Keunhee Han

Estimation of the scale parameter of the Rayleigh distribution with multiply type–II censored sample

Based on a multiply type-II censored sample, the maximum likelihood estimator (MLE) and Bayes estimator for the scale parameter and the reliability function of the Rayleigh distribution are derived. However, since the MLE does not exist an explicit form, an approximate MLE which is the maximizer of an approximate likelihood function will be given. The comparisons among estimators are investigated through Monte Carlo simulations. An illustrative example with the real data concerning the 23 ball bearing in the life test is presented.

Solving L(2,1)-labeling Problem of Graphs using Genetic Algorithms

L(2,1)-labeling of a graph G is a function f: V(G) → {0, 1, 2, ...} such that |f(u) – f(v)| ≥ 2 when d(u, v) = 1 and |f(u) – f(v)| ≥ 1 when d(u, v) = 2. L(2,1)-labeling number of G, denoted by λ(G), is the smallest number m such that G has an L(2,1)-labeling with no label greater than m. Since this problem has been proved to be NP-complete, in this article, we develop genetic algorithms for L(2,1)-labeling problem and show that the suggested genetic algorithm peforms very efficiently by applying the algorithms to the class of graphs with known optimum values.

Comparison of prediction performance using statistical postprocessing methods

As the 2018 Winter Olympics are to be held in Pyeongchang, both general weather information on Pyeongchang and specific weather information on this region, which can affect game operation and athletic performance, are required. An ensemble prediction system has been applied to provide more accurate weather information, but it has bias and dispersion due to the limitations and uncertainty of its model. In this study, homogeneous and nonhomogeneous regression models as well as Bayesian model averaging (BMA) were used to reduce the bias and dispersion existing in ensemble prediction and to provide probabilistic forecast. Prior to applying the prediction methods, reliability of the ensemble forecasts was tested by using a rank histogram and a residualquantile-quantile plot to identify the ensemble forecasts and the corresponding verifications. The ensemble forecasts had a consistent positive bias, indicating over-forecasting, and were under-dispersed. To correct such biases, statistical post-processing methods were applied using fixed and sliding windows. The prediction skills of methods were compared by using the mean absolute error, root mean square error, continuous ranked probability score, and continuous ranked probability skill score. Under the fixed window, BMA exhibited better prediction skill than the other methods in most observation station. Under the sliding window, on the other hand, homogeneous and non-homogeneous regression models with positive regression coefficients exhibited better prediction skill than BMA. In particular, the homogeneous regression model with positive regression coefficients exhibited the best prediction skill.

Comparison of Statistical Post-Processing Methods for Probabilistic Wind Speed Forecasting

In this study, the statistical post-processing methods that include bias-corrected and probabilistic forecasts of wind speed measured in PyeongChang, which is scheduled to host the 2018 Winter Olympics, are compared and analyzed to provide more accurate weather information. The six post-processing methods used in this study are as follows: mean bias-corrected forecast, mean and variance bias-corrected forecast, decaying averaging forecast, mean absolute bias-corrected forecast, and the alternative implementations of ensemble model output statistics (EMOS) and Bayesian model averaging (BMA) models, which are EMOS and BMA exchangeable models by assuming exchangeable ensemble members and simplified version of EMOS and BMA models. Observations for wind speed were obtained from the 26 stations in PyeongChang and 51 ensemble member forecasts derived from the European Centre for Medium-Range Weather Forecasts (ECMWF Directorate, 2012) that were obtained between 1 May 2013 and 18 March 2016. Prior to applying the post-processing methods, reliability analysis was conducted by using rank histograms to identify the statistical consistency of ensemble forecast and corresponding observations. Based on the results of our study, we found that the prediction skills of probabilistic forecasts of EMOS and BMA models were superior to the biascorrected forecasts in terms of deterministic prediction, whereas in probabilistic prediction, BMA models showed better prediction skill than EMOS. Even though the simplified version of BMA model exhibited best prediction skill among the mentioned six methods, the results showed that the differences of prediction skills between the versions of EMOS and BMA were negligible.

A Probabilistic Forecast of Wind Speed using Bayesian Model Averaging

This paper used the Bayesian model averaging (BMA) with gamma distribution that takes the form of probability density functions to calibrate probabilistic forecasts of wind speed. We considered the alternative implementation of BMA, which was BMA gamma exchangeable model. This method was applied for forecasting of wind speed over Pyeongchang area using 51 members of the Ensemble Prediction System for Global (EPSG). The performances were evaluated by rank histogram, means absolute error, root mean square error, continuous ranked probability score and skill score. The results showed that BMA gamma exchangeable models performed better in forecasting wind speed, compared to the raw ensemble and ensemble mean.

A Probabilistic Forecast of Wind Speed using Truncated Normal Distribution

This paper applied the ensemble model output statistics (EMOS) with truncated normal distribution, which are easy to implement postprocessing techniques, to calibrate probabilistic forecasts of wind speed that take the form of probability density functions. We also considered the alternative implementations of EMOS, which were EMOS exchangeable model and reduced EMOS model. These techniques were applied to the forecasts of wind speed over Pyeongchang area using 51 members of the Ensemble Prediction System for Global (EPSG). The performances were evaluated by rank histogram, mean absolute error, root mean square error and continuous ranked probability score. The results showed that EMOS models with truncated normal distribution performed better than the raw ensemble and ensemble mean. Especially, the reduced EMOS model exhibited better prediction skill than EMOS exchangeable model in most stations of study area.

Study for the Maximum Bipartite Subgraph Problem Using GRASP + Tabu Search

ABSTRACT Let G = (V, E) be a graph. Maximum Bipartite Subgraph Problem is to convert a graph G into a bipartite graph by removing minimum number of edges. This problem belongs to NP-complete; hence, in this research, we are suggesting a new metaheuristic algorithm which combines Tabu search and GRASP.Keywords:Graph, Bipartite Graph, Maximum Bipartite Subgraph Problem, Tabu Search, GRASP Maximum Bipartite Subgraph 문제를 위한 GRASP + Tabu Search 알고리즘 연구 한 근 희 † ⋅김 찬 수 †† 요 약 G = (V, E) 를 그래프라 하자. Maximum Bipartite Subgraph 문제는 주어진 그래프 G로부터 최소 개수의 간선을 제거함으로써 G 를 이분그래프로 변환시키는 문제이며 결합 최적화 문제들 중 대표적인 문제들 중의 하나로 알려 져 있다. 본 문제는 NP-complete 계열에 포함되는 문제로서 본 연구에서는 Tabu Search 및 GRASP 등을 조합한 새로운 메타휴리스틱 알고리즘을 제시하고자 한다. 키워드:그래프, 이분 그래프, Maximum Bipartite Subgraph 문제, Tabu Search, GRASP KIPS Tr. Software and Data Eng.Vol.3, No.3 pp.119~124 pISSN: 2287 - 5905 1. 서 론 1) G = (V, E) 를 정점 집합 V = {1, 2, ..., n} 및 간선 집합 E ⊆ V x V로 구성되는 단순 무 방향 그래프라 하고 |V| = n 및 |E| = m 이라 하자. 간선 e ∈ E 에 대하여 e 의 양 끝점을 u및 v라 하면 e = uv로 표기한다. X ⊆ V 라 하고 E(X) = {uv| u, v ∈ E} 라 하자. 만일 u, v ∈ X에 대하여 uv ∉ E라면 X 를 independent set이라 하며, 만일 V가 두 개의 independent set 인 X 및 Y (X ≠ O, Y ≠ O) 로 분할될 수 있다면 G를 이분 그래프 (Bipartite Graph) 라 하며 G = (X ∩ Y, E)로 표기된다. 이때 X 및 Y를 이분 그래프인 G 의 partite set 이라 한다. 만일 G가 이분 그래프가 아니라면 G로부터 적절한 간선들을 제거함으로써 G를 이분 그래프로 변환할 수 있다. 주

Solving Minimum Weight Triangulation Problem with Genetic Algorithm

Minimum Weight Triangulation (MWT) 는 최적화 문제로서 주어진 그래프에 대한 최소 무게 삼각화를 계산하는 문제이다. 본 문제는 많은 다른 그래프 문제들처럼 일반 그래프에 대하여 NP-hard 계열의 문제로 알려져 있으며 지금까지 simulated annealing 및 유전 알고리즘 등 heuristic algorithm 들이 제시되어 왔다. 본 논문에서는 MWT 문제에 대하여 GA-FF 라 불리우는 새로운 유전 알고리즘을 제시하며 또한 그성능이 기존의 유전 알고리즘보다 더욱 효율적임을 보인다. 【Minimum Weight Triangulation (MWT) problem is an optimization problem searching for the triangulation of a given graph with minimum weight. Like many other graph problems this problem is also known to be NP-hard for general graphs. Several heuristic algorithms have been proposed for this problem including simulated annealing and genetic algorithm. In this paper, we propose a new genetic algorithm called GA-FF and show that the performance of the proposed genetic algorithm outperforms the previous one.】

Applying Genetic Algorithm to the Minimum Vertex Cover Problem

G = (V, E) 를 단순 무방향성 그래프라 하자. Minimum Vertex Cover (MVC) 문제는 C 를 V 의 부분 집합이라 할 때 모든 간선들이 C 내의 최소 한 개 정점과 인접하게 되는 최소 집합 C 를 계산하는 것이다. 다른 많은 그래프 이론 문제와 마찬가지로 본 문제도 NP-hard 문제임이 증명되었다. 본 논문에서는 MVC 문제를 위한 LeafGA 라는 새로운 유전 알고리즘을 제시하며 또한 제시된 알고리즘을 널리 알려 진 기준 그래프들에 적용함으로써 그 효용성을 보인다. 【Let G = (V, E) be a simple undirected graph. The Minimum Vertex Cover (MVC) problem is to find a minimum subset C of V such that for every edge, at least one of its endpoints should be included in C. Like many other graph theoretic problems this problem is also known to be NP-hard. In this paper, we propose a genetic algorithm called LeafGA for MVC problem and show the performance of the proposed algorithm by applying it to several published benchmark graphs.】