Nonlinear Optimization Using Generalized Hopfield Networks

1989 ◽  
Vol 1 (4) ◽  
pp. 511-521 ◽  
Author(s):  
Athanasios G. Tsirukis ◽  
Gintaras V. Reklaitis ◽  
Manoel F. Tenorio
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Hopfield Network ◽  
Systems Of Nonlinear Equations ◽  
Hopfield Networks ◽  
Dynamic View ◽  
Study Results ◽  
Content Addressable Memories ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

A nonlinear neural framework, called the generalized Hopfield network (GHN), is proposed, which is able to solve in a parallel distributed manner systems of nonlinear equations. The method is applied to the general nonlinear optimization problem. We demonstrate GHNs implementing the three most important optimization algorithms, namely the augmented Lagrangian, generalized reduced gradient, and successive quadratic programming methods. The study results in a dynamic view of the optimization problem and offers a straightforward model for the parallelization of the optimization computations, thus significantly extending the practical limits of problems that can be formulated as an optimization problem and that can gain from the introduction of nonlinearities in their structure (e.g., pattern recognition, supervised learning, and design of content-addressable memories).

Optimal Design of a Mechanism Used for Opening and Shutting a Ship’s Hatch Cover

1984 ◽  
Vol 106 (4) ◽  
pp. 503-509
Author(s):  
Koichi Ito ◽  
Tadashi Kuroiwa ◽  
Shinsuke Akagi
Keyword(s):  
Optimal Design ◽  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Numerical Study ◽  
Optimal Solution ◽  
Optimization Method ◽  
Gradient Algorithm ◽  
Linkage Mechanism ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient

A nonlinear optimization method is proposed to design a linkage mechanism used for opening and shutting a ship’s hatch cover. Considering the maximum force of the oil cylinder necessary to move the hatch cover as the objective function to be minimized, the design problem to determine the optimal configuration of linkage mechanism is formulated as a nonlinear optimization problem of minimax type. It it shown that the optimal solution can be derived by adopting the generalized reduced gradient algorithm together with a linkage statical simulation model, and the effectiveness of the algorithm is ascertained through a numerical study.

Optimal Design of Semisubmersible’s Form Based on Systems Analysis

1984 ◽  
Vol 106 (4) ◽  
pp. 524-530 ◽  
Author(s):  
S. Akagi ◽  
R. Yokoyama ◽  
K. Ito
Keyword(s):  
Optimal Design ◽  
Computer Aided Design ◽  
Optimization Problem ◽  
Design Method ◽  
Gradient Algorithm ◽  
Interpretive Structural Modeling ◽  
Reduced Gradient ◽  
Optimal Design Method ◽  
Generalized Reduced Gradient ◽  
Aided Design

With the objective of developing a computer-aided design method to seek the optimal semisubmersible’s form, hierarchical relationships among many design objectives and conditions are investigated first based on the interpretive structural modeling method. Then, an optimal design method is formulated as a nonlinear multiobjective optimization problem by adopting three mutually conflicting design objectives. A set of Pareto optimal solutions is derived numerically by adopting the generalized reduced gradient algorithm, and it is ascertained that the designer can determine the optimal form more rationally by investigating the trade-off relationships among design objectives.

A New Method to Solve the Kinematic Problems of Parallel Robots Using Generalized Reduced Gradient Algorithm

2016 ◽  
Vol 28 (3) ◽  
pp. 404-417 ◽  
Author(s):  
Thanh Trung Trang ◽  
◽  
Wei Guang Li ◽  
Thanh Long Pham ◽  
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problems ◽  
Computing Time ◽  
Parallel Manipulators ◽  
Parallel Robots ◽  
New Method ◽  
Gradient Algorithm ◽  
Reduced Gradient ◽  
Generalized Reduced Gradient ◽  
Reduced Gradient Algorithm

[abstFig src='/00280003/17.jpg' width=""300"" text='Stewart Gough robot and the equivalent substitutional configuration' ] This paper proposes a new method of solving the kinematic problems for parallel robots. The paper content aims to solve nonlinear optimization problems with constraints rather than to directly solve high-order nonlinear systems of equations. The nonlinear optimization problems shall be efficiently solved by applying the Generalized Reduced Gradient algorithm and appropriate downgrade techniques. This new method can be able to find exact kinematic solutions by assigning constraints onto the parameters. The procedure can be done without filtering control results from mathematical solution, from which the control time of manipulators can be reduced. The numerical simulation results in this paper shall prove that the method can be applied to solve kinematic problems for a variety of parallel robots regardless of its structures and degree of freedom (DOF). There are several advantages of the proposed method including its simplicity leading to a shorter computing time as well as achieving high accuracy, high reliability, and quick convergence in final results. Hence, the applicability of this method in solving kinematic problems for parallel manipulators is remarkably high.

scholarly journals Single Neuronal Dynamical System in Self-Feedbacked Hopfield Networks and Its Application in Image Encryption

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 456
Author(s):  
Xitong Xu ◽  
Shengbo Chen
Keyword(s):  
Dynamical System ◽  
Image Encryption ◽  
Chaotic Dynamic ◽  
Security Analysis ◽  
High Sensitivity ◽  
Hopfield Network ◽  
Complex Structures ◽  
Hopfield Networks ◽  
Discrete Form ◽  
Chaotic Parameter

Image encryption is a confidential strategy to keep the information in digital images from being leaked. Due to excellent chaotic dynamic behavior, self-feedbacked Hopfield networks have been used to design image ciphers. However, Self-feedbacked Hopfield networks have complex structures, large computational amount and fixed parameters; these properties limit the application of them. In this paper, a single neuronal dynamical system in self-feedbacked Hopfield network is unveiled. The discrete form of single neuronal dynamical system is derived from a self-feedbacked Hopfield network. Chaotic performance evaluation indicates that the system has good complexity, high sensitivity, and a large chaotic parameter range. The system is also incorporated into a framework to improve its chaotic performance. The result shows the system is well adapted to this type of framework, which means that there is a lot of room for improvement in the system. To investigate its applications in image encryption, an image encryption scheme is then designed. Simulation results and security analysis indicate that the proposed scheme is highly resistant to various attacks and competitive with some exiting schemes.

Schedule-Constrained Demand Management in Two-Region Urban Networks

2021 ◽  
Author(s):  
Sakitha Kumarage ◽  
Mehmet Yildirimoglu ◽  
Mohsen Ramezani ◽  
Zuduo Zheng
Keyword(s):  
Nonlinear Optimization ◽  
Optimization Problem ◽  
Time Window ◽  
Demand Management ◽  
Urban Traffic ◽  
Fundamental Diagram ◽  
Constrained System ◽  
Nonlinear Optimization Problem ◽  
Management Platform ◽  
User Compliance

Demand management aiming to optimize system cost while ensuring user compliance in an urban traffic network is a challenging task. This paper introduces a cooperative demand redistribution strategy to optimize network performance through the retiming of departure times within a limited time window. The proposed model minimizes the total time spent in a two-region urban network by incurring minimal disruption to travelers’ departure schedules. Two traffic models based on the macroscopic fundamental diagram (MFD) are jointly implemented to redistribute demand and analyze travelers’ reaction. First, we establish equilibrium conditions via a day-to-day assignment process, which allows travelers to find their preferred departure times. The trip-based MFD model that incorporates individual traveler attributes is implemented in the day-to-day assignment, and it is conjugated with a network-level detour ratio model to incorporate the effect of congestion in individual traveler route choice. This allows us to consider travelers with individual preferences on departure times influenced by desired arrival times, trip lengths, and earliness and lateness costs. Second, we develop a nonlinear optimization problem to minimize the total time spent considering both observed and unobserved demand—that is, travelers opting in and out of the demand management platform. The accumulation-based MFD model that builds on aggregated system representation is implemented as part of the constraints in the nonlinear optimization problem. The results confirm the resourcefulness of the model to address complex two-region traffic dynamics and to increase overall performance by reaching a constrained system optimum scenario while ensuring the applicability at both full and partial user compliance conditions.

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