scholarly journals Numerical Optimal Control for Problems with Random Forced SPDE Constraints

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
R. Naseri ◽  
A. Malek
Keyword(s):  
Numerical Simulation ◽  
Optimal Control ◽  
Large Scale ◽  
Polynomial Chaos ◽  
Optimization Problems ◽  
Hybrid Approach ◽  
Chaos Expansion ◽  
The Finite Element Method ◽  
Stochastic Diffusion Equation ◽  
Spatial Part

A numerical algorithm for solving optimization problems with stochastic diffusion equation as a constraint is proposed. First, separation of random and deterministic variables is done via Karhunen-Loeve expansion. Then, the problem is discretized, in spatial part, using the finite element method and the polynomial chaos expansion in the stochastic part of the problem. This process leads to the optimal control problem with a large scale system in its constraint. To overcome these difficulties the adjoint technique for derivative computation to implementation of the optimal control issue in preconditioned Newton’s conjugate gradient method is used. By some numerical simulation, it is shown that this hybrid approach is efficient and simple to implement.

A Hybrid Approach of Heuristic and Neural Network for Packing Problems

1994 ◽  
Author(s):  
Zuo Dai ◽  
Jianzhong Cha
Keyword(s):  
Neural Network ◽  
Large Scale ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Hybrid Approach ◽  
Two Dimensions ◽  
Packing Problems ◽  
Combinatorial Optimization Problems ◽  
Complete Problems ◽  
Np Complete

Abstract Artificial Neural Networks, particularly the Hopfield-Tank network, have been effectively applied to the solution of a variety of tasks formulated as large scale combinatorial optimization problems, such as Travelling Salesman Problem and N Queens Problem [1]. The problem of optimally packing a set of geometries into a space with finite dimensions arises frequently in many applications and is far difficult than general NP-complete problems listed in [2]. Until now within accepted time limit, it can only be solved with heuristic methods for very simple cases (e.g. 2D layout). In this paper we propose a heuristic-based Hopfield neural network designed to solve the rectangular packing problems in two dimensions, which is still NP-complete [3]. By comparing the adequacy and efficiency of the results with that obtained by several other exact and heuristic approaches, it has been concluded that the proposed method has great potential in solving 2D packing problems.

Alternating direction based method for optimal control problem constrained by Stokes equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Yu Gao ◽  
Jingzhi Li ◽  
Yongcun Song ◽  
Chao Wang ◽  
Kai Zhang
Keyword(s):  
Optimal Control ◽  
Discrete System ◽  
Augmented Lagrangian ◽  
Stokes Equations ◽  
Optimization Problems ◽  
Augmented Lagrangian Method ◽  
Lagrangian Method ◽  
The Finite Element Method ◽  
Alternating Direction ◽  
Different Types

Abstract We consider the optimal control problems constrained by Stokes equations. It has been shown in the literature, the problem can be discretized by the finite element method to generate a discrete system, and the error estimate has also been established. In this paper, we focus on solving the discrete system by the alternating splitting augmented Lagrangian method, which is a direct extension of alternating direction method of multipliers and possesses a global O ⁢ ( 1 / k ) \mathcal{O}({1}/{k}) convergence rate. In addition, we propose an acceleration scheme based on the alternating splitting augmented Lagrangian method to improve the efficiency of the algorithm. The error estimates and convergence analysis of our algorithms are presented for several different types of optimization problems. Finally, numerical experiments are performed to verify the efficiency of the algorithms.

Computationally Efficient Hybrid Method for Transmission Network Expansion Planning

2017 ◽  
Vol 18 (2) ◽  
Author(s):  
Ashu Verma ◽  
Soumya Das ◽  
P. R. Bijwe
Keyword(s):  
Power System ◽  
Large Scale ◽  
Optimization Problems ◽  
Hybrid Approach ◽  
Solution Process ◽  
System Optimization ◽  
Mixed Integer ◽  
Transmission Network ◽  
Network Expansion ◽  
Expansion Planning

Abstract Transmission network expansion planning (TNEP) is an important and computationally very demanding problem in power system. Many computational approaches have been proposed to handle TNEP in the past. The problem is mixed integer, large scale and its complexity increases exponentially with the size of the system. Metaheuristic techniques have gained a lot of importance in last few years to solve the power system optimization problems, due to their ability to handle complex optimization functions and constraints. Many of them have been successfully applied for TNEP. The biggest challenge in these techniques is the requirement of large computational efforts. This paper uses a two-stage solution process to solve the TNEP problems. The first stage uses compensation based method to generate a quick, suboptimal solution. The valuable information contained in this solution is used to generate a set of heuristics aimed at drastically reducing the number of population for fitness evaluations required in the 2nd stage with application of metaheuristic method. The resulting hybrid approach produces very good quality solutions very efficiently. Results for 24 bus and 93 bus test systems have been obtained with the proposed method to ascertain the potential of the method in comparison to earlier approaches.

scholarly journals Fuzzy Simheuristics for Optimizing Transportation Systems: Dealing with Stochastic and Fuzzy Uncertainty

2021 ◽  
Vol 11 (17) ◽  
pp. 7950
Author(s):  
Rafael D. Tordecilla ◽  
Leandro do C. Martins ◽  
Javier Panadero ◽  
Pedro J. Copado ◽  
Elena Perez-Bernabeu ◽  
...  
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Smart Cities ◽  
Hybrid Approach ◽  
Transportation Systems ◽  
Telecommunication Networks ◽  
Routing Problem ◽  
Fuzzy Uncertainty ◽  
Hard Problems ◽  
Team Orienteering

In the context of logistics and transportation, this paper discusses how simheuristics can be extended by adding a fuzzy layer that allows us to deal with complex optimization problems with both stochastic and fuzzy uncertainty. This hybrid approach combines simulation, metaheuristics, and fuzzy logic to generate near-optimal solutions to large scale NP-hard problems that typically arise in many transportation activities, including the vehicle routing problem, the arc routing problem, or the team orienteering problem. The methodology allows us to model different components–such as travel times, service times, or customers’ demands–as deterministic, stochastic, or fuzzy. A series of computational experiments contribute to validate our hybrid approach, which can also be extended to other optimization problems in areas such as manufacturing and production, smart cities, telecommunication networks, etc.

scholarly journals Addressing a Humanitarian Relief Chain Considering Uncertain Demand and Deprivation Costs by a Hybrid LP-GA Method: An Earthquake in Kermanshah

2021 ◽  
Author(s):  
Amin Forughi ◽  
Babak Farhang Moghaddam ◽  
Mohammad Hassan behzadi ◽  
Farzad movahedi sobhani
Keyword(s):  
Optimization Model ◽  
Large Scale ◽  
Optimization Problems ◽  
Objective Assessment ◽  
Hybrid Approach ◽  
Transportation Cost ◽  
Humanitarian Logistics ◽  
Humanitarian Relief ◽  
Deprivation Costs ◽  
Disruption Risks

Abstract Today, a great deal of attention to numerous disasters such as earthquakes, floods and terrorist attacks is motivated by humanitarian logistics. A comprehensive plan for relief logistic items under uncertainty is a challengeable concern for both academic and logistics practitioners. This study contributes another robust plan for the humanitarian logistics for the earthquake disaster in Kermanshah, Iran. The proposed framework evaluates both operational and disruption risks simultaneously to study the Humanitarian Relief Chain (HRC) network after an earthquake. The main novelty is the simultaneous consideration of the deprivation costs and demand under uncertainty. The deprivation cost leads to a reduction in high social costs for the decision-makers of the HRC. The proposed HRC also guarantees the delivery of the essential supplies to beneficiaries under both operational and disruption risks. As an optimization model, it seeks to minimize total costs consisting of inventory holding cost, shortage cost, deprivation costs and transportation cost and maximizes each facility's weighted resilience level as the second objective. A robust optimization model is established to deal with uncertain levels of the transport network paths, supply condition, amount of demand and deprivation costs which are assumed uncertain. The resilience parameters used for the second objective are obtained by a Best Worst Method (BWM). Another significant contribution was a hybrid approach combining the LP-metric method and Genetic Algorithm (GA) as the LP–GA approach for optimizing large-scale instances. Regarding the analyses, including tuning, validation and comparison of the proposed approach, its performance is showed by several standard multi-objective assessment metrics. As a final point, the achieved outcomes demonstrate that the suggested model is highly sensitive to uncertain parameters. This encourages further development and application of the proposed HRC with the use of a hybrid LP-GA approach as a strong technique for solving optimization problems.

scholarly journals Robust Dynamic Optimization of a Dual-rotor System Based on Polynomial Chaos Expansion

2021 ◽  
Author(s):  
bensheng xu ◽  
chaoping zang ◽  
Xiaowei Wang ◽  
Genbei Zhang
Keyword(s):  
Dynamic Optimization ◽  
Polynomial Chaos ◽  
Polynomial Chaos Expansion ◽  
Rotor System ◽  
Operating Conditions ◽  
Design Parameters ◽  
Direct Monte Carlo Simulation ◽  
Chaos Expansion ◽  
The Finite Element Method ◽  
The Mean

Abstract A novel methodology of robust dynamic optimization of a dual-rotor system based on polynomial chaos expansion (PCE) is developed in this paper. The dual-rotor system model was built by the Timoshenko theory and the finite element method. Instead of the direct Monte Carlo simulation (MCS), the PCE of the present dual-rotor system under support stiffness uncertainty is generated to facilitate a rapid analysis of stochastic responses and yield desirable results in significantly less number of functional evaluations. The PCE is explored as a basis for robust optimization, focusing on the problem of minimizing the unbalance response at operating conditions while minimizing its sensitivity to uncertainty in the support stiffness. This strategy avoids the use of MCS in order to effectively increase the efficiency of the optimization and significantly reduce the computing cost and time spending. The robust dynamic optimization attempts to both optimize the mean performance and minimizes the variance of the performance simultaneously. The multi-objective optimization results show that vibration response can be decreased and is significantly less sensitive to the variation of design parameters compared with initial design case by matching of unbalance amplitude and phase angle differences. Implementation of the proposed robust dynamic optimization in the present dual-rotor system illustrates its potential for further complicated applications.

scholarly journals Numerical Simulation Study on Environment-Friendly Floating Reef in Offshore Ecological Belt under Wave Action

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2257
Author(s):  
Yun Pan ◽  
Huanhuan Tong ◽  
Yang Zhou ◽  
Can Liu ◽  
Dawen Xue
Keyword(s):  
Numerical Simulation ◽  
Structural Design ◽  
Large Scale ◽  
Water Mass ◽  
Floating Body ◽  
The Finite Element Method ◽  
Lumped Mass ◽  
Environment Friendly ◽  
Ecological Corridor ◽  
New Type

An artificial floating reef is an important part of the coastal ecological corridor. The large-scale construction of floating reefs by optimizing mooring methods can effectively improve the ecological effects of coastal projects. The artificial floating reef belongs to coastal engineering, and wave resistance is fundamental to its structural design. In this paper, the method for processing coupling forces and motion, the method for judging the floating reef out of water surface, and the method for correcting velocity and acceleration of water mass points are elaborated in detail by using the finite element method and lumped-mass mooring model. By comparing and analyzing the results of physical experiment and numerical simulation, the correctness of the numerical model is verified. Finally, the diachronic variation of pitching angle of floating reef, the tension of the mooring rope, and the total tension of the fixed points of the fishing net were analyzed by the dynamic response numerical mode with a new type of mooring. The purpose of the current study was to provide a basis for the optimization of structure shape, the matching of floating body, and the counterweight of artificial floating reef.

Sign in / Sign up

Export Citation Format

Share Document