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.

scholarly journals Application of genetic algorithm in solving the travelling Salesman problem

2021 ◽  
Vol 1208 (1) ◽  
pp. 012032
Author(s):  
Fatka Kulenović ◽  
Azra Hošić
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Path Selection ◽  
Exact Methods ◽  
Travelling Salesman ◽  
Combinatorial Optimization Problems ◽  
Mutation Operators ◽  
Complete Problems ◽  
The Given

Abstract The Travelling Salesman Problem is categorized as NP-complete problems called combinatorial optimization problems. For the growing number of cities it is unsolvable with the use of exact methods in a reasonable time. Genetic algorithms are evolutionary techniques used for optimization purposes according to survival of the fittest idea. These methods do not ensure optimal solutions, however they give good approximation usually in time. Studies have shown that the proposed genetic algorithm can find a shorter route in real time, compared with the existing manipulator model of path selection. The genetic algorithm depends on the selection criteria, crosses, and mutation operators described in detail in this paper. Possible settings of the genetic algorithm are listed and described, as well as the influence of mutation and crossing operators on the efficiency of the genetic algorithm. The optimization results are presented graphically in the MATLAB software package for different cases, after which a comparison of the efficiency of the genetic algorithm with respect to the given parameters is performed.

Neural Network Algorithm for Solving Large Scale Travelling Salesman Problems

2012 ◽  
Vol 542-543 ◽  
pp. 1398-1402
Author(s):  
Guo Zhong Cheng ◽  
Wei Feng ◽  
Fang Song Cui ◽  
Shi Lu Zhang
Keyword(s):  
Neural Network ◽  
Time Complexity ◽  
Large Scale ◽  
Travelling Salesman Problem ◽  
Effective Algorithm ◽  
Travelling Salesman ◽  
Satisfactory Solution ◽  
Network Algorithm ◽  
The Neural Network ◽  
Neural Network Algorithm

This study improves the neural network algorithm that was presented by J.J.Hopfield for solving TSP(travelling salesman problem) and gets an effective algorithm whose time complexity is O(n*n), so we can solve quickly TSP more than 500 cities in microcomputer. The paper considers the algorithm based on the replacement function of the V Value. The improved algorithm can greatly reduces the time and space complexities of Hopfield method. The TSP examples show that the proposed algorithm could efficiently find a satisfactory solution and has a fast convergence speed.

Neural Networks Model for Optimization an Study on Isomorphism Discernment

2010 ◽  
Vol 156-157 ◽  
pp. 492-495
Author(s):  
Miao Zhang ◽  
Ning Bo Liao ◽  
Chen Zhou
Keyword(s):  
Neural Networks ◽  
Large Scale ◽  
Optimization Problems ◽  
Isomorphism Problem ◽  
Processing Elements ◽  
Feedback Network ◽  
Simple Processing ◽  
Np Complete ◽  
Is Design ◽  
Complete Optimization

An artificial neural network is composed of large number of simple processing elements by direct links named connections, the benefits of neural networks extend beyond the high computation rates by massive parallelism. Optimization problems could be transferred into a feedback network, the network interconnects the neurons with a feedback path. Graphs isomorphism discernment is one of the most important and difficult issues in graphs theory based structures design. To solve the problem, a Hopfield neural networks (HNN) model is presented in this paper. The solution of HNN is design as a permutation matrix of two graphs, and some operators are improved to prevent premature convergence. It is concluded that the algorithm presented here is efficient for large-scale graphs isomorphism problem and other NP-complete optimization issues.

scholarly journals Combinatorial optimization by simulating adiabatic bifurcations in nonlinear Hamiltonian systems

2019 ◽  
Vol 5 (4) ◽  
pp. eaav2372 ◽  
Author(s):  
Hayato Goto ◽  
Kosuke Tatsumura ◽  
Alexander R. Dixon
Keyword(s):  
Combinatorial Optimization ◽  
Hamiltonian Systems ◽  
Large Scale ◽  
Optimization Problems ◽  
Approximate Solutions ◽  
Combinatorial Optimization Problems ◽  
Bifurcation Phenomena ◽  
Field Programmable ◽  
Max Cut Problem ◽  
Adiabatic Optimization

Combinatorial optimization problems are ubiquitous but difficult to solve. Hardware devices for these problems have recently been developed by various approaches, including quantum computers. Inspired by recently proposed quantum adiabatic optimization using a nonlinear oscillator network, we propose a new optimization algorithm simulating adiabatic evolutions of classical nonlinear Hamiltonian systems exhibiting bifurcation phenomena, which we call simulated bifurcation (SB). SB is based on adiabatic and chaotic (ergodic) evolutions of nonlinear Hamiltonian systems. SB is also suitable for parallel computing because of its simultaneous updating. Implementing SB with a field-programmable gate array, we demonstrate that the SB machine can obtain good approximate solutions of an all-to-all connected 2000-node MAX-CUT problem in 0.5 ms, which is about 10 times faster than a state-of-the-art laser-based machine called a coherent Ising machine. SB will accelerate large-scale combinatorial optimization harnessing digital computer technologies and also offer a new application of computational and mathematical physics.

A solution to combinatorial optimization problems using an accelerated hopfield neural network

1995 ◽  
Vol 115 (3) ◽  
pp. 76-84
Author(s):  
Takahumi Oohori ◽  
Hiroaki Yamamoto ◽  
Nenso Setsu ◽  
Kazuhisa Watanabe
Keyword(s):  
Neural Network ◽  
Combinatorial Optimization ◽  
Optimization Problems ◽  
Hopfield Neural Network ◽  
Combinatorial Optimization Problems

Computational Complexity Analysis of Selective Breeding Algorithm

2014 ◽  
Vol 591 ◽  
pp. 172-175
Author(s):  
M. Chandrasekaran ◽  
P. Sriramya ◽  
B. Parvathavarthini ◽  
M. Saravanamanikandan
Keyword(s):  
Computational Complexity ◽  
Selective Breeding ◽  
Heuristic Algorithms ◽  
Complexity Analysis ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Approximate Solutions ◽  
Problem Size ◽  
Combinatorial Optimization Problems ◽  
Complete Problems

In modern years, there has been growing importance in the design, analysis and to resolve extremely complex problems. Because of the complexity of problem variants and the difficult nature of the problems they deal with, it is arguably impracticable in the majority time to build appropriate guarantees about the number of fitness evaluations needed for an algorithm to and an optimal solution. In such situations, heuristic algorithms can solve approximate solutions; however suitable time and space complication take part an important role. In present, all recognized algorithms for NP-complete problems are requiring time that's exponential within the problem size. The acknowledged NP-hardness results imply that for several combinatorial optimization problems there are no efficient algorithms that realize a best resolution, or maybe a close to best resolution, on each instance. The study Computational Complexity Analysis of Selective Breeding algorithm involves both an algorithmic issue and a theoretical challenge and the excellence of a heuristic.

scholarly journals An Optimal Implementation on FPGA of a Hopfield Neural Network

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
W. Mansour ◽  
R. Ayoubi ◽  
H. Ziade ◽  
R. Velazco ◽  
W. EL Falou
Keyword(s):  
Neural Network ◽  
Artificial Neural Network ◽  
High Performance ◽  
Optimization Problems ◽  
Parallel Architecture ◽  
Hopfield Neural Network ◽  
Noise Removal ◽  
Combinatorial Optimization Problems ◽  
Artificial Neural Network Ann ◽  
Optimal Implementation

The associative Hopfield memory is a form of recurrent Artificial Neural Network (ANN) that can be used in applications such as pattern recognition, noise removal, information retrieval, and combinatorial optimization problems. This paper presents the implementation of the Hopfield Neural Network (HNN) parallel architecture on a SRAM-based FPGA. The main advantage of the proposed implementation is its high performance and cost effectiveness: it requires O(1) multiplications and O(log⁡ N) additions, whereas most others require O(N) multiplications and O(N) additions.

scholarly journals Reducing the Size of Combinatorial Optimization Problems Using the Operator Vaccine by Fuzzy Selector with Adaptive Heuristics

2015 ◽  
Vol 2015 ◽  
pp. 1-14
Author(s):  
Oscar Montiel ◽  
Francisco Javier Díaz Delgadillo
Keyword(s):  
Combinatorial Optimization ◽  
Fuzzy Inference ◽  
Optimization Problems ◽  
Travelling Salesman Problem ◽  
Combinatorial Problems ◽  
Reduction Step ◽  
Problem Size ◽  
Inference System ◽  
Combinatorial Optimization Problems ◽  
Adaptive Heuristics

Nowadays, solving optimally combinatorial problems is an open problem. Determining the best arrangement of elements proves being a very complex task that becomes critical when the problem size increases. Researchers have proposed various algorithms for solving Combinatorial Optimization Problems (COPs) that take into account the scalability; however, issues are still presented with larger COPs concerning hardware limitations such as memory and CPU speed. It has been shown that the Reduce-Optimize-Expand (ROE) method can solve COPs faster with the same resources; in this methodology, the reduction step is the most important procedure since inappropriate reductions, applied to the problem, will produce suboptimal results on the subsequent stages. In this work, an algorithm to improve the reduction step is proposed. It is based on a fuzzy inference system to classify portions of the problem and remove them, allowing COPs solving algorithms to utilize better the hardware resources by dealing with smaller problem sizes, and the use of metadata and adaptive heuristics. The Travelling Salesman Problem has been used as a case of study; instances that range from 343 to 3056 cities were used to prove that the fuzzy logic approach produces a higher percentage of successful reductions.

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