scholarly journals Solving the Short-Term Scheduling Problem of Hydrothermal Systems via Lagrangian Relaxation and Augmented Lagrangian

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Rafael N. Rodrigues ◽  
Edson L. da Silva ◽  
Erlon C. Finardi ◽  
Fabricio Y. K. Takigawa
Keyword(s):  
Lagrangian Relaxation ◽  
Large Scale ◽  
Augmented Lagrangian ◽  
Augmented Lagrangian Method ◽  
Real Life ◽  
Hydrothermal Systems ◽  
Bundle Method ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Short Term

This paper addresses the short-term scheduling problem of hydrothermal power systems, which results in a large-scale mixed-integer nonlinear programming problem. The objective consists in minimizing the operation cost over a two-day horizon with a one-hour time resolution. To solve this difficult problem, a Lagrangian Relaxation (LR) based on variable splitting is designed where the resulting dual problem is solved by a Bundle method. Given that the LR usually fails to find a feasible solution, we use an inexact Augmented Lagrangian method to improve the quality of the solution supplied by the LR. We assess our approach by using a real-life hydrothermal configuration extracted from the Brazilian power system, proving the conceptual and practical feasibility of the proposed algorithm. In summary, the main contributions of this paper are (i) a detailed and compatible modelling for this problem is presented; (ii) in order to solve efficiently the entire problem, a suitable decomposition strategy is presented. As a result of these contributions, the proposed model is able to find practical solutions with moderate computational burden, which is absolutely necessary in the modern power industry.

scholarly journals Lagrangian Relaxation Based on Improved Proximal Bundle Method for Short-Term Hydrothermal Scheduling

2021 ◽  
Vol 13 (9) ◽  
pp. 4706
Author(s):  
Zhiyu Yan ◽  
Shengli Liao ◽  
Chuntian Cheng ◽  
Josué Medellín-Azuara ◽  
Benxi Liu
Keyword(s):  
Lagrangian Relaxation ◽  
Lagrange Multipliers ◽  
Large Scale ◽  
Orthogonal Design ◽  
Solution Space ◽  
Economic Benefits ◽  
Bundle Method ◽  
Short Term ◽  
Hydrothermal Scheduling ◽  
Proximal Bundle Method

Short-term hydrothermal scheduling (STHS) can improve water use efficiency, reduce carbon emissions, and increase economic benefits by optimizing the commitment and dispatch of hydro and thermal generating units together. However, limited by the large system scale and complex hydraulic and electrical constraints, STHS poses great challenges in modeling for operators. This paper presents an improved proximal bundle method (IPBM) within the framework of Lagrangian relaxation for STHS, which incorporates the expert system (ES) technique into the proximal bundle method (PBM). In IPBM, initial values of Lagrange multipliers are firstly determined using the linear combination of optimal solutions in the ES. Then, each time PBM declares a null step in the iterations, the solution space is inferred from the ES, and an orthogonal design is performed in the solution space to derive new updates of the Lagrange multipliers. A case study in a large-scale hydrothermal system in China is implemented to demonstrate the effectiveness of the proposed method. Results in different cases indicate that IPBM is superior to standard PBM in global search ability and computational efficiency, providing an alternative for STHS.

scholarly journals Solving the nuclear dismantling project scheduling problem by combining mixed-integer and constraint programming techniques and metaheuristics

2021 ◽  
Author(s):  
Felix Hübner ◽  
Patrick Gerhards ◽  
Christian Stürck ◽  
Rebekka Volk
Keyword(s):  
Constraint Programming ◽  
Project Scheduling ◽  
Computational Study ◽  
Real Life ◽  
Mixed Integer ◽  
Extensive Literature ◽  
Scheduling Problem ◽  
Multiple Modes ◽  
Project Scheduling Problem ◽  
Optimisation Techniques

AbstractScheduling of megaprojects is very challenging because of typical characteristics, such as expected long project durations, many activities with multiple modes, scarce resources, and investment decisions. Furthermore, each megaproject has additional specific characteristics to be considered. Since the number of nuclear dismantling projects is expected to increase considerably worldwide in the coming decades, we use this type of megaproject as an application case in this paper. Therefore, we consider the specific characteristics of constrained renewable and non-renewable resources, multiple modes, precedence relations with and without no-wait condition, and a cost minimisation objective. To reliably plan at minimum costs considering all relevant characteristics, scheduling methods can be applied. But the extensive literature review conducted did not reveal a scheduling method considering the special characteristics of nuclear dismantling projects. Consequently, we introduce a novel scheduling problem referred to as the nuclear dismantling project scheduling problem. Furthermore, we developed and implemented an effective metaheuristic to obtain feasible schedules for projects with about 300 activities. We tested our approach with real-life data of three different nuclear dismantling projects in Germany. On average, it took less than a second to find an initial feasible solution for our samples. This solution could be further improved using metaheuristic procedures and exact optimisation techniques such as mixed-integer programming and constraint programming. The computational study shows that utilising exact optimisation techniques is beneficial compared to standard metaheuristics. The main result is the development of an initial solution finding procedure and an adaptive large neighbourhood search with iterative destroy and recreate operations that is competitive with state-of-the-art methods of related problems. The described problem and findings can be transferred to other megaprojects.

Study on the Scheduling Problem of Powder Painting Production - A Case Study

2010 ◽  
Vol 97-101 ◽  
pp. 2459-2464
Author(s):  
Zhang Yong Hu ◽  
Qiang Su ◽  
Jun Liu ◽  
Hai Xia Yang
Keyword(s):  
Large Scale ◽  
Production Efficiency ◽  
Production Performance ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Adaptive Search ◽  
Optimal Sequence ◽  
Integer Nonlinear Programming ◽  
Minlp Model

A large-scale powder-painting scheduling problem is explored. The purpose is to find out the optimal sequence of a number of batches that dynamically arrive from upstream processes within a given scheduling horizon. The objective is to enhance the production efficiency and decrease the production cost as well. To solve this problem, a mixed integer nonlinear programming (MINLP) model is constructed and an algorithm called greedy randomized adaptive search procedure (GRASP) is designed. Case studies demonstrate that the proposed approach can improve the production performance significantly.

scholarly journals An Improved Lagrangian Relaxation Algorithm for the Robust Generation Self-Scheduling Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Ping Che ◽  
Zhenhao Tang ◽  
Hua Gong ◽  
Xiaoli Zhao
Keyword(s):  
Lagrangian Relaxation ◽  
Single Unit ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Two Stage ◽  
Splitting Technique ◽  
Relaxation Algorithm ◽  
Special Cases ◽  
Lagrangian Relaxation Algorithm ◽  
Relaxed Problem

The robust generation self-scheduling problem under electricity price uncertainty is usually solved by the commercial solver, which is limited in computation time and memory requirement. This paper proposes an improved Lagrangian relaxation algorithm for the robust generation self-scheduling problem where the quadratic fuel cost and the time-dependent exponential startup cost are considered. By using the optimal duality theory, the robust generation self-scheduling problem, which has a max-min structure, is reformulated as a minimization mixed integer nonlinear programming (MINLP) problem. Upon the reformulation, the Lagrangian relaxation algorithm is developed. To obtain a solvable relaxed problem, the variable splitting technique is introduced before the relaxation. The obtained relaxed problem is decomposed into a linear programming-type subproblem and multiple single-unit subproblems. Each single-unit subproblem is solved optimally by a two-stage backward dynamic programming procedure. The special cases of the problem are discussed and a two-stage algorithm is proposed. The proposed algorithms are tested on test cases of different sizes and the numerical results show that the algorithms can find near-optimal solutions in a reasonable time.

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