scholarly journals Decompositions for MPC of Linear Dynamic Systems with Activation Constraints

Energies ◽  
2020 ◽  
Vol 13 (21) ◽  
pp. 5744
Author(s):  
Pedro Henrique Valderrama Bento da Silva ◽  
Eduardo Camponogara ◽  
Laio Oriel Seman ◽  
Gabriel Villarrubia González ◽  
Valderi Reis Quietinho Leithardt
Keyword(s):  
Benders Decomposition ◽  
Complex Dynamics ◽  
Hierarchical Control ◽  
Master Problem ◽  
Linear Dynamic Systems ◽  
Distributed Structure ◽  
Systems Model ◽  
Distributed Components ◽  
Scientists And Engineers ◽  
Single Controller

The interconnection of dynamic subsystems that share limited resources are found in many applications, and the control of such systems of subsystems has fueled significant attention from scientists and engineers. For the operation of such systems, model predictive control (MPC) has become a popular technique, arguably for its ability to deal with complex dynamics and system constraints. The MPC algorithms found in the literature are mostly centralized, with a single controller receiving the signals and performing the computations of output signals. However, the distributed structure of such interconnected subsystems is not necessarily explored by standard MPC. To this end, this work proposes hierarchical decomposition to split the computations between a master problem (centralized component) and a set of decoupled subproblems (distributed components) with activation constraints, which brings about organizational flexibility and distributed computation. Two general methods are considered for hierarchical control and optimization, namely Benders decomposition and outer approximation. Results are reported from a numerical analysis of the decompositions and a simulated application to energy management, in which a limited source of energy is distributed among batteries of electric vehicles.

A Benders Decomposition Approach for the Multivehicle Production Routing Problem with Order-up-to-Level Policy

2020 ◽  
Author(s):  
Zhenzhen Zhang ◽  
Zhixing Luo ◽  
Roberto Baldacci ◽  
Andrew Lim
Keyword(s):  
Benders Decomposition ◽  
Valid Inequalities ◽  
Planning Horizon ◽  
Set Partitioning ◽  
Master Problem ◽  
Inventory Level ◽  
Inventory Routing ◽  
Routing Problem ◽  
Decomposition Approach ◽  
Production Routing

The production routing problem (PRP) arises in the applications of integrated supply chain which jointly optimize the production, inventory, distribution, and routing decisions. The literature on this problem is quite rare due to its complexity. In this paper, we consider the multivehicle PRP (MVPRP) with order-up-to-level inventory replenishment policy, where every time a customer is visited, the quantity delivered is such that the maximum inventory level is reached. We propose an exact Benders’ decomposition approach to solve the MVPRP, which decomposes the problem as a master problem and a slave problem. The master problem decides whether to produce the product, the quantity to be produced, and the customers to be replenished for every period of the planning horizon. The resulting slave problem decomposes into a capacitated vehicle routing problem for each period of the planning horizon where each problem is solved using an exact algorithm based on the set partitioning model, and the identified feasibility and optimality cuts are added to the master problem to guide the solution process. Valid inequalities and initial optimality cuts are used to strengthen the linear programming relaxation of the master formulation. The exact method is tested on MVPRP instances and on instances of the multivehicle vendor-managed inventory routing problem, a special case of the MVPRP, and the good performance of the proposed approach is demonstrated.

scholarly journals A Decomposition Approach for Stochastic Shortest-Path Network Interdiction with Goal Threshold

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 237 ◽  
Author(s):  
Xiangyu Wei ◽  
Kai Xu ◽  
Peng Jiao ◽  
Quanjun Yin ◽  
Yabing Zha
Keyword(s):  
Shortest Path ◽  
Real World ◽  
Benders Decomposition ◽  
Research Problem ◽  
Resource Consumption ◽  
Network Interdiction ◽  
Master Problem ◽  
Decomposition Approach ◽  
Stochastic Shortest Path ◽  
T Path

Shortest-path network interdiction, where a defender strategically allocates interdiction resource on the arcs or nodes in a network and an attacker traverses the capacitated network along a shortest s-t path from a source to a terminus, is an important research problem with potential real-world impact. In this paper, based on game-theoretic methodologies, we consider a novel stochastic extension of the shortest-path network interdiction problem with goal threshold, abbreviated as SSPIT. The attacker attempts to minimize the length of the shortest path, while the defender attempts to force it to exceed a specific threshold with the least resource consumption. In our model, threshold constraint is introduced as a trade-off between utility maximization and resource consumption, and stochastic cases with some known probability p of successful interdiction are considered. Existing algorithms do not perform well when dealing with threshold and stochastic constraints. To address the NP-hard problem, SSPIT-D, a decomposition approach based on Benders decomposition, was adopted. To optimize the master problem and subproblem iteration, an efficient dual subgraph interdiction algorithm SSPIT-S and a local research based better-response algorithm SSPIT-DL were designed, adding to the SSPIT-D. Numerical experiments on networks of different sizes and attributes were used to illustrate and validate the decomposition approach. The results showed that the dual subgraph and better-response procedure can significantly improve the efficiency and scalability of the decomposition algorithm. In addition, the improved enhancement algorithms are less sensitive and robust to parameters. Furthermore, the application in a real-world road network demonstrates the scalability of our decomposition approach.

scholarly journals Stabilized Benders Methods for Large-Scale Combinatorial Optimization, with Application to Data Privacy

2020 ◽  
Vol 66 (7) ◽  
pp. 3051-3068 ◽  
Author(s):  
Daniel Baena ◽  
Jordi Castro ◽  
Antonio Frangioni
Keyword(s):  
Data Privacy ◽  
Large Scale ◽  
Benders Decomposition ◽  
Mixed Integer ◽  
Master Problem ◽  
Continuous Variables ◽  
Typical Structure ◽  
Disclosure Control ◽  
Current State ◽  
Statistical Disclosure

The cell-suppression problem (CSP) is a very large mixed-integer linear problem arising in statistical disclosure control. However, CSP has the typical structure that allows application of the Benders decomposition, which is known to suffer from oscillation and slow convergence, compounded with the fact that the master problem is combinatorial. To overcome this drawback, we present a stabilized Benders decomposition whose master is restricted to a neighborhood of successful candidates by local-branching constraints, which are dynamically adjusted, and even dropped, during the iterations. Our experiments with synthetic and real-world instances with up to 24,000 binary variables, 181 million (M) continuous variables, and 367M constraints show that our approach is competitive with both the current state-of-the-art code for CSP and the Benders implementation in CPLEX 12.7. In some instances, stabilized Benders provided a very good solution in less than 1 minute, whereas the other approaches found no feasible solution in 1 hour. This paper was accepted by Yinyu Ye, optimization.

The Options of Using Data Mining Methods in Process Control

2014 ◽  
Vol 693 ◽  
pp. 123-128
Author(s):  
Alena Kopcekova ◽  
Michal Kopcek ◽  
Pavol Tanuska
Keyword(s):  
Data Mining ◽  
Control Systems ◽  
Planning Process ◽  
Hierarchical Control ◽  
Basic Research ◽  
Systems Model ◽  
Mining Methods ◽  
Using Data ◽  
Definition Of ◽  
A Company

The term business intelligence (BI) represents the tools and systems that play a key role in the strategic planning process of the corporation. These systems allow a company to gather, store, access and analyze corporate data to aid in decision-making. Necessary fundamental definitions are offered and explained to better understand the basic principles and the role of this technology for a company management. The proposed article is logically divided into more sections, where the stages of basic research in the field of data mining are described gradually. This involves the definition of the technology and the list of main advantages and analytical methods incorporated in online analytical processing. Also some typical applications of above mentioned particular methods are introduced. The focus of this paper is to introduce the options of using the data mining methods on the control systems level within the hierarchical control systems model.

The Benders Dual Decomposition Method

2020 ◽  
Vol 68 (3) ◽  
pp. 878-895
Author(s):  
Ragheb Rahmaniani ◽  
Shabbir Ahmed ◽  
Teodor Gabriel Crainic ◽  
Michel Gendreau ◽  
Walter Rei
Keyword(s):  
Decomposition Method ◽  
High Performance ◽  
Large Scale ◽  
Benders Decomposition ◽  
Master Problem ◽  
Computational Results ◽  
Dual Decomposition ◽  
High Quality ◽  
Lagrangian Dual ◽  
Decomposition Strategies

Many methods that have been proposed to solve large-scale MILP problems rely on the use of decomposition strategies. These methods exploit either the primal or dual structures of the problems by applying the Benders decomposition or Lagrangian dual decomposition strategy, respectively. In “The Benders Dual Decomposition Method,” Rahmaniani, Ahmed, Crainic, Gendreau, and Rei propose a new and high-performance approach that combines the complementary advantages of both strategies. The authors show that this method (i) generates stronger feasibility and optimality cuts compared with the classical Benders method, (ii) can converge to the optimal integer solution at the root node of the Benders master problem, and (iii) is capable of generating high-quality incumbent solutions at the early iterations of the algorithm. The developed algorithm obtains encouraging computational results when used to solve various benchmark MILP problems.

scholarly journals Enhancing large neighbourhood search heuristics for Benders’ decomposition

2021 ◽  
Author(s):  
Stephen J. Maher
Keyword(s):  
Integer Programming ◽  
Mixed Integer Programming ◽  
Benders Decomposition ◽  
Trust Region ◽  
Mixed Integer ◽  
Master Problem ◽  
Search Heuristics ◽  
Neighbourhood Search ◽  
Large Neighbourhood ◽  
Large Neighbourhood Search

AbstractA general enhancement of the Benders’ decomposition (BD) algorithm can be achieved through the improved use of large neighbourhood search heuristics within mixed-integer programming solvers. While mixed-integer programming solvers are endowed with an array of large neighbourhood search heuristics, few, if any, have been designed for BD. Further, typically the use of large neighbourhood search heuristics is limited to finding solutions to the BD master problem. Given the lack of general frameworks for BD, only ad hoc approaches have been developed to enhance the ability of BD to find high quality primal feasible solutions through the use of large neighbourhood search heuristics. The general BD framework of SCIP has been extended with a trust region based heuristic and a general enhancement for large neighbourhood search heuristics. The general enhancement employs BD to solve the auxiliary problems of all large neighbourhood search heuristics to improve the quality of the identified solutions. The computational results demonstrate that the trust region heuristic and a general large neighbourhood search enhancement technique accelerate the improvement in the primal bound when applying BD.

Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design

2020 ◽  
Author(s):  
Teodor Gabriel Crainic ◽  
Mike Hewitt ◽  
Francesca Maggioni ◽  
Walter Rei
Keyword(s):  
Network Design ◽  
Solution Method ◽  
Benders Decomposition ◽  
Solution Process ◽  
Master Problem ◽  
Solution Quality ◽  
Stochastic Programs ◽  
Multicommodity Network Design ◽  
Planning Problems ◽  
Stability Of The Solution

Benders decomposition is a broadly used exact solution method for stochastic programs, which has been increasingly applied to solve transportation and logistics planning problems under uncertainty. However, this strategy comes with important drawbacks, such as a weak master problem following the relaxation step that confines the dual cuts to the scenario subproblems. In this paper, we propose a partial Benders decomposition methodology, based on the idea of including explicit information from the scenario subproblems in the master. To investigate the benefits of this methodology, we apply it to solve a general class of two-stage stochastic multicommodity network design models. Specifically, we solve the challenging variant of the model where both the demands and the arc capacities are stochastic. Through an extensive experimental campaign, we clearly show that the proposed methodology yields significant benefits in computational efficiency, solution quality, and stability of the solution process.

scholarly journals Using the Thermal Inertia of Transmission Lines for Coping with Post-Contingency Overflows

Energies ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 48
Author(s):  
Xiansi Lou ◽  
Wei Chen ◽  
Chuangxin Guo
Keyword(s):  
Transmission Lines ◽  
Power Flow ◽  
Optimal Power Flow ◽  
Benders Decomposition ◽  
Thermal Inertia ◽  
Master Problem ◽  
Preventive Control ◽  
Temperature Function ◽  
Equivalent Time ◽  
Generation Cost

For the corrective security-constrained optimal power flow (OPF) model, there exists a post-contingency stage due to the time delay of corrective measures. Line overflows in this stage may cause cascading failures. This paper proposes that the thermal inertia of transmission lines can be used to cope with post-contingency overflows. An enhanced security-constrained OPF model is established and line dynamic thermal behaviors are quantified. The post-contingency stage is divided into a response substage and a ramping substage and the highest temperatures are limited by thermal rating constraints. A solving strategy based on Benders decomposition is proposed to solve the established model. The original problem is decomposed into a master problem for preventive control and two subproblems for corrective control feasibility check and line thermal rating check. In each iteration, Benders cuts are generated for infeasible contingencies and returned into the master problem for adjusting the generation plan. Because the highest temperature function is implicit, an equivalent time method is presented to calculate its partial derivative in Benders cuts. The proposed model and approaches are validated on three test systems. Results show that the operation security is improved with a slight increase in total generation cost.

scholarly journals Generalized Benders Decomposition Method to Solve Big Mixed-Integer Nonlinear Optimization Problems with Convex Objective and Constraints Functions

Energies ◽  
2021 ◽  
Vol 14 (20) ◽  
pp. 6503
Author(s):  
Andrzej Karbowski
Keyword(s):  
Nonlinear Optimization ◽  
Benders Decomposition ◽  
Optimization Problems ◽  
Mixed Integer ◽  
Master Problem ◽  
Computational Algorithms ◽  
Generalized Benders Decomposition ◽  
Representation Theorems ◽  
Mixed Integer Nonlinear Optimization ◽  
Basic Approaches

The paper presents the Generalized Benders Decomposition (GBD) method, which is now one of the basic approaches to solve big mixed-integer nonlinear optimization problems. It concentrates on the basic formulation with convex objectives and constraints functions. Apart from the classical projection and representation theorems, a unified formulation of the master problem with nonlinear and linear cuts will be given. For the latter case the most effective and, at the same time, easy to implement computational algorithms will be pointed out.

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