Pitch Adjustment Rate Research Articles

Seismic Reliability–Based Multiobjective Design of Water Distribution System: Sensitivity Analysis

AbstractThis study proposes a seismic reliability–based water distribution system (WDS) optimal design model that minimizes total cost and maximizes seismic reliability. Here, seismic reliability is defined as the ratio of the available quantity of water to the required demand under stochastic earthquake events. A new evaluation model is used to assess seismic reliability, while a multiobjective harmony search (MOHS) based on a ranking approach is used for optimization. The Anytown network was modified for the demonstration of the proposed method. First, this study performs the sensitivity analysis of MOHS parameter values [i.e., harmony search consideration rate (HMCR) and pitch adjustment rate (PAR)] to identify the best parameter set in a pipe-sizing problem of an Anytown network. Then, Pareto optimal solutions with three different tank configurations are obtained and compared with respect to the final Pareto fronts and the system designs. For the sensitivity analysis, it reveals that higher PAR and lo...

Harmony search based remodularization for object-oriented software systems

Software remodularization is always a key task in the field of software reengineering. In recent years, search-based optimization techniques have been considered as an effective method to handle software remodularization problems. Recently, Harmony Search (HS), a metaheuristic algorithm has gained wide attention and has been demonstrated to be effective and convenient to solve various science and engineering problems. The applicability and usefulness of HS algorithm has not been studied by any researcher till date to solve the software remodularization problem. This paper proposes a Harmony Search-Based Remodularization Algorithm (HSBRA) to solve the software remodularization problem for object-oriented software (OOS) systems. To do so, several key improvements have been put forward like an efficient encoding of harmony memory, initialization of harmony memory, an effective strategy for improvisation of a new harmony. In addition, a new fitness function that considers coupling, cohesion, package count index and package size index is developed. Four different variants of HSBRA (i.e., HSBRA1, HSBRA2, HSBRA3, and HSBRA4) based on linear and exponential changes in Harmony Memory Consideration Rate (HMCR) and Pitch Adjusting Rate (PAR) have been formulated. The proposed approach is tested over 8 problem instances and results are compared with both the population based (Genetic Algorithm - GA, Differential Evolution – DE, and Artificial Bee Colony - ABC) and single-solution based (Simulated Annealing - SA and Hill-Climbing - HC) algorithms. A Wilcoxon test is performed to assess the pair wise statistical performance of the algorithms. The results show that HSBRA outperforms SA, HC, and GA algorithms and performs better than ABC algorithms. Out of four variants of HSBRA, exponential change based variants of HSBRA perform better than linear change based variants.

Topology optimization scheme for dynamic stiffness problems using harmony search method

This paper suggests a new topology optimization scheme for natural frequency problems based on the harmony search (HS) method. The HS method is expected to be very effective since its topology optimization procedure is similar to the procedure for tuning the instruments found in an orchestra. To apply the HS method to dynamic topology optimization, an objective function is defined as a natural frequency, and the design domain is defined as harmony memory (HM) in the HS method. The harmony rate update rule is introduced to obtain a robust topology. Through a parametric study of the harmony memory considering rate (HMCR), pitch adjusting rate (PAR), and bandwidth (BW), the proper ranges of the search variables are determined and applied to numerical examples. Some examples are provided to examine the effectiveness of the HS method compared to the artificial bee colony algorithm (ABCA) in dynamic topology optimization. Properly selected parameters for the suggested algorithm with the harmony rate update rule provide a robust topology, a fast convergence rate and a stable optimization process. It can be effectively expanded to apply to shape and topological shape optimization algorithms.

Stacking sequence optimization for maximum buckling load of composite plates using harmony search algorithm

This paper presents the application of the harmony search algorithm (HSA) and some of its variants in the optimization of the stacking sequence of laminated composites. The optimization objective is to maximize the bucking load of a symmetric and balanced laminated plate. Performance and sensitivity to the parameters harmony memory size (HMS), harmony memory consideration rate (HMCR) and pitch adjusting rate (PAR) are determined based on the algorithm apparent reliability. A modified version of the pitch adjustment is proposed and its positive impact on the reliability is demonstrated. The best performance of the basic HSA is obtained using low PAR with high HMS and HMCR. The variants of HSA consider a linear variation of the pitch adjusting rate during the optimization. Increasing PAR reduce the HSA sensitivity to this parameter and lead to fast rise of reliability in the beginning of the optimization and high reliability at the end of the search. Decreasing PAR resulted in excellent reliability for long searches, but the chance to find a global optimum is drastically reduced for short optimizations. The last example demonstrate that HSA is more efficient than other metaheuristic methods, although it is less reliable than a special version of genetic algorithm.

A modified harmony search method for biclustering microarray gene expression data

Microarray experiments generate vast amounts of data, leading to new requirements and challenges for bioinformatics. The crucial step in considering gene expression data is to discover a group of genes that have similar patterns. Biclustering is a two-dimensional clustering problem where the genes and samples are grouped simultaneously. Latest research showed that biclustering has a great potential in finding marker genes that are associated with certain tissues or diseases. Here, we present an efficient biclustering algorithm called Modified Harmony Search (MHS) method. The MHS algorithm includes a step for generating the new solution by using levy flight. Levy flight increases the diversity of the solutions of harmony search (HS) algorithm and the Pitch Adjusting Rate (PAR) is changed dynamically to escape from local optima. To know the performance of the MHS, it is applied on various benchmark optimisation functions and the benchmark gene expression data sets. The experimental results show that the MHS outperforms HS in optimisation functions and biclustering problems. Also, this work determines the biological relevance of the biclusters with Gene Ontology in terms of function, process and component.

Fuzzy harmony search algorithm based optimal power flow for power system security enhancement

Abstract This paper proposes the integration of fuzzy logic system with harmony search algorithm (FHSA) to find the optimal solution for optimal power flow (OPF) problem in a power system. The objective of the method is to minimize the total fuel cost of thermal generating units having quadratic cost characteristics and severity index (SI). The generator active power, generator bus voltage magnitude, transformer taps, VAR of shunts and the reactance of thyristor controlled series capacitor (TCSC) are taken as the control variables. The adjustment of proposed algorithm parameters such as pitch adjustment rate (PAR) and bandwidth (BW) is done through fuzzy logic system (FLS). The effectiveness of the proposed method has been tested on the standard IEEE 30 bus, IEEE 57 bus and IEEE 118 bus systems in MATLAB environment and their results are compared with conventional harmony search algorithm (HSA) and other heuristic methods reported in the literature recently.

A self adaptive harmony search based functional link higher order ANN for non-linear data classification

In the data classification process involving higher order ANNs, it’s a herculean task to determine the optimal ANN classification model due to non-linear nature of real world datasets. To add to the woe, it is tedious to adjust the set of weights of ANNs by using appropriate learning algorithm to obtain better classification accuracy. In this paper, an improved variant of harmony search (HS), called self-adaptive harmony search (SAHS) along with gradient descent learning is used with functional link artificial neural network (FLANN) for the task of classification in data mining. Using its past experiences, SAHS adjusts the harmonies according to the maximum and minimum values in the current harmony memory. The powerful combination of this unique strategy of SAHS and searching capabilities of gradient descent search is used to obtain optimal set of weights for FLANN. The proposed method (SAHS–FLANN) is implemented in MATLAB and the results are contrasted with other alternatives (FLANN, GA based FLANN, PSO based FLANN, HS based FLANN, improved HS based FLANN and TLBO based FLANN). To illustrate its effectiveness, SAHS–FLANN is tested on various benchmark datasets from UCI machine learning repository by using 5-fold cross validation technique. Under the null-hypothesis, the proposed method is analyzed by using various statistical tests for statistical correctness of results. The performance of the SAHS–FLANN is found to be better and statistically significant in comparison with other alternatives. The SAHS–FLANN differs from HS–FLANN (HS based FLANN) by the elimination of constant parameters (bandwidth and pitch adjustment rate). Furthermore, it leads to the simplification of steps for the improvisation of weight-sets in IHS–FLANN (improved HS based FLANN) by incorporating adjustments of new weight-sets according to the weight-sets with maximum and minimum fitness.

Hybrid HS–random search algorithm considering ensemble and pitch violation for unit commitment problem

Harmony search (HS) is a population-based metaheuristics search algorithm inspired from the musical process of searching for a perfect state of harmony. The pitch of each musical instrument determines the aesthetic quality, just as the fitness function value determines the quality of decision variables. In the musical improvisation process, all players sound pitches within possible range together to make one harmony. If all the pitches make a good harmony, each player stores in his memory that experience and the possibility of making a good harmony is increased next time. Even though HS has the ability to escape from local minima, it does not require differential gradients and initial value setting for the variables, is free from divergence and has strong ability to explore the regions of solution space in a reasonable time. However, it has lower exploitation ability in later period and it easily trapped into local optima and converges very slowly. To improve the exploitation ability of HS algorithm in later stage and provide global optimal solution, a novel and hybrid version of harmony search combined with random search algorithm is presented in the proposed research to solve single-area unit commitment problem of electric power system. The proposed algorithm is tested for standard IEEE systems consisting of 4, 10, 20 and 40 generating units. The effectiveness of proposed hybrid algorithm is compared with other well-known evolutionary, heuristics and metaheuristics search algorithms, and it has been found that performance of proposed algorithm is much better than of classical harmony search algorithm and improved harmony search algorithm as well as recently developed algorithms. Sensitivity analysis on proposed algorithm shows that low value of pitch adjustment rate results in better cost, and parametric test on proposed algorithm shows the rejection of the null hypothesis at the alpha significance level.

The identification of electric load simulator for gun control systems based on variable-structure WNN with adaptive differential evolution

Owing to the complex nonlinearities of the electric load simulator (ELS) for the gun control system (GCS), the surplus torque plays a great negative impact on the performance of the loading system. This paper proposes a variable-structure wavelet-neural-network (VSWNN) identification strategy based on adaptive differential evolution (ADE). First of all, a mathematical model is established based on the structure and the working principle of the ELS. Then an intelligent identification method is applied, where the wavelet function is chosen as the excitation function, which improves the generalization and approximation ability of the neural network. The ADE is used to optimize the parameters, which solves the difficulty of determining the structure of the WNN. In order to reduce the computation complexity and speed up the convergence of the identification system, the adaptive laws of the pitch adjusting rate (PAR), band width (BW) and variable numbers of neurons are proposed. Finally, a pseudo random multilevel signal and a linear frequency modulation signal are chosen as input signals for the hardware-in-the-loop simulation. The test results show that the proposed ADE-VSWNN algorithm has superior validity and practicability, especially when the identification algorithm is used in the working circumstances with different inertial torque. Further, the high precision and strong robustness of the identification algorithm are further verified.

Using Harmony Search Algorithm for Load Balancing in Cloud Computing

Background: In this paper, we have surveyed the load modification and the trust capability in the cloud computing data centers. Method: The components of harmony search Algorithm include the harmony memory, the pitch adjustment rate and the random selection. The harmony memory checks and selects the responses. HMCR (Harmony Memory Considering Rate) is used for showing the possibility of selection from the memory and the pitch adjustment rate is used for causing a new harmony. Findings: Standard deviation and the resource exploitation average are the most important criteria at the load balancing. In this paper, the proposed Algorithm has been compared with the Genetic Algorithm and the simulation results show that the proposed Algorithm has a better competence than the Genetic Algorithm as the HSD (Harmony Search Degertekin ) rate of the proposed method is less than the HSD rate of Genetic Algorithm and the average of utilization from resources in the proposed method is more as well as with the increasing number of tasks, the performance of the algorithm is improved. Application/Improvement: Using this method of load balancing, the satisfaction of users is maximized, the time of response is minimized and the utilization of resources is increased.

A self-adaptive multi-objective harmony search algorithm based on harmony memory variance

Although harmony search (HS) algorithm has shown many advantages in solving global optimization problems, its parameters need to be set by users according to experience and problem characteristics. This causes great difficulties for novice users. In order to overcome this difficulty, a self-adaptive multi-objective harmony search (SAMOHS) algorithm based on harmony memory variance is proposed in this paper. In the SAMOHS algorithm, a modified self-adaptive bandwidth is employed, moreover, the self-adaptive parameter setting based on variation of harmony memory variance is proposed for harmony memory considering rate (HMCR) and pitch adjusting rate (PAR). To solve multi-objective optimization problems (MOPs), the proposed SAMOHS uses non-dominated sorting and truncating procedure to update harmony memory (HM). To demonstrate the effectiveness of the SAMOHS, it is tested with many benchmark problems and applied to solve a practical engineering optimization problem. The experimental results show that the SAMOHS is competitive in convergence performance and diversity performance, compared with other multi-objective evolutionary algorithms (MOEAs). In the experiment, the impact of harmony memory size (HMS) on the performance of SAMOHS is also analyzed.

A self-adaptive harmony PSO search algorithm and its performance analysis

Harmony Search (HS) algorithm is a new population-based meta-heuristic which imitates the music improvisation process and has been successfully applied to a variety of combination optimization problems. In this paper, a self-adaptive harmony particle swarm optimization search algorithm, named SHPSOS, is proposed to solve global continuous optimization problems. Firstly, an efficient initialization scheme based on the PSO algorithm is presented for improving the solution quality of the initial harmony memory (HM). Secondly, a new self-adaptive adjusting scheme for pitch adjusting rate (PAR) and distance bandwidth (BW), which can balance fast convergence and large diversity during the improvisation step, are designed. PAR is dynamically adapted by symmetrical sigmoid curve, and BW is dynamically adjusted by the median of the harmony vector at each generation. Meanwhile, a new effective improvisation scheme based on differential evolution and the best harmony (best individual) is developed to accelerate convergence performance and to improve solution accuracy. Besides, Gaussian mutation strategy is presented and embedded in the SHPSOS algorithm to reinforce the robustness and avoid premature convergence in the evolution process of candidates. Finally, the global convergence performance of the SHPSOS is analyzed with the Markov model to testify the stability of algorithm. Experimental results on thirty-two standard benchmark functions demonstrate that SHPSOS outperforms original HS and the other related algorithms in terms of the solution quality and the stability.

Solving large-scale multidimensional knapsack problems with a new binary harmony search algorithm

Harmony search (HS) is a meta-heuristic method that has been applied widely to continuous optimization problems. In this study, a new binary coded version of HS, named NBHS, is developed for solving large-scale multidimensional knapsack problem (MKP). In the proposed method, focus is given to the probability distribution rather than the exact value of each decision variable and the concept of mean harmony is introduced in the memory consideration. Unlike the existing HS variants which require specifications of parameters such as the pitch adjustment rate and step bandwidth, an ingenious pitch adjustment scheme without parameter specification is executed in the proposed HS according to the difference between two randomly selected harmonies stored in the harmony memory to generate a new candidate harmony. Moreover, to guarantee the availability of harmonies in the harmony memory, a simple but effective repair operator derived from specific heuristic knowledge of the MKP is embedded in the proposed method. Finally, extensive numerical simulations are conducted on two sets of large-scale benchmark problems, and the results reveal that the proposed method is robust and effective for solving the multidimensional knapsack problems with large dimension sizes.

A simplified binary harmony search algorithm for large scale 0–1 knapsack problems

As an important subset of combinatorial optimization, 0–1 knapsack problems, especially the high-dimensional ones, are often difficult to solve. This study aims to provide a new simplified binary harmony search (SBHS) algorithm to tackle such NP-hard problems arising in diverse research fields. The key difference between SBHS and other HS methods is in the process of improvisation. The differences among harmonies stored in harmony memory rather than the pitch adjustment rate (PAR) and step bandwidth (bw) are employed to produce new solutions and this can greatly alleviate the burden of setting these important factors manually. Moreover, the harmony memory considering rate (HMCR) is dynamically adjusted in terms of the dimension size to improve convergence of the algorithm. Therefore, the proposed method does not require any tedious process of proper parameter setting. To further enhance the population diversity, a specific heuristic based local search around infeasible solutions is carried out to obtain better quality solutions. A set of 10 low dimensional knapsack problems as well as large scale instances with up to 10,000 items are used to test the effectiveness of the proposed algorithm. Extensive comparisons are made with the most well-known state-of-the-art HS methods including 9 continuous versions and 5 binary-coded variants. The results reveal that the proposed algorithm can obtain better solutions in almost all cases and outperforms the other considered HS methods with statistical significance, especially for the large scale problems.

Dynamic Harmony Search with Polynomial Mutation Algorithm for Valve-Point Economic Load Dispatch.

Economic load dispatch (ELD) problem is an important issue in the operation and control of modern control system. The ELD problem is complex and nonlinear with equality and inequality constraints which makes it hard to be efficiently solved. This paper presents a new modification of harmony search (HS) algorithm named as dynamic harmony search with polynomial mutation (DHSPM) algorithm to solve ORPD problem. In DHSPM algorithm the key parameters of HS algorithm like harmony memory considering rate (HMCR) and pitch adjusting rate (PAR) are changed dynamically and there is no need to predefine these parameters. Additionally polynomial mutation is inserted in the updating step of HS algorithm to favor exploration and exploitation of the search space. The DHSPM algorithm is tested with three power system cases consisting of 3, 13, and 40 thermal units. The computational results show that the DHSPM algorithm is more effective in finding better solutions than other computational intelligence based methods.

Harmony Search Algorithm with Opposition-Based Learning for Power System Economic Load Dispatch

A harmony search algorithm with opposition-based learning techniques (HS-OBL) to solve power system economic load dispatch has been presented. The proposed algorithm integrates the opposition-based learning operation with the improvisation process to prevent the HS-OBL algorithm from being trapped into the local optimum effectively. Besides, a new adjusting strategy is designed to dynamic adjust pitch adjusting rate (PAR) and harmony memory consideration rate (HMCR), which is to further improve the performance of algorithm. The HS-OBL is employed to solve 6 units and 13 units power system, the numerical results indicate that the HS-OBL has perform much better than harmony search(HS) algorithm and other improved algorithms that reported in recent literature.

An Analysis of the Parameter Modifications in Varieties of Harmony Search Algorithm

A Harmony Search (HS) algorithm is a population based-meta-heuristics approach that is superior in solving diversified and large scale optimization problems. Several studies have pointed out that Harmony Search is an efficient and flexible tool to resolve optimization problems in diverse areas of construction, engineering, robotics, telecommunication, health and energy. Considering its increasing usage in diverse areas, this paper aims to present the historical development of HS, highlighting on its different features, modifications for improvements and limitations. Based on the description of the fundamental concept of HS, recent variations of the extended HS were analyzed focusing on its algorithm’s theory as well as its fundamental and primary concepts. It was found that the enhancements made on the extended HS are mainly on the modification of the parameters, such as the harmony memory consideration rate (HMCR), pitch adjusting rate (PAR) and distance bandwidth (BW). This analysis provides a useful motivation for researchers interested to improve the achievement of the standard HS algorithm and enhance the solution convergence rate and flexibility.

A Modified Harmony Search Algorithm Solve Numerical Optimization Problems

This paper proposes a new effective MHS algorithm to solve numerical optimization problems. The MHS algorithm first adopt a novel self-studying strategy, which makes it easy balance the global search ability and local development ability, prevent the MHS algorithm trapped into local optimal value. besides, the harmony memory consideration rate (HMCR), pitch adjustment rate (PAR) and bandwidth distance (bw) is changed with function values dynamically, it can effectively improve the convergence speed and precision of the algorithm Based on five test functions , experiments results obtained by the MHS algorithm are better than those obtained using HS, IHS and NGHS algorithm in the literature.

하모니 검색 알고리즘을 이용한 포트홀 발생 개수 예측 모형

Abstract : A bunch of asphalt roads have been damaged frequently in relation to the rapid climate change. To solve and prevent this type of problems, many nationalities in the world have performed various researches. In this regard, the objective of this study is to develop prediction model as to the number of potholes occurred in seoul. At the same time, we have utilized empirical and statistical approaches in order for us to identify factors which is affecting the actual occurrence. The predictive model was determinded by using BHS (Basic Harmony Search) algorithm. Prediction was based on the weather and traffic data as well as data occurrence data of porthole. To assess the influences which are PAR(Pitch Adjusting Rate) and HMCR(Harmony Memory Considering Rate), we determined suitability by changing the values. In the process of the determining a predictive model, the predictive model composed Training data (2011, 2012 and 2013yrs data). To determine the suitability of the model, we have utilized Testing Set (2009 and 2010 yrs data). The suitability of the basic prediction model has been from RMSE(Root Mean Squared Error), MAE(Mean Absolute Error) and Coefficient of determination.

Clustering using modified harmony search algorithm

Metaheuristic techniques are being successfully used as optimisation methods in various application areas. This paper presents modification in one such metaheuristic called as harmony search (HS) that is inspired from music improvisation process. The two parameters, harmony memory consideration rate (HMCR) and pitch adjusting rate (PAR), in HS play important role in improvisation of new harmony. Instead of keeping the parameters fixed, as reported in many existing algorithms, these are being allowed to change dynamically during the process of improvisation in the proposed algorithm. This paper further examines the effect on the results when K-means is initialised with solution returned by the proposed algorithm. The effect of harmony memory size has also been investigated on proposed approach. The experiments are performed for data clustering on nine benchmark datasets. The clustering performance of proposed algorithm is compared with K-means, fuzzy C-means, genetic algorithm, and four recently proposed variants of HS. The results are encouraging and demonstrate that the proposed algorithm provides much better values in terms of precision, recall, G-measure, inter-cluster and intra-cluster distances.