Harmony Memory Research Articles

Research on Financial Early-warning based on GIHS Improved BP_AdaBoost Algorithm

To improve the accuracy of the financial early warning of the company, aiming at defects of slow learning speed, trapped in local solution and inaccurate operating result of the traditional BP neural network with random initial weights and thresholds, a parallel ensemble learning algorithm based on improved harmony search algorithm using good point set (GIHS) optimize the BP_Adaboost is proposed. Firstly, the good-point set is used to construct a more high quality initial harmony library, and it adjusts the parameters dynamically during the search process and generates several solutions in each iteration so as to make full use of information of harmony memory to improve the global search ability and convergence speed of algorithm. Secondly, ten financial indicators are chosen as the inputs of BP neural network value, and GIHS algorithm and BP neural network are combined to construct the parallel ensemble learning algorithm to optimize BP neural network initial weights value and output threshold value. Finally, many of these weak classifier is composed as strong classifier through the AdaBoost algorithm. The improved algorithm is validated in the company's financial early warning. Simulation results show that the performance of GIHS algorithm is better than the basic HS and IHS algorithm, and the GIHS-BP_AdaBoost classifier has higher classification and prediction accuracy.

A hybrid harmony search algorithm with efficient job sequence scheme and variable neighborhood search for the permutation flow shop scheduling problems

The permutation flow shop scheduling problem (PFSSP), one of the most widely studied production scheduling problems, is a typical NP-hard combinatorial optimization problem. In this paper, a hybrid harmony search algorithm with efficient job sequence mapping scheme and variable neighborhood search (VNS), named HHS, is proposed to solve the PFFSP with the objective to minimize the makespan. First of all, to extend the HHS algorithm to solve the PFSSP effectively, an efficient smallest order value (SOV) rule based on random key is introduced to convert continuous harmony vector into a discrete job permutation after fully investigating the effect of different job sequence mapping schemes. Secondly, an effective initialization scheme, which is based on NEH heuristic mechanism combining with chaotic sequence, is employed with the aim of improving the solution’s quality of the initial harmony memory (HM). Thirdly, an opposition-based learning technique in the selection process and the best harmony (best individual) in the pitch adjustment process are made full use of to accelerate convergence performances and improve solution accuracy. Meanwhile, the parameter sensitivity is studied to investigate the properties of HHS, and the recommended values of parameters adopted in HHS are presented. Finally, by making use of a novel variable neighborhood search, the efficient insert and swap structures are incorporated into the HHS to adequately emphasize local exploitation ability. Experimental simulations and comparisons on both continuous and combinatorial benchmark problems demonstrate that the HHS algorithm outperforms the standard HS algorithm and other recently proposed efficient algorithms in terms of solution quality and stability.

Modified Parameters of Harmony Search Algorithm for Better Searching

The scheduling and rostering problems are deliberated as integrated due to they depend on each other whereby the input of rostering problems is a scheduling problems. In this research, the integrated scheduling and rostering bus driver problems are defined as maximising the balance of the assignment of tasks in term of distribution of shifts and routes. It is essential to achieve is fairer among driver because this can bring to increase in driver levels of satisfaction. The latest approaches still unable to address the fairness problem that has emerged, thus this research proposes a strategy to adopt an amendment of a harmony search algorithm in order to address the fairness issue and thus the level of fairness will be escalate. The harmony search algorithm is classified as a meta-heuristics algorithm that is capable of solving hard and combinatorial or discrete optimisation problems. In this respect, the three main operators in HS, namely the Harmony Memory Consideration Rate (HMCR), Pitch Adjustment Rate (PAR) and Bandwidth (BW) play a vital role in balancing local exploitation and global exploration. These parameters influence the overall performance of the HS algorithm, and therefore it is crucial to fine-tune them. The contributions to this research are the HMCR parameter using step function while the fret spacing concept on guitars that is associated with mathematical formulae is also applied in the BW parameter. The model of constant step function is introduced in the alteration of HMCR parameter. The experimental results revealed that our proposed approach is superior than parameter adaptive harmony search algorithm. In conclusion, this proposed approach managed to generate a fairer roster and was thus capable of maximising the balancing distribution of shifts and routes among drivers, which contributed to the lowering of illness, incidents, absenteeism and accidents.

A Cascaded Improved Harmony Search for Line Impedance Estimation in a Radial Power System

This paper develops cascaded improved harmony search (CIHS) based on meta-heuristics called harmony search (HS) and its variant, called improved harmony search (IHS). CIHS literally cascades several IHSs serially. Even though seemingly CIHS is simple to implement, it is effective in escaping poor local optima which HS and its variants have suffered from. The proposed CIHS is less sensitive to parameter setting and less time-consuming at each iteration than a conventional IHS with the same harmony memory size, since a much smaller-scale IHS is carried out in CIHS. Using the proposed CIHS, we formulate a line impedance estimation problem to which CIHS can be practically applied. We derive detailed line impedance estimation procedures for a general radial system. Finally, the performance of CIHS is validated through line impedance estimation.

Parallel algorithm of multiobjective optimization harmony search based on cloud computing

In order to solve the problems of traditional harmony search in complex function multiobjective optimization, such as low precision, slow convergence, and easy to fall into local optimum, this article proposes a multiobjective optimization harmony search parallel algorithm based on cloud computing. First, according to the characteristics that the traditional harmony search algorithm uses a single harmony library for storing and processing the memory harmony, and it is divided into multiple harmony sublibraries according to different harmony. At the same time, the roulette selection and dynamic trade-off factor strategies are used for the dynamic setting of harmony memory library value-taking probability, pitch fine-tuning probability, pitch fine-tuning bandwidth, and other parameters which the traditional harmony search algorithm mainly relies on. Then, MapReduce programming model is used to establish Map and Reduce core parallel computing functions, to construct the parallel algorithm of dynamic parameter harmony search based on cloud computing. Finally, the algorithm optimization comparison test is conducted on Hadoop platform and compared with several existing optimal harmony search algorithms, the searching precision of this algorithm is improved by eight orders of magnitude, and the iteration number on the convergence speed is reduced by 6500 times, and the parallel achieves the linear acceleration ratio. Experimental results show that the optimization efficiency of this algorithm is higher than several existing optimal harmony search algorithms.

Topology optimization based on the harmony search method

A new topology optimization scheme based on a Harmony search (HS) as a metaheuristic method was proposed and applied to static stiffness topology optimization problems. To apply the HS to topology optimization, the variables in HS were transformed to those in topology optimization. Compliance was used as an objective function, and harmony memory was defined as the set of the optimized topology. Also, a parametric study for Harmony memory considering rate (HMCR), Pitch adjusting rate (PAR), and Bandwidth (BW) was performed to find the appropriate range for topology optimization. Various techniques were employed such as a filtering scheme, simple average scheme and harmony rate. To provide a robust optimized topology, the concept of the harmony rate update rule was also implemented. Numerical examples are provided to verify the effectiveness of the HS by comparing the optimal layouts of the HS with those of Bidirectional evolutionary structural optimization (BESO) and Artificial bee colony algorithm (ABCA). The following conclusions could be made: (1) The proposed topology scheme is very effective for static stiffness topology optimization problems in terms of stability, robustness and convergence rate. (2) The suggested method provides a symmetric optimized topology despite the fact that the HS is a stochastic method like the ABCA. (3) The proposed scheme is applicable and practical in manufacturing since it produces a solid-void design of the optimized topology. (4) The suggested method appears to be very effective for large scale problems like topology optimization.

Optimum design of aircraft panels based on adaptive dynamic harmony search

Aiming at the optimization of aircraft panels, a modified version of harmony search (HS) algorithm is proposed based on the information of the harmony memory (a memory location where all the solution vectors are stored) for improvisation procedure, named as adaptive dynamic harmony search (ADHS) algorithm. In order to reduce the amount of calculation, response surface method is employed, and second-order polynomial with cross terms is used to construct the model. To demonstrate the advantage of the proposed algorithm, typical aircraft panels under buckling constraint are established, and several existing HS algorithms are compared. The effects of the number of improvisation (NI) and harmony memory size (HMS) are investigated and discussed in detail. Results indicate that the proposed ADHS can provide an optimum design in a robust manner, and local optimum solutions may be reduced based on the ADHS for optimization problems with multiple local minima. Finally, several useful information is obtained for the design of stiffened panels with cutouts.

A dynamic parameter controlled harmony search algorithm for assembly sequence planning

Assembly sequence planning (ASP) plays an important role in intelligent manufacturing. As ASP is a non-deterministic polynomial (NP) hard problem, it is scarcely possible for a brute force approach to find out the optimal solution. Therefore, increasing meta-heuristic algorithms are introduced to solve the ASP problem. However, due to the discreteness and strong constraints of ASP problem, most meta-heuristics are unsuitable or inefficient to optimize it. Harmony search (HS) algorithm is one of the most suitable meta-heuristics for solving the problem. This paper proposes a dynamic parameter controlled harmony search (DPCHS) for solving ASP problems including a transformation of the assembly sequences by the largest position value (LPV) rule, initializing harmony memory with opposition-based learning (OBL) and designing dynamic parameters to control evolution. The key improvement to former work lies in the introduction of a dynamic pitch adjusting rate and bandwidth, which are adapting their value during the evolution. The performances of the DPCHS and the fixed harmony search algorithm are compared thoroughly in the case studies. Meantime, the efficiency of this algorithm in solving ASP problems is tested using two cases, and the results of other popular algorithms are compared. Furthermore, the DPCHS has been successfully applied to an industrial ASP problem.

Selective Refining Harmony Search: A new optimization algorithm

While music improvisation is an NP-hard problem, it has always been handled by musicians successfully. Harmony search is a class of meta-heuristics inspired by the improvisation process of musicians. Inexperienced musicians usually make several harmonies until they find the desired one. However, experienced musicians more rely on their knowledge and experience instead of brute-force searching for a desired harmony. When making a harmony, they are able to distinguish the undesired notes of the current harmony and just modify them instead of throwing away the total harmony and making a new one. This approach of experienced musicians was adopted in this paper to allow the harmony search algorithm to exploit the knowledge and experience accumulated in the harmony memory to refine current harmonies. The underlying algorithm is called Selective Refining Harmony Search in which a new harmony memory update has been utilized. The main differences between the proposed method and the original harmony search are the integration of selection in the improvisation step and introduction of refinement concept. The improvements provided by the proposed method originate from its superior ability to imitate the behavior of musicians in the sense that instead of total harmonies, decision variables are considered during the memory update process. This modification provided outstanding performance to minimize the objective functions of the underlying problems, while computational loads are also better than other methods in most cases. During refinement procedure, two new parameters were employed to make a trade-off between effectiveness and efficiency of the algorithm. During the experiments, the proposed method exhibited robust performance against its two new parameters. Several algorithms including original harmony search and its state-of-the-art variants were implemented to conduct comprehensive comparisons. All of the algorithms were evaluated over IEEE CEC 2010 suite, one of the well-known and challenging benchmark test sets. Several studies have evidenced that the utilization of harmony search has been fostered in diverse application fields. Thus, the improvements to harmony search algorithm provided by the proposed method makes it more efficient for those fields and possible to be employed for more challenging problems.

Modified harmony search and its application to cost minimization of RC columns

This paper presents a variant of the Harmony Search Algorithm (HS) and its application to discrete optimization. The main proposed modifications regarding original HS are related to stopping criterion and reinitialization of population, called Harmony Memory. In order to investigate the efficiency of the algorithm, it was applied for obtaining optimal sections of reinforced concrete columns subjected to uniaxial flexural compression. To minimize the cost of the section, the amount and diameters of the reinforcement bars and the dimensions of the columns cross sections were considered as design variables. The obtained results were compared to those generated by other optimization methods. Since, to the examples, Harmony Search reached the same results achieved by Simulated Annealing, some additional analysis are presented in order to compare these methods regarding success rate and number of iterations to reach the optimum.

Semi-self-adaptive harmony search algorithm

This paper proposes a semi-self-adaptive harmony search algorithm (SSaHS) with the self-adaptive adjustment of the bandwidth and the elitist learning strategy of particle swarm optimization. SSaHS employs a self-adaptive adjusting strategy for with the difference between the maximum and minimum components in the harmony memory as the bandwidth. It can dynamically adjust the bandwidth for the specific problem to strengthen local exploitation ability and improve the accuracy of optimization results. Comparison results show that the semi-self-adaptive harmony search algorithm can find better solutions when comparing with both basic harmony search algorithm and several enhanced harmony search algorithms, including an improved harmony search, a global-best harmony search and a novel global harmony search.

Improved Harmony Search Algorithm: LHS

In this paper, we propose an improved harmony search algorithm named LHS with three key features: (i) adaptive global pitch adjustment is designed to enhance the exploitation ability of solution space; (ii) opposition-based learning technique is blended to increase the diversity of solution; (iii) competition selection mechanism is established to improve solution precision and enhance the ability of escaping local optima. The performance of the LHS algorithm with respect to harmony memory size (HMS) and harmony memory considering rate (HMCR) are also analyzed in detail. To further evaluate the performance of the proposed LHS algorithm, comparison with ten state-of-the-art harmony search variants over a large number of benchmark functions with different characteristics is carried out. The numerical results confirm the superiority of the proposed LHS algorithm in terms of accuracy, convergence speed and robustness.

A New Fuzzy Harmony Search Algorithm Using Fuzzy Logic for Dynamic Parameter Adaptation

In this paper, a new fuzzy harmony search algorithm (FHS) for solving optimization problems is presented. FHS is based on a recent method using fuzzy logic for dynamic adaptation of the harmony memory accepting (HMR) and pitch adjustment (PArate) parameters that improve the convergence rate of traditional harmony search algorithm (HS). The objective of the method is to dynamically adjust the parameters in the range from 0.7 to 1. The impact of using fixed parameters in the harmony search algorithm is discussed and a strategy for efficiently tuning these parameters using fuzzy logic is presented. The FHS algorithm was successfully applied to different benchmarking optimization problems. The results of simulation and comparison studies demonstrate the effectiveness and efficiency of the proposed approach.

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.

Modeling the behavior of FRP-confined concrete using dynamic harmony search algorithm

The accurate prediction of ultimate conditions for fiber reinforced polymer (FRP)-confined concrete is essential for the reliable structural analysis and design of resulting structural members. Nonlinear mathematical models can be used for accurate calibration of strength and strain enhancement ratios of FRP-confined concrete. In this paper, a new procedure is proposed to calibrate the nonlinear mathematical functions, which involved the use of a dynamic harmony search (DHS) algorithm. The harmony memory is dynamically adjusted based on a novel pitch generation scheme using a dynamic bandwidth and random number with normal standard distribution in DHS. A new design-oriented confinement model is proposed based on three influential factors of FRP area ratio ($$ \rho_{a} $$źa), lateral confinement stiffness ratio ($$ \rho_{E} $$źE), and strain ratio ($$ \rho_{\varepsilon } $$źź). Five nonlinear mathematical design-oriented models are regressed on approximately 1000 axial compression tests of FRP-confined concrete in circular sections based on the proposed DHS algorithm. The proposed models for the prediction of the ultimate axial stress and strain of FRP-confined concrete are compared with the existing models. It has been shown that the DHS algorithm offers the best performance in terms of both accuracy and fast convergence rate in comparison with the other modified versions of harmony search algorithms for optimization problems. The proposed design-oriented model provides improved accuracy over the existing models.

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.

Predicting anomalous zone ahead of tunnel face utilizing electrical resistivity: I. Algorithm and measuring system development

This study applies the harmony search (HS) inverse analysis algorithm and develops the tunnel resistivity prediction (TRP) system for predicting the location, thickness, permittivity ratio, and conductivity of the anomalous zone ahead of the tunnel face by utilizing electrical resistivity. The relationship between the four characteristic values of the anomalous zone and the electrical resistance is derived using Gauss’ laws and Ohm’s laws. The optimum values of HS algorithm operators (such as the harmony memory considering rate (HMCR) and the pitch adjust rate (PAR)) are proposed that can provide the best inverse analysis that correlates the four characteristic values with the electrical resistance. Also, the prediction accuracy of inverse analysis using the proposed HS algorithm is verified by laboratory tests on the artificially formed ground with an anomaly. An electrical resistance measuring system is devised to obtain the electrical resistance of the ground, and inverse analyses are performed from the measured resistance to estimate the four characteristic values of the artificial anomaly. The test results from laboratory scale experiments show that the characteristics of the anomalies are predicted reasonably well, resulting in less than 3% average error. This paper is part 1 of the companion papers; the second paper will verify the developed system through the field tests.

Integrated approach of network reconfiguration with distributed generation and shunt capacitors placement for power loss minimization in radial distribution networks

This article presents the significance of efficient hybrid heuristic search algorithm(HS-PABC) based on Harmony search algorithm (HSA) and particle artificial bee colony algorithm (PABC) in the context of performance enhancement of distribution network through simultaneous network reconfiguration along with optimal allocation and sizing of distributed generators and shunt capacitors. The premature and slow convergence over multi model fitness landscape is the main limitation in standard HSA. In the proposed hybrid algorithm the harmony memory vector of HSA is intelligently enhanced through PABC algorithm during the optimization process to reach the optimal solution within the search space. In hybrid approach, the exploration ability of HSA and the exploitation ability of PABC algorithm are integrated to blend the potency of both algorithms. The box plot and Wilcoxon rank sum tests are used to show the quality of the solution obtained by hybrid HS-PABC with respect to HSA.The computational results prove the integrated approach of the network reconfiguration problem along with optimal placement and sizing of DG units and shunt capacitors as an efficient approach with respect to power loss reduction and voltage profile enhancement. The results obtained on 69 and 118 node network by hybrid HS-PABC method and the standard HSA reveals the effeciency of the proposed approach which guarantees to achieve global optimal solution with less iteration.

Gaussian global-best harmony search algorithm for optimization problems

In this paper, a novel optimization approach is proposed using Gaussian distribution function to improve harmony search (HS) algorithm, namely “Gaussian global-best harmony search” (GGHS) algorithm. The harmony memory (HM) is adjusted using Gaussian random generation in GGHS. The GGHS algorithm consists of two adjustment steps; in the first stage, the harmony memory is adjusted by a dynamic bandwidth and the Gaussian distribution with a mean of 0 and a standard deviation of 1. In the second stage, the best memory is adjusted using a random Gaussian number with a mean of 0 and a dynamic standard deviation. The dynamic bandwidth and standard deviation are adaptively determined based on iteration number, the maximum and minimum of each design variable in the HM. Accuracy and efficiency of the GGHS algorithm have been evaluated using several benchmark mathematical examples. The numerical results illustrate that the GGHS algorithm is more accurate and efficient than other existing modified versions of harmony search algorithm. The capability of the dynamic bandwidth enhances the performance of this modified HS algorithm. The GGHS produces the better optimum results in comparison with other improved versions of harmony search algorithm.

A Hybrid Harmony Search algorithm for discrete sizing optimization of truss structure

This paper presents a new variant of the Harmony Search (HS) algorithm. This Hybrid Harmony Search (HHS) algorithm follows a new approach to improvisation: while retaining HS algorithm Harmony Memory and pitch adjustment functions, it replaces the HS algorithm randomization function with Global-best Particle Swarm Optimization (PSO) search and neighbourhood search. HHS algorithm performance is tested on six discrete truss structure optimization problems under multiple loading conditions. Optimization results demonstrate the excellent performance of the HHS algorithm in terms of both optimum solution and the convergence behaviour in comparison with various alternative optimization methods.