scholarly journals Efficient Solution Methods for Large-scale Optimization Problems Constrained by Time-dependent Partial Differential Equations (Final Report)

2019 ◽  
Author(s):  
Andrei Draganescu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Large Scale ◽  
Efficient Solution ◽  
Optimization Problems ◽  
Time Dependent ◽  
Final Report ◽  
Large Scale Optimization ◽  
Solution Methods ◽  
Scale Optimization

A new three-term spectral conjugate gradient algorithm with higher numerical performance for solving large scale optimization problems based on Quasi-Newton equation

2021 ◽  
pp. 2150053
Author(s):  
Jie Guo ◽  
Zhong Wan
Keyword(s):  
Conjugate Gradient ◽  
Large Scale ◽  
Line Search ◽  
Optimization Problems ◽  
Gradient Algorithm ◽  
Large Scale Optimization ◽  
Newton Equation ◽  
Numerical Performance ◽  
Scale Optimization ◽  
Quasi Newton

A new spectral three-term conjugate gradient algorithm in virtue of the Quasi-Newton equation is developed for solving large-scale unconstrained optimization problems. It is proved that the search directions in this algorithm always satisfy a sufficiently descent condition independent of any line search. Global convergence is established for general objective functions if the strong Wolfe line search is used. Numerical experiments are employed to show its high numerical performance in solving large-scale optimization problems. Particularly, the developed algorithm is implemented to solve the 100 benchmark test problems from CUTE with different sizes from 1000 to 10,000, in comparison with some similar ones in the literature. The numerical results demonstrate that our algorithm outperforms the state-of-the-art ones in terms of less CPU time, less number of iteration or less number of function evaluation.

A modified competitive swarm optimizer for large scale optimization problems

2017 ◽  
Vol 59 ◽  
pp. 340-362 ◽  
Author(s):  
Prabhujit Mohapatra ◽  
Kedar Nath Das ◽  
Santanu Roy
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Large Scale Optimization ◽  
Scale Optimization

scholarly journals An Adaptive Multi-Swarm Competition Particle Swarm Optimizer for Large-Scale Optimization

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 521 ◽  
Author(s):  
Fanrong Kong ◽  
Jianhui Jiang ◽  
Yan Huang
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Particle Swarm ◽  
The Other ◽  
Large Scale Optimization ◽  
Particle Swarm Optimizer ◽  
Competition Mechanism ◽  
Benchmark Suite ◽  
Scale Optimization ◽  
The One

As a powerful tool in optimization, particle swarm optimizers have been widely applied to many different optimization areas and drawn much attention. However, for large-scale optimization problems, the algorithms exhibit poor ability to pursue satisfactory results due to the lack of ability in diversity maintenance. In this paper, an adaptive multi-swarm particle swarm optimizer is proposed, which adaptively divides a swarm into several sub-swarms and a competition mechanism is employed to select exemplars. In this way, on the one hand, the diversity of exemplars increases, which helps the swarm preserve the exploitation ability. On the other hand, the number of sub-swarms adaptively changes from a large value to a small value, which helps the algorithm make a suitable balance between exploitation and exploration. By employing several peer algorithms, we conducted comparisons to validate the proposed algorithm on a large-scale optimization benchmark suite of CEC 2013. The experiments results demonstrate the proposed algorithm is effective and competitive to address large-scale optimization problems.

scholarly journals An Entropy-Assisted Particle Swarm Optimizer for Large-Scale Optimization Problem

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 414 ◽  
Author(s):  
Weian Guo ◽  
Lei Zhu ◽  
Lei Wang ◽  
Qidi Wu ◽  
Fanrong Kong
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Particle Swarm ◽  
Large Scale Optimization ◽  
Particle Swarm Optimizer ◽  
Fitness Evaluation ◽  
Diversity Maintenance ◽  
Entropy Measurement ◽  
Benchmark Suite ◽  
Scale Optimization

Diversity maintenance is crucial for particle swarm optimizer’s (PSO) performance. However, the update mechanism for particles in the conventional PSO is poor in the performance of diversity maintenance, which usually results in a premature convergence or a stagnation of exploration in the searching space. To help particle swarm optimization enhance the ability in diversity maintenance, many works have proposed to adjust the distances among particles. However, such operators will result in a situation where the diversity maintenance and fitness evaluation are conducted in the same distance-based space. Therefore, it also brings a new challenge in trade-off between convergence speed and diversity preserving. In this paper, a novel PSO is proposed that employs competitive strategy and entropy measurement to manage convergence operator and diversity maintenance respectively. The proposed algorithm was applied to the large-scale optimization benchmark suite on CEC 2013 and the results demonstrate the proposed algorithm is feasible and competitive to address large scale optimization problems.

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