Realization of Aggregated Multicast with Lagrange Relaxation Algorithm

2006 ◽  
Author(s):  
Hua Wang ◽  
Zuquan Ge ◽  
Jun Ma
Keyword(s):  
Lagrange Relaxation ◽  
Relaxation Algorithm

scholarly journals A Lagrange Relaxation Based Decomposition Algorithm for Large-Scale Offshore Oil Production Planning Optimization

Processes ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 1257
Author(s):  
Xiaoyong Gao ◽  
Yue Zhao ◽  
Yuhong Wang ◽  
Xin Zuo ◽  
Tao Chen
Keyword(s):  
Production Planning ◽  
Large Scale ◽  
Oil Production ◽  
Original Model ◽  
Decomposition Algorithm ◽  
Scale Model ◽  
Lagrange Relaxation ◽  
Planning Optimization ◽  
Offshore Oil Production ◽  
Offshore Oil

In this paper, a new Lagrange relaxation based decomposition algorithm for the integrated offshore oil production planning optimization is presented. In our previous study (Gao et al. Computers and Chemical Engineering, 2020, 133, 106674), a multiperiod mixed-integer nonlinear programming (MINLP) model considering both well operation and flow assurance simultaneously had been proposed. However, due to the large-scale nature of the problem, i.e., too many oil wells and long planning time cycle, the optimization problem makes it difficult to get a satisfactory solution in a reasonable time. As an effective method, Lagrange relaxation based decomposition algorithms can provide more compact bounds and thus result in a smaller duality gap. Specifically, Lagrange multiplier is introduced to relax coupling constraints of multi-batch units and thus some moderate scale sub-problems result. Moreover, dual problem is constructed for iteration. As a result, the original integrated large-scale model is decomposed into several single-batch subproblems and solved simultaneously by commercial solvers. Computational results show that the proposed method can reduce the solving time up to 43% or even more. Meanwhile, the planning results are close to those obtained by the original model. Moreover, the larger the problem size, the better the proposed LR algorithm is than the original model.

Modeling and Solution Techniques Used for Hydro Generation Scheduling

Water ◽  
2019 ◽  
Vol 11 (7) ◽  
pp. 1392 ◽  
Author(s):  
Iram Parvez ◽  
JianJian Shen ◽  
Mehran Khan ◽  
Chuntian Cheng
Keyword(s):  
Genetic Algorithm ◽  
Dynamic Programming ◽  
Stochastic Programming ◽  
Short Interval ◽  
Optimization Techniques ◽  
Mixed Integer ◽  
Fuzzy Logics ◽  
Spinning Reserve ◽  
Lagrange Relaxation ◽  
Generation Scheduling

The hydro generation scheduling problem has a unit commitment sub-problem which deals with start-up/shut-down costs related hydropower units. Hydro power is the only renewable energy source for many countries, so there is a need to find better methods which give optimal hydro scheduling. In this paper, the different optimization techniques like lagrange relaxation, augmented lagrange relaxation, mixed integer programming methods, heuristic methods like genetic algorithm, fuzzy logics, nonlinear approach, stochastic programming and dynamic programming techniques are discussed. The lagrange relaxation approach deals with constraints of pumped storage hydro plants and gives efficient results. Dynamic programming handles simple constraints and it is easily adaptable but its major drawback is curse of dimensionality. However, the mixed integer nonlinear programming, mixed integer linear programming, sequential lagrange and non-linear approach deals with network constraints and head sensitive cascaded hydropower plants. The stochastic programming, fuzzy logics and simulated annealing is helpful in satisfying the ramping rate, spinning reserve and power balance constraints. Genetic algorithm has the ability to obtain the results in a short interval. Fuzzy logic never needs a mathematical formulation but it is very complex. Future work is also suggested.

Multi Project Scheduling and Material Planning Using Lagrangian Relaxation Algorithm

2021 ◽  
Vol 20 (4) ◽  
pp. 580-587
Author(s):  
Alim Al Ayub Ahmed ◽  
Ngakan Ketut Acwin Dwijendra ◽  
NareshBabu Bynagari ◽  
A.K. Modenov ◽  
M. Kavitha ◽  
...  
Keyword(s):  
Lagrangian Relaxation ◽  
Project Scheduling ◽  
Relaxation Algorithm ◽  
Lagrangian Relaxation Algorithm
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