scholarly journals A bilevel optimization approach to decide the feasibility of bookings in the European gas market

2021 ◽  
Author(s):  
Fränk Plein ◽  
Johannes Thürauf ◽  
Martine Labbé ◽  
Martin Schmidt
Keyword(s):  
Gas Flow ◽  
Mathematical Problem ◽  
Bilevel Optimization ◽  
Optimization Approach ◽  
Single Level ◽  
Active Elements ◽  
System Operator ◽  
Passive Networks ◽  
Gas Market ◽  
Upper Level

AbstractThe European gas market is organized as a so-called entry-exit system with the main goal to decouple transport and trading. To this end, gas traders and the transmission system operator (TSO) sign so-called booking contracts that grant capacity rights to traders to inject or withdraw gas at certain nodes up to this capacity. On a day-ahead basis, traders then nominate the actual amount of gas within the previously booked capacities. By signing a booking contract, the TSO guarantees that all nominations within the booking bounds can be transported through the network. This results in a highly challenging mathematical problem. Using potential-based flows to model stationary gas physics, feasible bookings on passive networks, i.e., networks without controllable elements, have been characterized in the recent literature. In this paper, we consider networks with linearly modeled active elements such as compressors or control valves. Since these active elements allow the TSO to control the gas flow, the single-level approaches for passive networks from the literature are no longer applicable. We thus present a bilevel model to decide the feasibility of bookings in networks with active elements. While this model is well-defined for general active networks, we focus on the class of networks for which active elements do not lie on cycles. This assumption allows us to reformulate the original bilevel model such that the lower-level problem is linear for every given upper-level decision. Consequently, we derive several single-level reformulations for this case. Besides the classic Karush–Kuhn–Tucker reformulation, we obtain three problem-specific optimal-value-function reformulations. The latter also lead to novel characterizations of feasible bookings in networks with active elements that do not lie on cycles. We compare the performance of our methods by a case study based on data from the .

Reduction of the Dimension of the Upper Level Problem in a Bilevel Optimization Model

2015 ◽  
pp. 289-308
Author(s):  
Stephan Dempe ◽  
Vyacheslav Kalashnikov ◽  
Gerardo A. Pérez-Valdés ◽  
Nataliya Kalashnykova
Keyword(s):  
Optimization Model ◽  
Bilevel Optimization ◽  
Level Problem ◽  
Upper Level

scholarly journals Bi-Level Operation Scheduling of Distribution Systems with Multi-Microgrids Considering Uncertainties

Electronics ◽  
2020 ◽  
Vol 9 (9) ◽  
pp. 1441
Author(s):  
Saeid Esmaeili ◽  
Amjad Anvari-Moghaddam ◽  
Erfan Azimi ◽  
Alireza Nateghi ◽  
João P. S. Catalão
Keyword(s):  
Distribution System ◽  
Distribution Systems ◽  
Optimization Problem ◽  
Point Of View ◽  
Mixed Integer ◽  
Wholesale Market ◽  
System Operator ◽  
Level Model ◽  
Upper Level ◽  
Operation Scheduling

A bi-level operation scheduling of distribution system operator (DSO) and multi-microgrids (MMGs) considering both the wholesale market and retail market is presented in this paper. To this end, the upper-level optimization problem minimizes the total costs from DSO’s point of view, while the profits of microgrids (MGs) are maximized in the lower-level optimization problem. Besides, a scenario-based stochastic programming framework using the heuristic moment matching (HMM) method is developed to tackle the uncertain nature of the problem. In this regard, the HMM technique is employed to model the scenario matrix with a reduced number of scenarios, which is effectively suitable to achieve the correlations among uncertainties. In order to solve the proposed non-linear bi-level model, Karush–Kuhn–Tucker (KKT) optimality conditions and linearization techniques are employed to transform the bi-level problem into a single-level mixed-integer linear programming (MILP) optimization problem. The effectiveness of the proposed model is demonstrated on a real-test MMG system.

scholarly journals Flexible Emergency Vehicle Network Design considering Stochastic Demands and Inverse-Direction Lanes

2018 ◽  
Vol 2018 ◽  
pp. 1-14
Author(s):  
Hua Wang ◽  
Ling Xiao ◽  
Zhang Chen
Keyword(s):  
Network Design ◽  
Transportation Network ◽  
Bilevel Optimization ◽  
User Equilibrium ◽  
Emergency Vehicle ◽  
Stochastic Demands ◽  
Road Users ◽  
Level Model ◽  
Access Rights ◽  
Upper Level

We study transportation network design with stochastic demands and emergency vehicle (EV) lanes. Different from previous studies, this paper considers two groups of users, auto and EV travelers, whose road access rights are differentiated in the network, and addresses the value of incorporating inverse-direction lanes in network design. We formulate the problem as a bilevel optimization model, where the upper-level model aims to determine the optimal design of EV lanes and the lower-level model uses the user equilibrium principle to forecast the route choice of road users. A simulation-based genetic algorithm is proposed to solve the model. With numerical experiments, we demonstrate the value of deploying inverse-direction EV lanes and the computational efficiency of the proposed algorithm. We reach an intriguing finding that both regular and EV lane users can benefit from building EV lanes.

scholarly journals Service Arms with Unconventional Robotic Parameters for Intricate Workstations: Optimal Number and Dimensional Synthesis

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Satwinder Singh ◽  
Ekta Singla
Keyword(s):  
Degrees Of Freedom ◽  
Solution Space ◽  
Bilevel Optimization ◽  
Optimal Number ◽  
Dimensional Synthesis ◽  
Cluttered Environments ◽  
Link Service ◽  
Upper Level ◽  
Feasible Solutions ◽  
Task Oriented

A task-oriented design strategy is presented in this paper for service manipulators. The tasks are normally defined in the form of working locations where the end-effector can work while avoiding the obstacles. To acquire feasible solutions in cluttered environments, the robotic parameters (D-H parameters) are allowed to take unconventional values. This enhances the solution space and it is observed that, by inducing this flexibility, the required number of degrees of freedom for fulfilling a given task can be reduced. A bilevel optimization problem is formulated with the outer layer utilizing the binary search method for minimizing the number of degrees of freedom. To enlarge the applicability domain of the proposed strategy, the upper limit of the number of joints is kept more than six. These allowable redundant joints would help in providing solution for intricate workcells. For each iteration of the upper level, a constrained nonlinear problem is solved for dimensional synthesis of the manipulator. The methodology is demonstrated through a case study of a realistic environment of a cluttered server room. A7-link service arm, synthesized using the proposed method, is able to fulfill two different tasks effectively.

scholarly journals Administrative corruption in the static model of balancing common and private interests

2021 ◽  
pp. 9-19
Author(s):  
Olga Ivanovna Gorbaneva
Keyword(s):  
Level Sets ◽  
Lower Boundary ◽  
Static Model ◽  
Optimization Approach ◽  
Level System ◽  
Private Interests ◽  
Descriptive Approach ◽  
Upper Level ◽  
The Impact

  This article is dedicated to examination of corruption in the previously researched static model of balancing common and private interests (SOCHI-models). In the previously considered two-level system, between the upper non-corrupted level and the lower – agents, is introduced the average level which in exchange for a bribe, can weaken the influence of the upper level. The upper level sets the minimum amount of resources for an agent to spend on general purposes. A supervisor, in exchange for a bribe, the role of which is played by the share of agent’s private income, can reduce this lower boundary, allowing the latter to spend more resources on private purposes. This article reviews the three-level hierarchical system “Principal-Supervisor-Agents”, where the supervisor uses the administrative corruption mechanism, which requires two descriptive and optimization approaches towards its examination. The descriptive approach suggests that the considered functions of bribery are known; while the optimization approach implies the use of Germeyer’s theorem. The author explores the impact of administrative corruption upon systemic congruence of the SOCHI-model: it is proven that the administrative corruption can only reduce congruence. The author finds the conditions that can beat or reduce administrative corruption can, as well as conditions when corruption is disadvantageous for supervisor or agent. The article determines the circle of agents that supervisor can exert influence upon.  

Path Planning and Control of Redundant Manipulators Using Bilevel Optimization

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Uriel Nusbaum ◽  
Miri Weiss Cohen ◽  
Yoram Halevi
Keyword(s):  
Optimal Control ◽  
Dynamic Systems ◽  
Bilevel Optimization ◽  
Complex Tasks ◽  
Planning And Control ◽  
Optimal Inputs ◽  
Saturation Constraints ◽  
Level Problem ◽  
Upper Level ◽  
And Control

Abstract Redundancy is a useful feature in dynamic systems which can be exploited to enhance performance in various tasks. In this work, redundancy will be utilized to minimize the energy consumption of a linear manipulator, while in some cases an additional task of end-effector tracking will also be required and achieved. Optimal control theory has been extensively used for the optimization of dynamic systems; however, complex tasks and redundancy make these problems computationally expensive, numerically difficult to solve, and in many cases, ill-defined. In this paper, evolutionary bilevel optimization for the problem is presented. This is done by setting up an upper level optimization problem for a set of decision variables and a lower level one that actually calculates the optimal inputs and trajectories. The upper level problem is solved by a genetic algorithm (GA), whereas the lower level problem uses classical optimal control. As a result, the proposed algorithm allows the optimization of complex tasks that usually cannot be solved in practice using standard optimal control tools. In addition, despite the use of penalty functions to enforce saturation constraints, the algorithm leads to global energy minimization. Illustrative examples of a redundant x-y robotic manipulator with complex overall tasks will be presented, solved, and discussed.

Sign in / Sign up

Export Citation Format

Share Document