scholarly journals A Parallel Bioinspired Algorithm for Chinese Postman Problem Based on Molecular Computing

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Zhaocai Wang ◽  
Xiaoguang Bao ◽  
Tunhua Wu
Keyword(s):  
Computational Complexity ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Solution Space ◽  
Research Direction ◽  
Chinese Postman Problem ◽  
Combinatorial Optimization Problems ◽  
Chinese Postman ◽  
Dna Algorithm

The Chinese postman problem is a classic resource allocation and scheduling problem, which has been widely used in practice. As a classical nondeterministic polynomial problem, finding its efficient algorithm has always been the research direction of scholars. In this paper, a new bioinspired algorithm is proposed to solve the Chinese postman problem based on molecular computation, which has the advantages of high computational efficiency, large storage capacity, and strong parallel computing ability. In the calculation, DNA chain is used to properly represent the vertex, edge, and corresponding weight, and then all possible path combinations are effectively generated through biochemical reactions. The feasible solution space is obtained by deleting the nonfeasible solution chains, and the optimal solution is solved by algorithm. Then the computational complexity and feasibility of the DNA algorithm are proved. By comparison, it is found that the computational complexity of the DNA algorithm is significantly better than that of previous algorithms. The correctness of the algorithm is verified by simulation experiments. With the maturity of biological operation technology, this algorithm has a broad application space in solving large-scale 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 Optimization of Traveling Salesman Problem Using Affinity Propagation Clustering and Genetic Algorithm

2015 ◽  
Vol 5 (4) ◽  
pp. 239-245 ◽  
Author(s):  
Ahmad Fouad El-Samak ◽  
Wesam Ashour
Keyword(s):  
Genetic Algorithm ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Solution Space ◽  
Affinity Propagation ◽  
Computational Time ◽  
Combinatorial Optimization Problems ◽  
Affinity Propagation Clustering ◽  
Core Idea ◽  
Computation Algorithms

Abstract Combinatorial optimization problems, such as travel salesman problem, are usually NP-hard and the solution space of this problem is very large. Therefore the set of feasible solutions cannot be evaluated one by one. The simple genetic algorithm is one of the most used evolutionary computation algorithms, that give a good solution for TSP, however, it takes much computational time. In this paper, Affinity Propagation Clustering Technique (AP) is used to optimize the performance of the Genetic Algorithm (GA) for solving TSP. The core idea, which is clustering cities into smaller clusters and solving each cluster using GA separately, thus the access to the optimal solution will be in less computational time. Numerical experiments show that the proposed algorithm can give a good results for TSP problem more than the simple GA.

scholarly journals Alpha-T: Learning to Traverse over Graphs with An AlphaZero-inspired Self-Play Framework

2021 ◽  
Author(s):  
Qi Wang
Keyword(s):  
Large Scale ◽  
Optimization Problems ◽  
Optimal Path ◽  
Solution Space ◽  
Approximate Solutions ◽  
Small Scale ◽  
Traditional Methods ◽  
Routing Problem ◽  
Monte Carlo Tree Search ◽  
Combinatorial Optimization Problems

Abstract The combinatorial optimization problems on the graph are the core and classic problems in artificial intelligence and operations research. For example, the Vehicle Routing Problem (VRP) and Traveling Salesman Problem (TSP) are not only very interesting NP-hard problems but also have important significance for the actual transportation system. Traditional methods such as heuristics methods, precise algorithms, and solution solvers can already find approximate solutions on small-scale graphs. However, they are helpless for large-scale graphs and other problems with similar structures. Moreover, traditional methods often require artificially designed heuristic functions to assist decision-making. In recent years, more and more work has focused on the application of deep learning and reinforcement learning (RL) to learn heuristics, which allows us to learn the internal structure of the graph end-to-end and find the optimal path under the guidance of heuristic rules, but most of these still need manual assistance, and the RL method used has the problems of low sampling efficiency and small searchable space. In this paper, we propose a novel framework (called Alpha-T) based on AlphaZero, which does not require expert experience or label data but is trained through self-play. We divide the learning into two stages: in the first stage we employ graph attention network (GAT) and GRU to learn node representations and memory history trajectories, and in the second stage we employ Monte Carlo tree search (MCTS) and deep RL to search the solution space and train the model.

A parallel biological computing algorithm to solve the vertex coloring problem with polynomial time complexity

2021 ◽  
pp. 1-11
Author(s):  
Zhaocai Wang ◽  
Dangwei Wang ◽  
Xiaoguang Bao ◽  
Tunhua Wu
Keyword(s):  
Time Complexity ◽  
Optimization Problems ◽  
Combinatorial Problem ◽  
Vertex Coloring ◽  
Intelligent Computing ◽  
Coloring Problem ◽  
Combinatorial Optimization Problems ◽  
Computing Algorithm ◽  
Vertex Coloring Problem ◽  
Dna Algorithm

The vertex coloring problem is a well-known combinatorial problem that requires each vertex to be assigned a corresponding color so that the colors on adjacent vertices are different, and the total number of colors used is minimized. It is a famous NP-hard problem in graph theory. As of now, there is no effective algorithm to solve it. As a kind of intelligent computing algorithm, DNA computing has the advantages of high parallelism and high storage density, so it is widely used in solving classical combinatorial optimization problems. In this paper, we propose a new DNA algorithm that uses DNA molecular operations to solve the vertex coloring problem. For a simple n-vertex graph and k different kinds of color, we appropriately use DNA strands to indicate edges and vertices. Through basic biochemical reaction operations, the solution to the problem is obtained in the O (kn2) time complexity. Our proposed DNA algorithm is a new attempt and application for solving Nondeterministic Polynomial (NP) problem, and it provides clear evidence for the ability of DNA calculations to perform such difficult computational problems in the future.

Application of High-Performance Computing to Numerical Simulation of Human Movement

1995 ◽  
Vol 117 (1) ◽  
pp. 155-157 ◽  
Author(s):  
F. C. Anderson ◽  
J. M. Ziegler ◽  
M. G. Pandy ◽  
R. T. Whalen
Keyword(s):  
Computer Architecture ◽  
High Performance ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Human Movement ◽  
Parallel Machine ◽  
Optimal Controls ◽  
Processing Machine ◽  
Vector Processing

We have examined the feasibility of using massively-parallel and vector-processing supercomputers to solve large-scale optimization problems for human movement. Specifically, we compared the computational expense of determining the optimal controls for the single support phase of gait using a conventional serial machine (SGI Iris 4D25), a MIMD parallel machine (Intel iPSC/860), and a parallel-vector-processing machine (Cray Y-MP 8/864). With the human body modeled as a 14 degree-of-freedom linkage actuated by 46 musculotendinous units, computation of the optimal controls for gait could take up to 3 months of CPU time on the Iris. Both the Cray and the Intel are able to reduce this time to practical levels. The optimal solution for gait can be found with about 77 hours of CPU on the Cray and with about 88 hours of CPU on the Intel. Although the overall speeds of the Cray and the Intel were found to be similar, the unique capabilities of each machine are better suited to different portions of the computational algorithm used. The Intel was best suited to computing the derivatives of the performance criterion and the constraints whereas the Cray was best suited to parameter optimization of the controls. These results suggest that the ideal computer architecture for solving very large-scale optimal control problems is a hybrid system in which a vector-processing machine is integrated into the communication network of a MIMD parallel machine.

Space Contraction and Partition Algorithm for Combinatorial Optimization

2011 ◽  
Vol 421 ◽  
pp. 559-563
Author(s):  
Yong Chao Gao ◽  
Li Mei Liu ◽  
Heng Qian ◽  
Ding Wang
Keyword(s):  
Combinatorial Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Solution Space ◽  
Search Space ◽  
Small Scale ◽  
Optimal Solutions ◽  
Solution Quality ◽  
Intelligent Algorithms ◽  
Combinatorial Optimization Problems

The scale and complexity of search space are important factors deciding the solving difficulty of an optimization problem. The information of solution space may lead searching to optimal solutions. Based on this, an algorithm for combinatorial optimization is proposed. This algorithm makes use of the good solutions found by intelligent algorithms, contracts the search space and partitions it into one or several optimal regions by backbones of combinatorial optimization solutions. And optimization of small-scale problems is carried out in optimal regions. Statistical analysis is not necessary before or through the solving process in this algorithm, and solution information is used to estimate the landscape of search space, which enhances the speed of solving and solution quality. The algorithm breaks a new path for solving combinatorial optimization problems, and the results of experiments also testify its efficiency.

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.

Genetic Algorithm and Other Meta-Heuristics

2005 ◽  
pp. 144-173 ◽  
Author(s):  
Bernard K.S. Cheung
Keyword(s):  
Genetic Algorithm ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Schema Theory ◽  
Heuristic Methods ◽  
Optimal Solutions ◽  
Corporate Globalization ◽  
Global Optimal ◽  
Mutation And Selection

Genetic algorithms have been applied in solving various types of large-scale, NP-hard optimization problems. Many researchers have been investigating its global convergence properties using Schema Theory, Markov Chain, etc. A more realistic approach, however, is to estimate the probability of success in finding the global optimal solution within a prescribed number of generations under some function landscapes. Further investigation reveals that its inherent weaknesses that affect its performance can be remedied, while its efficiency can be significantly enhanced through the design of an adaptive scheme that integrates the crossover, mutation and selection operations. The advance of Information Technology and the extensive corporate globalization create great challenges for the solution of modern supply chain models that become more and more complex and size formidable. Meta-heuristic methods have to be employed to obtain near optimal solutions. Recently, a genetic algorithm has been reported to solve these problems satisfactorily and there are reasons for this.

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.

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