Projected Neural Network for a Class of Non-Lipschitz Optimization Problems With Linear Constraints

2020 ◽  
Vol 31 (9) ◽  
pp. 3361-3373
Author(s):  
Wenjing Li ◽  
Wei Bian ◽  
Xiaoping Xue
Keyword(s):  
Neural Network ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Lipschitz Optimization

Optimizing the Learning Process of Feedforward Neural Networks Using Lightning Search Algorithm

2016 ◽  
Vol 25 (06) ◽  
pp. 1650033 ◽  
Author(s):  
Hossam Faris ◽  
Ibrahim Aljarah ◽  
Nailah Al-Madi ◽  
Seyedali Mirjalili
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Optimization Technique ◽  
Back Propagation ◽  
Feedforward Neural Networks ◽  
Training Algorithms ◽  
Local Optima ◽  
Local Solutions

Evolutionary Neural Networks are proven to be beneficial in solving challenging datasets mainly due to the high local optima avoidance. Stochastic operators in such techniques reduce the probability of stagnation in local solutions and assist them to supersede conventional training algorithms such as Back Propagation (BP) and Levenberg-Marquardt (LM). According to the No-Free-Lunch (NFL), however, there is no optimization technique for solving all optimization problems. This means that a Neural Network trained by a new algorithm has the potential to solve a new set of problems or outperform the current techniques in solving existing problems. This motivates our attempts to investigate the efficiency of the recently proposed Evolutionary Algorithm called Lightning Search Algorithm (LSA) in training Neural Network for the first time in the literature. The LSA-based trainer is benchmarked on 16 popular medical diagnosis problems and compared to BP, LM, and 6 other evolutionary trainers. The quantitative and qualitative results show that the LSA algorithm is able to show not only better local solutions avoidance but also faster convergence speed compared to the other algorithms employed. In addition, the statistical test conducted proves that the LSA-based trainer is significantly superior in comparison with the current algorithms on the majority of datasets.

A Dynamics-Based Optimal Trajectory Generation for Controlling an Automated Excavator

2010 ◽  
Vol 224 (10) ◽  
pp. 2109-2119 ◽  
Author(s):  
S Yoo ◽  
C-G Park ◽  
S-H You ◽  
B Lim
Keyword(s):  
Optimal Trajectory ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Control Points ◽  
Weighting Functions ◽  
B Splines ◽  
Finite Dimensional ◽  
Motion Optimization ◽  
Save Energy

This article presents a new methodology to generate optimal trajectories in controlling an automated excavator. By parameterizing all the actuator displacements with B-splines of the same order and with the same number of control points, the coupled actuator limits, associated with the maximum pump flowrate, are described as the finite-dimensional set of linear constraints to the motion optimization problem. Several weighting functions are introduced on the generalized actuator torque so that the solution to each optimization problems contains the physical meaning. Numerical results showing that the generated motions of the excavator are fairly smooth and effectively save energy, which can prevent mechanical wearing and possibly save fuel consumption, are presented. A typical operator's manoeuvre from experiments is referred to bring out the standing features of the optimized motion.

Effects of the chaotic noise on the performance of a neural network model for optimization problems

1995 ◽  
Vol 51 (4) ◽  
pp. R2693-R2696 ◽  
Author(s):  
Yoshinori Hayakawa ◽  
Atsushi Marumoto ◽  
Yasuji Sawada
Keyword(s):  
Neural Network ◽  
Network Model ◽  
Neural Network Model ◽  
Optimization Problems

Nonlinear Optimal Design of Dynamic Mechanical Systems

1992 ◽  
Author(s):  
T. E. Potter ◽  
K. D. Willmert ◽  
M. Sathyamoorthy
Keyword(s):  
Objective Function ◽  
Optimization Problems ◽  
Iteration Process ◽  
Optimization Method ◽  
Linear Constraints ◽  
Sum Of Squares ◽  
Function Evaluation ◽  
Deformation Analysis ◽  
Nonlinear Constraints ◽  
Quadratic Constraints

Abstract Mechanism path generation problems which use link deformations to improve the design lead to optimization problems involving a nonlinear sum-of-squares objective function subjected to a set of linear and nonlinear constraints. Inclusion of the deformation analysis causes the objective function evaluation to be computationally expensive. An optimization method is presented which requires relatively few objective function evaluations. The algorithm, based on the Gauss method for unconstrained problems, is developed as an extension of the Gauss constrained technique for linear constraints and revises the Gauss nonlinearly constrained method for quadratic constraints. The derivation of the algorithm, using a Lagrange multiplier approach, is based on the Kuhn-Tucker conditions so that when the iteration process terminates, these conditions are automatically satisfied. Although the technique was developed for mechanism problems, it is applicable to any optimization problem having the form of a sum of squares objective function subjected to nonlinear constraints.

Hahn-Banach-Type Theorems and Subdifferentials for Invariant and Equivariant Order Continuous Vector Lattice-Valued Operators with Applications to Optimization

2021 ◽  
Vol 78 (1) ◽  
pp. 139-156
Author(s):  
Antonio Boccuto
Keyword(s):  
Optimality Conditions ◽  
Vector Lattice ◽  
Optimization Problems ◽  
Linear Constraints ◽  
Continuous Vector ◽  
Fixed Group ◽  
Composite Functions ◽  
Order Continuous

Abstract We give some versions of Hahn-Banach, sandwich, duality, Moreau--Rockafellar-type theorems, optimality conditions and a formula for the subdifferential of composite functions for order continuous vector lattice-valued operators, invariant or equivariant with respect to a fixed group G of homomorphisms. As applications to optimization problems with both convex and linear constraints, we present some Farkas and Kuhn-Tucker-type results.

scholarly journals Flame Failures and Recovery in Industrial Furnaces: A Neural Network Steady-State Model for the Firing Rate Setpoint Rearrangement

2018 ◽  
Vol 2018 ◽  
pp. 1-15
Author(s):  
Tahmineh Adili ◽  
Zohreh Rostamnezhad ◽  
Ali Chaibakhsh ◽  
Ali Jamali
Keyword(s):  
Neural Network ◽  
Steady State ◽  
Optimization Problems ◽  
Network Models ◽  
Economic Loss ◽  
Neural Network Models ◽  
Firing Rates ◽  
State Models ◽  
Major Equipment ◽  
Artificial Neural Network Models

Burner failures are common abnormal conditions associated with industrial fired heaters. Preventing from economic loss and major equipment damages can be attained by compensating the lost heat due to burners’ failures, which can be possible by defining appropriate setpoints to rearrange the firing rates for healthy burners. In this study, artificial neural network models were developed for estimating the appropriate setpoints for the combustion control system to recover an industrial fired-heater furnace from abnormal conditions. For this purpose, based on an accurate high-order mathematical model, constrained nonlinear optimization problems were solved using the genetic algorithm. For different failure scenarios, the best possible excess firing rates for healthy burners to recover the furnace from abnormal conditions were obtained and data were recorded for training and testing stages. The performances of the developed neural steady-state models were evaluated through simulation experiments. The obtained results indicated the feasibility of the proposed technique to deal with the failures in the combustion system.

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