Random coloring method in the combinatorial problem of Erdős and Lovász

2011 ◽  
Vol 40 (2) ◽  
pp. 227-253 ◽  
Author(s):  
Dmitry A. Shabanov
Keyword(s):  
Combinatorial Problem ◽  
Random Coloring

A Combinatorial Problem Which Is Complete in Polynomial Space

1976 ◽  
Vol 23 (4) ◽  
pp. 710-719 ◽  
Author(s):  
S. Even ◽  
R. E. Tarjan
Keyword(s):  
Combinatorial Problem ◽  
Polynomial Space

scholarly journals Feature Selection and Parameter Optimization of Support Vector Machines Based on Modified Artificial Fish Swarm Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Kuan-Cheng Lin ◽  
Sih-Yang Chen ◽  
Jason C. Hung
Keyword(s):  
Feature Selection ◽  
Parameter Optimization ◽  
Combinatorial Problem ◽  
Combinatorial Problems ◽  
Support Vector ◽  
Local Optimum ◽  
Artificial Fish Swarm Algorithm ◽  
Swarm Algorithms ◽  
Artificial Fish Swarm ◽  
Information And Communication

Rapid advances in information and communication technology have made ubiquitous computing and the Internet of Things popular and practicable. These applications create enormous volumes of data, which are available for analysis and classification as an aid to decision-making. Among the classification methods used to deal with big data, feature selection has proven particularly effective. One common approach involves searching through a subset of the features that are the most relevant to the topic or represent the most accurate description of the dataset. Unfortunately, searching through this kind of subset is a combinatorial problem that can be very time consuming. Meaheuristic algorithms are commonly used to facilitate the selection of features. The artificial fish swarm algorithm (AFSA) employs the intelligence underlying fish swarming behavior as a means to overcome optimization of combinatorial problems. AFSA has proven highly successful in a diversity of applications; however, there remain shortcomings, such as the likelihood of falling into a local optimum and a lack of multiplicity. This study proposes a modified AFSA (MAFSA) to improve feature selection and parameter optimization for support vector machine classifiers. Experiment results demonstrate the superiority of MAFSA in classification accuracy using subsets with fewer features for given UCI datasets, compared to the original FASA.

scholarly journals Actor-critic learning-based energy optimization for UAV access and backhaul networks

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Yaxiong Yuan ◽  
Lei Lei ◽  
Thang X. Vu ◽  
Symeon Chatzinotas ◽  
Sumei Sun ◽  
...  
Keyword(s):  
Power Allocation ◽  
Heuristic Algorithms ◽  
Piecewise Linear ◽  
Access Network ◽  
Computation Time ◽  
Combinatorial Problem ◽  
Base Station ◽  
Piecewise Linear Approximation ◽  
Group Scheduling ◽  
User Group

AbstractIn unmanned aerial vehicle (UAV)-assisted networks, UAV acts as an aerial base station which acquires the requested data via backhaul link and then serves ground users (GUs) through an access network. In this paper, we investigate an energy minimization problem with a limited power supply for both backhaul and access links. The difficulties for solving such a non-convex and combinatorial problem lie at the high computational complexity/time. In solution development, we consider the approaches from both actor-critic deep reinforcement learning (AC-DRL) and optimization perspectives. First, two offline non-learning algorithms, i.e., an optimal and a heuristic algorithms, based on piecewise linear approximation and relaxation are developed as benchmarks. Second, toward real-time decision-making, we improve the conventional AC-DRL and propose two learning schemes: AC-based user group scheduling and backhaul power allocation (ACGP), and joint AC-based user group scheduling and optimization-based backhaul power allocation (ACGOP). Numerical results show that the computation time of both ACGP and ACGOP is reduced tenfold to hundredfold compared to the offline approaches, and ACGOP is better than ACGP in energy savings. The results also verify the superiority of proposed learning solutions in terms of guaranteeing the feasibility and minimizing the system energy compared to the conventional AC-DRL.

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.

Optimization of Restoration Paths of Power System after Blackout

2013 ◽  
Vol 347-350 ◽  
pp. 1467-1472
Author(s):  
Wen Wei Huang ◽  
Gang Yao ◽  
Xiao Yan Qiu ◽  
Nian Liu ◽  
Guang Tang Chen
Keyword(s):  
Power System ◽  
Transmission Lines ◽  
Reactive Power ◽  
Minimum Spanning Tree ◽  
Operation Time ◽  
Combinatorial Problem ◽  
Weather Conditions ◽  
Recovery Process ◽  
Point Of View ◽  
Improved Genetic Algorithm

Optimization of restoration paths of power system after blackout is a multi-stage, multi-target, multi-variable combinatorial problem in the power system restoration. This paper presents a reasonable model and effectually method. The proposed model is considered as a typical partial minimum spanning tree problem from the mathematical point of view which considering all kinds of constraints. Improved data envelopment analysis (DEA) was used to get the weight which considering line charging reactive power, weather conditions, operation time and betweenness of transmission lines. The improved genetic algorithm method is employed to solve this problem. Finally, an example is given which proves the strategy of the line restoration can effectively handle the uncertainty of the system recovery process, to guarantee the system successfully restored after the catastrophic accidents.

On a Vector Space Representation in Genetic Algorithms for Sensor Scheduling in Wireless Sensor Networks

2014 ◽  
Vol 22 (3) ◽  
pp. 361-403 ◽  
Author(s):  
F. V. C. Martins ◽  
E. G. Carrano ◽  
E. F. Wanner ◽  
R. H. C. Takahashi ◽  
G. R. Mateus ◽  
...  
Keyword(s):  
Fitness Landscape ◽  
Combinatorial Problem ◽  
Wireless Sensor ◽  
Space Representation ◽  
Network Dynamic ◽  
Decision Variable ◽  
Exact Methods ◽  
Variable Space ◽  
Combinatorial Space ◽  
Evolutionary Operators

Recent works raised the hypothesis that the assignment of a geometry to the decision variable space of a combinatorial problem could be useful both for providing meaningful descriptions of the fitness landscape and for supporting the systematic construction of evolutionary operators (the geometric operators) that make a consistent usage of the space geometric properties in the search for problem optima. This paper introduces some new geometric operators that constitute the realization of searches along the combinatorial space versions of the geometric entities descent directions and subspaces. The new geometric operators are stated in the specific context of the wireless sensor network dynamic coverage and connectivity problem (WSN-DCCP). A genetic algorithm (GA) is developed for the WSN-DCCP using the proposed operators, being compared with a formulation based on integer linear programming (ILP) which is solved with exact methods. That ILP formulation adopts a proxy objective function based on the minimization of energy consumption in the network, in order to approximate the objective of network lifetime maximization, and a greedy approach for dealing with the system's dynamics. To the authors’ knowledge, the proposed GA is the first algorithm to outperform the lifetime of networks as synthesized by the ILP formulation, also running in much smaller computational times for large instances.

A Method to Define the Best Weld Sequence Using a Limited Number of Welding Simulation Analysis

2015 ◽  
Author(s):  
Mahyar Asadi ◽  
Ghazi Alsoruji
Keyword(s):  
Simulation Model ◽  
Surrogate Model ◽  
Simulation Analysis ◽  
Combinatorial Problem ◽  
Fem Analysis ◽  
Simulation Models ◽  
Computational Time ◽  
Optimal Sequence ◽  
Welded Structure ◽  
Welding Sequence

Weld sequence optimization, which is determining the best (and worst) welding sequence for welding work pieces, is a very common problem in welding design. The solution for such a combinatorial problem is limited by available resources. Although there are fast simulation models that support sequencing design, still it takes long because of many possible combinations, e.g. millions in a welded structure involving 10 passes. It is not feasible to choose the optimal sequence by evaluating all possible combinations, therefore this paper employs surrogate modeling that partially explores the design space and constructs an approximation model from some combinations of solutions of the expensive simulation model to mimic the behavior of the simulation model as closely as possible but at a much lower computational time and cost. This surrogate model, then, could be used to approximate the behavior of the other combinations and to find the best (and worst) sequence in terms of distortion. The technique is developed and tested on a simple panel structure with 4 weld passes, but essentially can be generalized to many weld passes. A comparison between the results of the surrogate model and the full transient FEM analysis all possible combinations shows the accuracy of the algorithm/model.

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