport Service

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Hongzhi Lin
Keyword(s):  
Bilevel Programming ◽  
Central Government ◽  
Programming Model ◽  
Service Level ◽  
User Equilibrium ◽  
Population Migration ◽  
Transport Service ◽  
Level Model ◽  
Upper Level ◽  
Bilevel Programming Model

The population of Beijing has already come to its loading capacity. The China central government plans to build an ideal city named Xiong’an nearby Beijing. The city is expected to work as a carrying hub for noncapital functions of Beijing. The central government does not rush to build before a deliberated urban planning is accomplished. For sustainable development, a difficulty faced by urban planners is that the maximum number of people can be migrated from Beijing to Xiong’an with constraint on level of transport service. This paper developed a specialized bilevel programming model where the upper level is to ensure a predetermined transport service level regarding to population migration, while the lower level is feedback equilibrium between trip generation and traffic assignment. To be more specific, trip is generated by the gravity model, and traffic is assigned by the user equilibrium model. It is well known that the bilevel programming problem is tough and challenging. A try-and-error algorithm is designed for the upper-level model, and a method of successive average (MSA) is developed for the lower-level model. The effectiveness of the model and algorithm is validated by an experimental study using the current transport network between Beijing and Xiong’an. It shows that the methods can be very useful to identify the maximum population migration subject to level of transport service.

scholarly journals Bilevel programming model and algorithms for flight gate assignment problem

2020 ◽  
Vol 124 (1281) ◽  
pp. 1667-1682
Author(s):  
J. Lin ◽  
X. Ding ◽  
H. Li ◽  
J. Zhou
Keyword(s):  
Bilevel Programming ◽  
Programming Model ◽  
Eastern China ◽  
The Other ◽  
Adaptive Genetic Algorithm ◽  
Transfer Time ◽  
Objective Functions ◽  
Upper Level ◽  
Bilevel Programming Model ◽  
Bilevel Optimisation

ABSTRACTConsidering the decision-making requirements of airport, airlines and passengers, a bilevel programming model which contains two parts was proposed in this paper. One part is to improve the utilization of gates of the airport (upper level), so the objective function of the upper level to the minimum overall variance of slack time between two consecutive air crafts at the same gate. The other part looks at maximize the airline revenue and passengers more conveniently and comfortably (lower level). The lower level has two objective functions — the minimum passenger transfer failure and the minimum passenger average transfer time, respectively. According to the latest data of an airport in Eastern China, the adaptive genetic algorithm is used to solve the above-mentioned bilevel optimisation problems. The numerical experiment shows that the model not only reduces the variance of the relaxation time, but also optimises the flight gate allocation and achieves the initial goal.

FUZZY BILEVEL PROGRAMMING: MULTI-OBJECTIVE AND MULTI-FOLLOWER WITH SHARED VARIABLES

2008 ◽  
Vol 16 (supp02) ◽  
pp. 105-133 ◽  
Author(s):  
GUANGQUAN ZHANG ◽  
JIE LU ◽  
YA GAO
Keyword(s):  
Bilevel Programming ◽  
Optimization Problems ◽  
Programming Model ◽  
Hierarchical Optimization ◽  
Multi Objective ◽  
Decision Variables ◽  
Shared Variables ◽  
Upper Level ◽  
Bilevel Programming Model ◽  
Multiple Followers

Bilevel programming deals with hierarchical optimization problems in which the leader at the upper level attempts to optimize his or her objectives, but subject to a set of constraints and the follower's reactions. Typical bilevel programming considers one leader one follower situation and supposes each of them has only one objective. In real world situations, multiple followers may be involved and they may be with different relationships such as sharing decision variables or not, sharing objectives or not. Therefore, the leader's decision will be affected not only by those followers' reactions but also by their relationships. In addition, any of the leader and/or these followers may have multiple conflict objectives that should be optimized simultaneously. Furthermore, the parameters of a bilevel programming model may be described by uncertain values. This paper addresses all these three issues as a whole by particularly focusing on the situation of sharing decision variables among followers. It first proposes a set of fuzzy multi-objective multi-follower bilevel programming (FMMBP) models to describe the complex issue. It then presents an approximation branch-and-bound algorithm to solve the FMMBP problems. Finally, two examples illustrate the proposed models and algorithm.

scholarly journals A Bilevel Programming Model and Algorithm for the Static Bike Repositioning Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-19 ◽  
Author(s):  
Qiong Tang ◽  
Zhuo Fu ◽  
Meng Qiu
Keyword(s):  
Bilevel Programming ◽  
Programming Model ◽  
Iterated Local Search ◽  
Transportation Mode ◽  
Bike Sharing ◽  
Loading And Unloading ◽  
Upper Level ◽  
Route Cost ◽  
Bilevel Programming Model ◽  
Transportation Route

In this paper, by taking the outsourcing transportation mode into account, a bilevel programming model is proposed to formulate the static bike repositioning (SBR) problem, which can be used to determine the number of bikes loaded and unloaded at each station and the optimal truck routes in bike sharing systems (BSS). The upper-level BSS providers determine the optimal loading and unloading quantities at stations to minimize the total penalties. The lower-level truck owner pursues the minimum transportation route cost. An iterated local search and tabu search are developed to solve the model. Computational tests on a set of instances from 20 to 200 bikes demonstrate the effectiveness of the model and algorithms proposed, together with some insightful findings.

scholarly journals Parcel Locker Location Based on a Bilevel Programming Model

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Gege Yang ◽  
Yin Huang ◽  
Ying Fu ◽  
Biao Huang ◽  
Sishi Sheng ◽  
...  
Keyword(s):  
Genetic Algorithm ◽  
Bilevel Programming ◽  
Consumer Satisfaction ◽  
Programming Model ◽  
Optimal Location ◽  
Network Efficiency ◽  
Demand Distribution ◽  
Level Model ◽  
Upper Level ◽  
Bilevel Programming Model

In order to improve delivery network efficiency and to solve consumer satisfaction problems, parcel locker location optimisation scheme is proposed based on the delivery demand under the e-commerce environment. In this paper, a bilevel programming (BLP) model is established to identify the optimal location for parcel lockers by considering benefits of consumers and logistics planning departments. The upper-level model is to determine the optimal location by minimising the planners’ cost, and the lower one gives an equilibrium demand distribution by minimising the consumers’ pick-up cost. On the special form of constraints, a bilevel genetic algorithm is proposed based on GIS data and a genetic algorithm. Finally, a numerical example is employed to demonstrate the application of the method, which indicates that the model can solve the problem of parcel locker location.

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