Pitch Adjustment Operator Research Articles

Optimum Location and Parameter Setting of STATCOM Based on Improved Differential Evolution Harmony Search Algorithm

Identification of the optimum location and capacity of Static Synchronous Compensator (STATCOM) in power grids has been given much attention to maximize its technical performance while minimizing operational cost. In this regard, a new multi-objective optimization model that minimizes power loss, enhances system stability and reduces operational cost of STATCOMs is presented in this paper. To overcome the issue of the harmony search (HS) optimization algorithm in solving high-dimensional multi-objective optimization problem, an improved differential evolution harmony search (DEHS) algorithm is proposed. In this algorithm, mutation and crossover operations are adopted instead of the original pitch adjustment operation adopted in the HS optimization algorithm, which enhances the algorithm global search ability. Moreover, opposition-based learning technique is incorporated to the process to broaden the diversity of variables and hence improving the search efficiency of the algorithm. The proposed algorithm is employed to identify the optimal allocation and sizing of multiple STATCOMs within the IEEE 30-bus system. Results reveal the superiority of the proposed optimization algorithm over the conventional multi-objectives adaptive harmony search algorithm.

Adaptive probabilistic harmony search for binary optimization problems

Harmony search (HS) is an optimization technique that uses several operators such as pitch adjustments to provide local improvement to candidate solutions during the optimization process. A standard pitch adjustment operator is known to be inefficient for binary domain optimization problems. A novel adaptive probabilistic harmony search (APHS) algorithm for binary optimization problems is proposed in this paper. APHS combines the power of the standard harmony search with the modelling capability of probabilistic search algorithms, with almost no extra user-tuned parameters. In APHS, the expected value of the search probability distribution is adapted using a sample of “good” vectors among the population to minimize the cross entropy between the actual distribution and the measured one. Moreover, Bernoulli probability distribution was used to enhance the pitch adjustment operator to fit the binary optimization domain. The effectiveness and the robustness of the proposed algorithm are shown by a thorough comparison with state-of-the-art existing techniques in a number of binary space optimization problems with variant complexities and sizes. The set of binary space optimization problems investigated in this paper include: Max-One problem, Order-3 deceptive problem, Bipolar Order-6 deceptive problem, Muehlenbein’s Order-5 problem, Knapsack problem, Multi-Knapsack problem, and finally a real-world problem of the satellite broadcast scheduling. Experimental results show that our proposed algorithm is indeed very effective and outperforms the existing algorithms by finding optimal solutions for almost all tested benchmarks.

Hybridizing harmony search algorithm with cuckoo search for global numerical optimization

For the purpose of enhancing the search ability of the cuckoo search (CS) algorithm, an improved robust approach, called HS/CS, is put forward to address the optimization problems. In HS/CS method, the pitch adjustment operation in harmony search (HS) that can be considered as a mutation operator is added to the process of the cuckoo updating so as to speed up convergence. Several benchmarks are applied to verify the proposed method and it is demonstrated that, in most cases, HS/CS performs better than the standard CS and other comparative methods. The parameters used in HS/CS are also investigated by various simulations.

Optimum Cost Design of Reinforced Concrete Retaining Walls Using Hybrid Firefly Algorithm

This paper develops a novel optimization method namely hybrid firefly algorithm with harmony search technique (IFA-HS), to obtain the optimal cost of the reinforced concrete retaining walls satisfying the stability criteria. The hybrid IFA-HS is utilized to find the economical design adhering to provisions of ACI 318-05. Also Coulomb lateral earth pressure theory is used to derive the lateral total thrust on the wall. Some design examples are tested using the new method. The results carried out on these examples confirm the validity of the proposed algorithm. The IFA-HS method can be considered as an improvement of the recently developed firefly algorithm. The improvements include the utilizing of a memory that contains some information extracted online during the search, adding of pitch adjustment operation in harmony search serving as mutation operator during the process of the firefly updating, and modifying the movement phase of firefly algorithm. The detailed implementation procedure for this improved meta-heuristic method is also described.

VARIANCE-BASED HARMONY SEARCH ALGORITHM FOR UNIMODAL AND MULTIMODAL OPTIMIZATION PROBLEMS WITH APPLICATION TO CLUSTERING

This article presents a novel variance-based harmony search algorithm (VHS) for solving optimization problems. VHS incorporates the concepts borrowed from the invasive weed optimization technique to improve the performance of the harmony search algorithm (HS). This eliminates the main problem of constant parameter setting in the algorithm proposed recently and named as explorative HS. It uses the variance of a current population as well as presents a solution vector to improvise the harmony memory. In addition, the dynamic pitch adjustment operator is used to avoid solution oscillation. The proposed algorithm is evaluated on 14 standard benchmark functions of various characteristics. The performance of the proposed algorithm is investigated and compared with classical HS, an improved version of HS, the global best HS, self-adaptive HS, explorative HS, and the recently proposed state-of-art gravitational search algorithm. Experimental results reveal that the proposed algorithm outperforms the above-mentioned approaches. The effects of scalability, noise, harmony memory size, and harmony memory consideration rate have also been investigated with the proposed algorithm. The proposed algorithm is then employed for a data clustering problem. Four real-life datasets selected from the UCI machine learning repository have been used. The results indicate that the VHS-based clustering outperforms the existing well-known clustering algorithms.

A self adaptive differential harmony search based optimized extreme learning machine for financial time series prediction

This paper proposes a hybrid learning framework called Self Adaptive Differential Harmony Search Based Optimized Extreme Learning Machine (SADHS-OELM) for single hidden layer feed forward neural network (SLFN). The new learning paradigm seeks to take advantage of the generalization ability of extreme learning machines (ELM) along with the global learning capability of a self adaptive differential harmony search technique in order to optimize the fitting performance of SLFNs. SADHS is a variant of harmony search technique that uses the current to best mutation scheme of DE in the pitch adjustment operation for harmony improvisation process. SADHS has been used for optimal selection of the hidden layer parameters, the bias of neurons of the hidden-layer, and the regularization factor of robust least squares, whereas ELM has been applied to obtain the output weights analytically using a robust least squares solution. The proposed learning algorithm is applied on two SLFNs i.e. RBF and a low complexity Functional link Artificial Neural Networks (CEFLANN) for prediction of closing price and volatility of five different stock indices. The proposed learning scheme is also compared with other learning schemes like ELM, DE-OELM, DE, SADHS and two other variants of harmony search algorithm. Performance comparison of CEFLANN and RBF with different learning schemes clearly reveals that CEFLANN model trained with SADHS-OELM outperforms other learning methods and also the RBF model for both stock index and volatility prediction.

Improved Global Harmony Search Algorithm for Numerical Optimization

To intend to improve the optimization performance of harmony search (HS) algorithm, an improved global harmony search (IGHS) algorithm was presented in this paper. In this algorithm, inspired by swarm intelligence, the global best harmony are borrowed to enhance the optimization accuracy of HS; and mutation and crossover operation instead of pitch adjustment operation to improved the algorithm convergence rate. The key parameters are adjusted to balance the local and global search. Several benchmark experiment simulations, the IGHS has demonstrated stronger convergence and stability than original harmony search (HS) algorithm and its other three improved algorithms (IHS, GHS and SGHS) that reported in recent literature.

Hybrid Differential Evolution Harmony Search Algorithm for Power Economic Dispatch Problems

In this paper, a hybrid differential evolution harmony search (HDEHS) algorithm was presented for solving power economic dispatch problems. In this algorithm, mutation and crossover operation instead of harmony memory consideration and pitch adjustment operation, this improved the algorithm convergence rate. Moreover, dynamically adjust the key parameter (e.g. mutagenic factor F, crossover rate CR) to balance the local and global search. Based on a 13 units power system experiment simulations, the HDEHS has demonstrated stronger convergence and stability than original harmony search (HS) algorithm and its three improved algorithms (IHS, GHS and NGHS) that reported in recent literature.

A New Variant Harmony Search Algorithm for Unconstrained Numerical Optimization Problems

Harmony search (HS) algorithm is a good meta-heuristic intelligent optimization method and it does depend on imitating the music improvisation process to generate a perfect state of harmony. However, intelligent optimization methods is easily trapped into local optimal, HS is no exception. In order to modify the optimization performance of HS, a new variant of harmony search algorithm is proposed in this paper. The variant integrate the position updating of the particle swarm optimization algorithm with pitch adjustment operation, and dynamically adjust the key parameter pitch adjusting rate (PAR) and bandwidth (BW). Several standard benchmarks are to be tested. The numerical results demonstrated the superiority of the proposed method to the HS and recently developed variants (IHS, and GHS).

Solving Optimal Power Flow Problems Using Chaotic Self-adaptive Differential Harmony Search Algorithm

Optimal power flow is the basic tool that allows an electric utility to determine the economic and secure operating conditions of an electric power system. This article presents a chaotic self-adaptive differential harmony search algorithm to solve optimal power flow problems with non-smooth and non-convex cost functions. The searching capacity of the proposed chaotic self-adaptive differential harmony search algorithm has been improved by introducing a chaotic self-adaptive differential mutation operator instead of a pitch adjustment operator in the harmony search algorithm. The effectiveness of the proposed chaotic self-adaptive differential harmony search algorithm has been tested with IEEE 30-bus, IEEE 300-bus, and 66-bus Indian utility systems. The simulation results obtained using the proposed algorithm are compared with other variants of the improved harmony search algorithm, such as the differential harmony search algorithm, the chaotic differential harmony search algorithm, the interior point method, and other techniques reported in the literature, to show its effectiveness. The results obtained by the proposed algorithm are found to be better than the results obtained by the differential harmony search, chaotic differential harmony search, interior point method, and other algorithms reported in the literature in terms of solution quality and standard deviation of generation cost. In terms of speed of convergence and computational time, the proposed algorithm is better than the differential harmony search and chaotic differential harmony search algorithms.

Chaotic self-adaptive differential harmony search algorithm based dynamic economic dispatch

Dynamic economic dispatch (DED) is one of the main optimization problems in electrical power system operation and control. DED problem is a non-smooth and non-convex problem when valve point effect, ramp-rate limits and prohibited operating zones of generation units are taken into account. This paper proposes an efficient chaotic self-adaptive differential harmony search (CSADHS) algorithm to solve the complicated DED problem in the presence of valve point effect, ramp-rate limits and prohibited operating zones constraints. In the proposed algorithm, chaotic self-adaptive differential mutation operator is used instead of pitch adjustment operator in the harmony search (HS) algorithm, to enhance the searching performance to find the quality solution. The effectiveness of the proposed algorithm is demonstrated on 10, 15 and 30 unit systems for a period of 24h. The simulation results obtained by the proposed algorithm are compared with the results obtained, using differential harmony search (DHS) algorithm, chaotic differential harmony search (CDHS) algorithm, and also with the results of other methods available in the literature. In terms of solution quality, the proposed algorithm is found to be better than other algorithms and in terms of speed of convergence, standard deviation of generation cost, and computational time, the proposed algorithm is better than DHS and CDHS algorithm.

An improved adaptive binary Harmony Search algorithm

Harmony Search (HS), inspired by the music improvisation process, is a new meta-heuristic optimization method and has been successfully used to tackle the optimization problems in discrete or continuous space. Although the standard HS algorithm is able to solve binary-coded optimization problems, the pitch adjustment operator of HS is degenerated in the binary space, which spoils the performance of the algorithm. Based on the analysis of the drawback of the standard HS, an improved adaptive binary Harmony Search (ABHS) algorithm is proposed in this paper to solve the binary-coded problems more effectively. Various adaptive mechanisms are examined and investigated, and a scalable adaptive strategy is developed for ABHS to enhance its search ability and robustness. The experimental results on the benchmark functions and 0–1 knapsack problems demonstrate that the proposed ABHS is efficient and effective, which outperforms the binary Harmony Search, the novel global Harmony Search algorithm and the discrete binary Particle Swarm Optimization in terms of the search accuracy and convergence speed.

A Novel Hybrid Bat Algorithm with Harmony Search for Global Numerical Optimization

A novel robust hybrid metaheuristic optimization approach, which can be considered as an improvement of the recently developed bat algorithm, is proposed to solve global numerical optimization problems. The improvement includes the addition of pitch adjustment operation in HS serving as a mutation operator during the process of the bat updating with the aim of speeding up convergence, thus making the approach more feasible for a wider range of real-world applications. The detailed implementation procedure for this improved metaheuristic method is also described. Fourteen standard benchmark functions are applied to verify the effects of these improvements, and it is demonstrated that, in most situations, the performance of this hybrid metaheuristic method (HS/BA) is superior to, or at least highly competitive with, the standard BA and other population-based optimization methods, such as ACO, BA, BBO, DE, ES, GA, HS, PSO, and SGA. The effect of the HS/BA parameters is also analyzed.

An effective differential harmony search algorithm for the solving non-convex economic load dispatch problems

Solving the non-convex economic load dispatch (ELD) problem with evolutionary algorithms has gained increasing research in recent years. In this paper, a differential harmony search (DHS) algorithm is proposed by combining the mechanisms of both differential evolution and harmony search. In the DHS, the pitch adjustment operation is cooperated with the different mutation operation to enhance the exploitation ability of harmony search, and both the memory consideration and the pitch adjustment are used to enhance the exploration ability of evolution search. In addition, a repair procedure and three simple selection rules are proposed for constraint handling. Numerical simulations are carried out based on different kinds of testing problems with various constraints including valve point effects, multi-fuels, ramp rate limit and prohibited operation zones. Simulation results and comparisons with the some existing algorithms demonstrate the effectiveness, efficiency and robustness of the proposed DHS algorithm. Finally, the effect of parameter setting on the DHS is investigated as well.

Solving the task assignment problem using Harmony Search algorithm

This paper presents an improved version of a music-inspired meta-heuristic algorithm, Harmony Search (HS), for successfully solving the NP-complete task assignment problem (TAP) in distributed computing systems. Task assignment is an important and core step in distributed systems where program tasks must be properly allocated to the processors to effectively harness the computing power by better exploitation of the system parallelism and improving system performance. The proposed HS-based algorithm explores the search space effectively and efficiently by exploiting the factors of randomness, experience, and variation of experience. Our main contributions in this work are: introducing a modification in the pitch adjustment operator of the Harmony Search, mapping Harmony Search solutions to the clustering methodology which shows its superiority in solving TAP, and using a local refinement heuristic to improve a given assignment. The effectiveness of the proposed HS-based algorithm is demonstrated by comparing it with a recently reported Harmony Search algorithm, NGHS, and with a wide variety of other earlier reported meta-heuristic techniques such as GA, SA, PSO and many others, to solve the TAP. Simulation results indicate that the proposed HS-based algorithm is a viable approach for the TAP, which could find better quality (or even optimal) solutions within reasonable computation time.