scholarly journals A Nonlinear Projection Neural Network for Solving Interval Quadratic Programming Problems and Its Stability Analysis

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Huaiqin Wu ◽  
Rui Shi ◽  
Leijie Qin ◽  
Feng Tao ◽  
Lijun He
Keyword(s):  
Neural Network ◽  
Global Exponential Stability ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Saddle Point Theorem ◽  
Set Constraints ◽  
Nonlinear Projection ◽  
Quadratic Programming Problems ◽  
Projection Neural Network ◽  
Interval Quadratic Programming

This paper presents a nonlinear projection neural network for solving interval quadratic programs subject to box-set constraints in engineering applications. Based on the Saddle point theorem, the equilibrium point of the proposed neural network is proved to be equivalent to the optimal solution of the interval quadratic optimization problems. By employing Lyapunov function approach, the global exponential stability of the proposed neural network is analyzed. Two illustrative examples are provided to show the feasibility and the efficiency of the proposed method in this paper.

A DELAYED NEURAL NETWORK METHOD FOR SOLVING CONVEX OPTIMIZATION PROBLEMS

2006 ◽  
Vol 16 (04) ◽  
pp. 295-303 ◽  
Author(s):  
YONGQING YANG ◽  
JINDE CAO
Keyword(s):  
Neural Network ◽  
Convex Programming ◽  
Global Exponential Stability ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Existence Of Solution ◽  
Convex Programming Problem ◽  
Convex Optimization Problems ◽  
Network Method ◽  
Projection Neural Network

In this paper, the delayed projection neural network for a class of solving convex programming problem is proposed. The existence of solution and global exponential stability of the proposed network are proved, which can guarantee to converge at an exact optimal solution of the convex programming problems. Several examples are given to show the effectiveness of the proposed network.

Solving Interval Quadratic Program with Box Set Constraints in Engineering by a Projection Neural Network

2010 ◽  
Vol 9 (8) ◽  
pp. 1615-1621 ◽  
Author(s):  
Huaiqin Wu ◽  
Lijun He . ◽  
Leijie Qin ◽  
Tao Feng ◽  
Rui Shi
Keyword(s):  
Neural Network ◽  
Quadratic Program ◽  
Set Constraints ◽  
Projection Neural Network

Neural Network-Based Metaheuristic Parameterization with Application to the Vehicle Matching Problem in Ride-Hailing Services

2019 ◽  
Vol 2673 (10) ◽  
pp. 311-320
Author(s):  
Arslan Ali Syed ◽  
Irina Gaponova ◽  
Klaus Bogenberger
Keyword(s):  
Neural Network ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Computation Time ◽  
Problem Instance ◽  
Neighborhood Search ◽  
Matching Problem ◽  
Solution Quality ◽  
Actual Problem ◽  
Parameter Values

The majority of transportation problems include optimizing some sort of cost function. These optimization problems are often NP-hard and have an exponential increase in computation time with the increase in the model size. The problem of matching vehicles to passenger requests in ride hailing (RH) contexts typically falls into this category.Metaheuristics are often utilized for such problems with the aim of finding a global optimal solution. However, such algorithms usually include lots of parameters that need to be tuned to obtain a good performance. Typically multiple simulations are run on diverse small size problems and the parameters values that perform the best on average are chosen for subsequent larger simulations.In contrast to the above approach, we propose training a neural network to predict the parameter values that work the best for an instance of the given problem. We show that various features, based on the problem instance and shareability graph statistics, can be used to predict the solution quality of a matching problem in RH services. Consequently, the values corresponding to the best predicted solution can be selected for the actual problem. We study the effectiveness of above described approach for the static assignment of vehicles to passengers in RH services. We utilized the DriveNow data from Bavarian Motor Works (BMW) for generating passenger requests inside Munich, and for the metaheuristic, we used a large neighborhood search (LNS) algorithm combined with a shareability graph.

An Interactive Neural Network for Constrained Multi-Objective Optimization with Application to the Design of Digital Filters

2012 ◽  
Vol 433-440 ◽  
pp. 2808-2816
Author(s):  
Jian Jin Zheng ◽  
You Shen Xia
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Computational Complexity ◽  
Digital Filters ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Multi Objective Optimization ◽  
Multi Objective ◽  
Single Objective

This paper presents a new interactive neural network for solving constrained multi-objective optimization problems. The constrained multi-objective optimization problem is reformulated into two constrained single objective optimization problems and two neural networks are designed to obtain the optimal weight and the optimal solution of the two optimization problems respectively. The proposed algorithm has a low computational complexity and is easy to be implemented. Moreover, the proposed algorithm is well applied to the design of digital filters. Computed results illustrate the good performance of the proposed algorithm.

A NEURAL NETWORK IMPLEMENTATION FOR THE TRAFFIC CONTROL PROBLEM ON CROSSBAR SWITCH NETWORKS

1992 ◽  
Vol 03 (02) ◽  
pp. 209-218 ◽  
Author(s):  
K.T. Sun ◽  
H.C. Fu
Keyword(s):  
Neural Network ◽  
Control Problem ◽  
Energy Function ◽  
Traffic Control ◽  
Feasible Solution ◽  
Optimization Problems ◽  
Stable State ◽  
Optimal Solution ◽  
Neural Network Approach ◽  
Crossbar Switch

In this paper, we propose a neural network for the traffic control problem on crossbar switch networks. First, we represent this problem by an energy function, then apply the proposed neural network to update the state of the energy function until a stable state is reached. Within O(n) iteration steps, where n is the size of an n×n network, the energy function reaches a stable state which corresponds to a feasible solution of the traffic control problem. Also, the simulation results show that our neural network generates either optimal or near optimal solutions. Based on our neural network approach, many problems of applying neural networks to optimization problems are overcome, for example, the unpredictable converging time to reach a stable state, the probability of converging to a local minimum which corresponds to an invalid solution and the selecting of proper parameters of an energy function for obtaining a good (near optimal) solution, etc.

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