새로운 메타 휴리스틱 최적화 알고리즘의 개발: Exponential Bandwidth Harmony Search with Centralized Global Search

김영남,이의훈 한국산학기술학회 2020 한국산학기술학회논문지 Vol.21 No.2

An Exponential Bandwidth Harmony Search with Centralized Global Search (EBHS-CGS) was developed to enhance the performance of a Harmony Search (HS). EBHS-CGS added two methods to improve the performance of HS. The first method is an improvement of bandwidth (bw) that enhances the local search. This method replaces the existing bw with an exponential bw and reduces the bw value as the iteration proceeds. This form of bw allows for an accurate local search, which enables the algorithm to obtain more accurate values. The second method is to reduce the search range for an efficient global search. This method reduces the search space by considering the best decision variable in Harmony Memory (HM). This process is carried out separately from the global search of the HS by the new parameter, Centralized Global Search Rate (CGSR). The reduced search space enables an effective global search, which improves the performance of the algorithm. The proposed algorithm was applied to a representative optimization problem (math and engineering), and the results of the application were compared with the HS and better Improved Harmony Search (IHS). 본 연구에서는 기존의 Harmony Search(HS)의 성능을 강화한 Exponential Bandwidth Harmony Search with Centralized Global Search(EBHS-CGS)를 개발하였다. EBHS-CGS는 HS의 성능 강화를 위해 총 두 가지 방법을 추가하였다. 첫 번째 방법은 지역탐색을 강화하기 위한 Bandwidth(bw) 개량방안이다. 이 방법은 기존 bw를 지수형태의 bw로 대체하여 적용함으로써 반복시산이 진행되면서 bw값을 줄인다. 이러한 형태의 bw는 정밀한 지역탐색을 가능하고, 이를 통해 알고리즘은 더욱 정밀한 값을 구할 수 있다. 두 번째 방법은 효과적인 전역탐색을 위한 탐색범위 축소이다. 이 방법은 Harmony Memory(HM) 내에서 가장 좋은 결정변수를 고려하여 탐색범위를 축소한다. 이를 Centralized Global Search(CGS)라 하며, 이 과정은 새로운 매개변수 Centralized Global Search Rate(CGSR)에 의해 HS의 전역탐색과는 별도로 진행된다. 축소된 탐색범위는 효과적인 전역탐색을 가능하게 하며, 이를 통해 알고리즘의 성능이 향상된다. EBHS-CGS를 대표적인 최적화 문제(수학 및 공학 분야)에 적용하고, 그 결과를 HS와 Improved Harmony Search(IHS)와 비교하여 제시하였다.

Harmony Search 알고리즘의 수렴성 개선에 관한 연구

이상경(SangKyung Lee),고광은(Kwang-Enu Ko),심귀보(Kwee-Bo Sim) 한국지능시스템학회 2011 한국지능시스템학회논문지 Vol.21 No.3

복잡해진 최적화문제를 전통적인 방법보다 효율적으로 해결하기위해 유전알고리즘이나 개미군집화, 하모니서치알고리즘과 같은 다양한 메타휴리스틱이 개발되었다. 그 중에서 하모니 서치알고리즘이 다른 메타휴리스틱알고리즘보다 좋은 결과를 보이고 있다. 하모니 서치 알고리즘은 음악을 작곡할 때 아름다운 소리를 내는 하모니를 찾는 과정을 모방했다. 성능은 하모니 메모리에서 선택하는 비율인 HMCR값과 하모니 메모리에서 선택된 값의 조정 비율을 결정하는 PAR값에 따라 달라지는 것으로 알려져 있다. 다르게 말하면 두 변수의 기반이 되는 하모니 메모리의 사용방법의 문제로 볼 수 있다. 본 논문은 설정한 기간 동안 더 좋은 최적해를 찾지 못할 경우 하모니 메모리의 일부를 좋은 하모니로 구성되게 수정하는 방법을 제안했다. 테스트 함수를 이용한 검증 실험결과에서 하모니 메모리를 수정할 경우 정확도 변화가 적어 신뢰성 있는 정확도를 보였으며, Iteration이 짧더라도 최적값에 근접한 값을 찾았다. In order to solve a complex optimization problem more efficiently than traditional approaches, various meta-heuristic algorithms such as genetic algorithm, ant-colony algorithm, and harmony search algorithm have been extensively researched. Compared with other meta-heuristic algorithm, harmony search algorithm shows a better result to resolve the complex optimization issues. Harmony search algorithm is inspired by the improvision process of musician for most suitable harmony. In general, the performance of harmony search algorithm is determined by the value of harmony memory considering rate, and pitch adjust rate. In this paper, modified harmony search algorithm is proposed in order to derive best harmony. If the optimal solution of a specific problem can not be found for a certain period of time, a part of original harmony memory is updated as the selected suitable harmonies. Experimental results using test function demonstrate that the updated harmony memory can induce the approximation of reliable optimal solution in the short iteration, because of a few change of fitness.

Advanced nonlinear Muskingum model incorporating lateral flow를 위한 exponential bandwidth harmony search with centralized global search의 적용

김영남,이의훈 한국수자원학회 2020 한국수자원학회논문집 Vol.53 No.8

Muskingum, a hydrologic channel flood routing, is a method of predicting outflow by using the relationship between inflow, outflow, and storage. As many studies for Muskingum model were suggested, parameters were gradually increased and the calculation process was complicated by many parameters. To solve this problem, an optimization algorithm was applied to the parameter estimation of Muskingum model. This study applied the Advanced Nonlinear Muskingum Model considering continuous flow (ANLMM-L) to Wilson flood data and Sutculer flood data and compared results of the Linear Nonsingum Model incorporating Lateral flow (LMM-L), and Kinematic Wave Model (KWM). The Sum of Squares (SSQ) was used as an index for comparing simulated and observed results. Exponential Bandwidth Harmony Search with Centralized Global Search (EBHS-CGS) was applied to the parameter estimation of ANLMM-L. In Wilson flood data, ANLMM-L showed more accurate results than LMM-L. In the Sutculer flood data, ANLMM-L showed better results than KWM, but SSQ was larger than in the case of Wilson flood data because the flow rate of Sutculer flood data is large. EBHS-CGS could be appplied to be appplicable to various water resources engineering problems as well as Muskingum flood routing in this study. 하도홍수추적을 위한 수문학적 방법인 머스킹검 방법은 유입량, 유출량 그리고 저류량의 관계를 활용하여 유출량을 예측하는 방법이다. 머스킹검 방법에 관한 많은 연구가 진행되면서 필요한 매개변수들은 점점 늘어나게 되었고, 많은 매개변수로 인해 계산과정이 복잡해졌다. 이러한 문제를 해결하기 위해 최적화 알고리즘을 머스킹검 방법의 매개변수 산정에 적용하였다. 본 연구는 Advanced Nonlinear Muskingum Model considering continuous flow (ANLMM-L)를 Wilson 홍수자료와 Sutculer 홍수자료에 적용하여 Linear Munsingum Model incorporating Lateral flow (LMM-L)과 Kinematic Wave Model (KWM)의 결과와 비교하였다. 관측 유출량과 모의 유출량과의 비교를 위한 지표로 Sum of Squares (SSQ)를 사용하였다. Exponential Bandwidth Harmony Search with Centralized Global Search (EBHS-CGS)가 ANLMM-L의 매개변수 산정에 적용되었다. Wilson 홍수자료에 적용한 결과 LMM-L보다 ANLMM-L이 정확한 결과를 나타냈다. Sutculer 홍수자료에서는 ANLMM-L이 KWM보다 좋은 결과를 보이긴 했으나, Sutculer 홍수자료의 유량이 크기 때문에 Wilson 홍수자료의 경우에 비해 SSQ가 크게 나타났다. EBHS-CGS는 본 연구에서 적용한 머스킹검 홍수추적뿐만 아니라 다양한 수자원 공학 문제에 적용할 수 있을 것이다.

대청댐 유입량 예측을 위한 Adaptive Moments와 Improved Harmony Search의 결합을 이용한 다층퍼셉트론 성능향상

이원진,이의훈 한국수자원학회 2023 한국수자원학회논문집 Vol.56 No.1

High-reliability prediction of dam inflow is necessary for efficient dam operation. Recently, studies were conducted to predict the inflow of dams using Multi Layer Perceptron (MLP). Existing studies used the Gradient Descent (GD)-based optimizer as the optimizer among MLP operators to find the optimal correlation between data. However, the GD-based optimizers have disadvantages in that the prediction performance is deteriorated due to the possibility of convergence to the local optimal value and the absence of storage space. This study improved the shortcomings of the GD-based optimizer by developing Adaptive moments combined with Improved Harmony Search (AdamIHS), which combines Adaptive moments among GD-based optimizers and Improved Harmony Search (IHS). In order to evaluate the learning and prediction performance of MLP using AdamIHS, Daecheong Dam inflow was learned and predicted and compared with the learning and prediction performance of MLP using GD-based optimizer. Comparing the learning results, the Mean Squared Error (MSE) of MLP, which is 5 hidden layers using AdamIHS, was the lowest at 11,577. Comparing the prediction results, the average MSE of MLP, which is one hidden layer using AdamIHS, was the lowest at 413,262. Using AdamIHS developed in this study, it will be possible to show improved prediction performance in various fields.

Partial Transmit Sequence Optimization Using Improved Harmony Search Algorithm for PAPR Reduction in OFDM

Mangal Singh,Sarat Kumar Patra 한국전자통신연구원 2017 ETRI Journal Vol.39 No.6

This paper considers the use of the Partial Transmit Sequence (PTS) technique to reduce the Peak-to-Average Power Ratio (PAPR) of an Orthogonal Frequency Division Multiplexing signal in wireless communication systems. Search complexity is very high in the traditional PTS scheme because it involves an extensive random search over all combinations of allowed phase vectors, and it increases exponentially with the number of phase vectors. In this paper, a suboptimal metaheuristic algorithm for phase optimization based on an improved harmony search (IHS) is applied to explore the optimal combination of phase vectors that provides improved performance compared with existing evolutionary algorithms such as the harmony search algorithm and firefly algorithm. IHS enhances the accuracy and convergence rate of the conventional algorithms with very few parameters to adjust. Simulation results show that an improved harmony search-based PTS algorithm can achieve a significant reduction in PAPR using a simple network structure compared with conventional algorithms.

A New Image Clustering Method Based on the Fuzzy Harmony Search Algorithm and Fourier Transform

( Ibtissem Bekkouche ),( Hadria Fizazi ) 한국정보처리학회 2016 Journal of information processing systems Vol.12 No.4

In the conventional clustering algorithms, an object could be assigned to only one group. However, this is sometimes not the case in reality, there are cases where the data do not belong to one group. As against, the fuzzy clustering takes into consideration the degree of fuzzy membership of each pixel relative to different classes. In order to overcome some shortcoming with traditional clustering methods, such as slow convergence and their sensitivity to initialization values, we have used the Harmony Search algorithm. It is based on the population metaheuristic algorithm, imitating the musical improvisation process. The major thrust of this algorithm lies in its ability to integrate the key components of population-based methods and local search-based methods in a simple optimization model. We propose in this paper a new unsupervised clustering method called the Fuzzy Harmony Search-Fourier Transform (FHS-FT). It is based on hybridization fuzzy clustering and the harmony search algorithm to increase its exploitation process and to further improve the generated solution, while the Fourier transform to increase the size of the image`s data. The results show that the proposed method is able to provide viable solutions as compared to previous work.

4성부 화성학 기초학습을 위한 컴퓨팅 구현과 화성학 규칙에 관한 연구

김동삼,박종원,송무경,김준호,윤창호 한국음악교육공학회 2020 음악교육공학 Vol.0 No.44

The goal of this study is to explicate a series of process relevant to the development of online-based harmony learning contents and to verify the validity of outputs by activating the automatic music composition algorithm based on artificial intelligence(AI) technology. Automatic music composition is a field that many researchers who study AI become interested in; and diverse attempts to adapt harmony to automatic music composition have been ceaselessly made and still ongoing. In this study, we took Monte Carlo Tree Search and had AI as an objective evaluator evaluate a learner’s solution using the rules and weights for the learning theory of harmony. In addition, we presented an exemplar to the various plausible solutions using artificial intelligence techniques that automatically generate music in accordance with the theory of harmony. The study has designed three types of voice-leading exercises in the four-voice setting: one fills out the lower three voices against a given soprano; one writes out the upper three against a given bass; and one provides the outer voices against given inner ones. The study has shown that the automatic music composition algorithm took appropriate recommendations from AI via MCTS and thus generated legitimate instances of harmony and voice leading and that scores assigned to the harmony rules successfully guide exemplars conforming to the rules. This study has limited the scope of harmony rules for beginners: the appropriate rules were singled out and defined; and then the algorithm was developed to enable automatic music composition according to these rules. This algorithm and learning methodology are expected to be of a great help in online harmony learning. 본 연구는 인공지능을 활용한 자동 음악 작곡 알고리즘을 도입하여 온라인 기반의 화성학 교수-학습 콘텐츠 개발과 관련된 일련의 과정을 설명하고 그 결과를 검증하는 데 목적이 있다. 자동 음악 작곡은 인공지능을 연구하는 많은 연구자들이 관심을 갖는 분야로서 자동 음악 작곡에 화성학 이론을 도입하려는 시도는 오랜 동안 이루어졌으며 여전히 진행 중이다. 본 연구는 몬테카를로 트리 탐색(Monte Carlo Tree Search; 이하 MCTS)을 활용하여 객관적 평정자로서의 인공지능이 기 학습했던 화성학 규칙과 그 규칙에 대한 가중치를 적용하여 학습자의 4성부 기반 화성풀이를 평가하도록 기획하였다. 또한, 화성학 문항에 대한 모범풀이와 적절한 피드백을 제시하도록 하였다. 본 연구는 소프라노 선율에 하3성 채우기, 베이스 선율에 상3성 채우기, 그리고 외성에 내성 채우기에 이르는 세 가지 유형의 연습문제를 설계하였는데, MCTS를 활용해 화음 선택과 성부진행의 경로에 대한 추천을 받음으로써 적법한 성부진행을 구현하였다. 화성 및 성부진행 규칙에 맞는 진행에 부여된 가점이 모범답안을 유도함을 확인하였다. 본 연구는 화성학의 범위를 초급으로 규정하고, 이에 따른 규칙을 추출 및 정의하여, 이 규칙에 따라 자동으로 음악 작곡을 할 수 있도록 알고리즘을 개발하였다. 알고리즘 및 이를 활용한 화성학 교수-학습 방법론은 온라인 화성학 교육에 큰 도움이 될 것으로 기대된다.

Mine blast harmony search: A new hybrid optimization method for improving exploration and exploitation capabilities

Sadollah, Ali,Sayyaadi, Hassan,Yoo, Do Guen,Lee, Ho Min,Kim, Joong Hoon Elsevier 2018 Applied soft computing Vol.68 No.-

<P><B>Abstract</B></P> <P>This paper proposes a hybrid optimization method that combines the power of the harmony search (HS) with the mine blast algorithm (MBA). The resulting mine blast harmony search (MBHS) uses MBA for exploration and HS for exploitation. The HS is inspired by the improvisation process of musicians, while the MBA is derived based on explosion of landmines. The HS used in the hybrid algorithm is an improved version, introducing a new concept for the harmony memory size, while the MBA is modified in terms of its mathematical formulation. Several numerical problems and benchmarks with many design variables and constraints are used to validate MBHS, and the optimization results are compared with those from various algorithms in the literature. The numerical results show that the proposed hybrid method provides better exploitation ability (especially in the final iterations) and enjoys mature convergence to the optimum solution.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Improving exploration and exploitation capabilities of the HS and MBA. </LI> <LI> Mine Blast Harmony Search (MBHS) enjoys performances of the MBA and HS. </LI> <LI> MBHS is applied for solving several benchmarks and engineering problems. </LI> <LI> MBHS offers cheaper design cost and the minimum weights for reported problems. </LI> <LI> MBHS utilizes fast convergence and better exploitation ability of the MBA and HS. </LI> </UL> </P> <P><B>Graphical abstract</B></P> <P>[DISPLAY OMISSION]</P>

응용 및 융합 기술 : HS 알고리즘을 이용한 계단응답으로부터 FOPDT 모델 인식

이태봉 ( Tae-bong Lee ) 한국항행학회 2015 韓國航行學會論文誌 Vol.19 No.6

본 논문에서는 계단응답으로부터 시 지연을 갖는 선형 연속시스템을 식별하기 위해 HS 최적화 알고리즘을 적용에 관하여 연구하였다. 인식 모델은 1차 시 지연 모델 (FOPDT)로써, FOPDT은 많은 화학 공정과 HAVC 공정에 실효성이 있으며 PID 튜닝에도적합하다. 최근에 개발된 HS 알고리즘은 완벽한 하모니를 찾아가는 음악적 과정을 개념화 한 것이다. 수학을 기반으로 하는 전통적 기법과 달리 HS는 확률적인 방법을 사용하므로 미분과 같은 수학적 접근을 필요로 하지 않는다. 제시된 인식 방법의 효과를 입증하기 위해 많은 수치 예를 수행하여 결과를 제시하였다. This paper presents an application of heuristic harmony search (HS) optimization algorithm for the identification of linear continuous time.delay system from step response. Identification model is first-order plus dead time (FOPDT), which describes a linear monotonic process quite well in most chemical processes and HAVC process and is often sufficient for PID controller tuning. This recently developed HS algorithm is conceptualized using the musical process of searching for a perfect state of harmony. It uses a stochastic random search instead of a gradient search so that derivative information is unnecessary. The effectiveness of the identification method has been demonstrated through a number of simulation examples.

최대 반복 횟수 없이 튜닝에 기반을 둔 HS 최적화 구현

이태봉(Tae-bong Lee) 대한전기학회 2018 전기학회논문지 P Vol.67 No.3

Harmony search (HS) is a relatively recently developed meta-heuristic optimization method imitating the music improvisation process where musicians improvise their instruments’ pitches searching for a perfect state of harmony. In the conventional HS algorithm, it is necessary to determine the maximum number of iterations with some algorithm parameters. However, there is no criterion for determining the number of iterations, which is a very difficult problem. To solve this problem, a new method is proposed to perform the algorithm without setting the maximum number of iterations in this paper. The new method allows the algorithm to be performed until the desired tuning is achieved. To do this, a new variable bandwidth is introduced. In addition, the types and probability of harmonies composed of variables is analyzed to help to decide the value of HMCR. The performance of the proposed method is investigated and compared with classical HS. The experiments conducted show that the new method generally outperformed conventional HS when applied to seven benchmark problems.