A dynamical search space harmony search for unconstrained optimization problems

This paper presents a new modification of Harmony Search (HS) algorithm for solving global continuous optimization problems. The proposed algorithm is named self-adaptive dynamic Harmony Search (SDHS). In this modification, firstly, harmony memory consideration rate (HMCR), pitch adjusting rate (PAR) and bandwidth distance (BW), are dynamically adjusted simultaneously to keep a good balance between exploration and exploitation in the search process and different search spaces. Secondly, we introduced X best (the best value so far) to produce candidate harmony and adjust of the parameter BW. Experimental results tested on sixteen benchmark functions show that SDHS performs more effectively or at least similar to other approaches on most of test functions.

Software testing is the primary phase, which is performed during software development and it is carried by a sequence of instructions of test inputs followed by expected output.The Harmony Search (HS) algorithm is based on the improvisation process of music.In comparison to other algorithms, the HSA has gain popularity and superiority in the field of evolutionary computation.When musicians compose the harmony through different possible combinations of the music, at that time the pitches are stored in the harmony memory and the optimization can be done by adjusting the input pitches and generate the perfect harmony.The test case generation process is used to identify test cases with resources and also identifies critical domain requirements.In this paper, the role of Harmony search meta-heuristic search technique is analyzed in generating random test data and optimized those test data.Test data are generated and optimized by applying in a case study i.e. a withdrawal task in Bank ATM through Harmony search.It is observed that this algorithm generates suitable test cases as well as test data and gives brief details about the Harmony search method.It is used for test data generation and optimization.

Optimal design of Complementary Metal Oxide Semiconductor (CMOS) differential amplifier circuit using Opposition based Harmony Search technique (OHS) is reported in this work. The original Harmony Search (HS) algorithm is chosen as heart of the OHS for near-global convergence. Each solution in Harmony Memory (HM) is generated on the basis of memory consideration rule, a pitch adjustment rule and a reinitialization process which gives the optimum result corresponding to the least error fitness in multidimensional search space. Incorporation of different control parameters in basic HS algorithm results in balancing of exploration and exploitation of search space. The proposed OHS based CMOS analog amplifier circuit design has alleviated from inherent drawbacks of premature convergence and stagnation, unlike Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Differential Evolution (DE). To confirm the superiority of the OHS based technique, SPICE simulation is also carried out by using the optimized parameters achieved by employing OHS. Results presented for the optimally designed amplifier circuit confirm the superiority of the proposed OHS based technique over DE, harmony search (HS), artificial bee colony (ABC) and PSO in terms of convergence speed, design criteria and design objectives. Simulation results confirm that OHS based designed amplifier circuit not only provides the least MOS transistor area, but it also provides improved gain and dissipates least power than the reported works.

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.

Job shop scheduling problem (JSSP) has drawn a lot of attention as it is one of the vital combinational optimization problems in manufacturing systems. In this paper, a differential-based harmony search (DHS) algorithm with variable neighborhood search (VNS) is proposed for solving JSSP with the objective of minimized makespan. Since the standard harmony search algorithm is constructed for global optimization problems, the smallest position value is introduced to map a harmony vector to an active schedule. The active decoding scheme is employed to improve the search efficiency of DHS. In the pitch-adjustment process, the best individual of the current harmony memory is employed to accelerate the convergence speed. After the pitch-adjustment process, the differential-based enhanced mechanism is designed to maintain the diversity of the population. The modified VNS, which is based on the blocks on the critical path, is embedded into DHS to search for a better solution around the current harmony vector. Besides, the runtime of DHS is analyzed according to the level-based theorem. Compared with various HS-based algorithms and other state-of-the-art algorithms on a set of typical benchmark instances, the DHS is superior to the compared algorithms in terms of solution quality, convergence speed, and stability. The DHS lays a solid foundation for solving optimization problems of expert and intelligent systems.

Harmony Search (HS) algorithm is a new meta-heuristic global search algorithm. To solve the algorithm easily fall into the local optimal problem, this paper proposes an adaptive novel global harmony search (ANGHS) algorithm based on NGHS algorithm. First, a new location update strategy is given using the adjustment parameter F. Then, the mutation operation is introduced in the case of excluding the small probability Pm. In order to avoid blind adjustment of the step size in the late search and effectively adjust the structure of the solution, the definition of the norm is introduced to adjust parameter bw dynamically. In this paper, 7 standard Benchmark functions are used to simulate the experiment. The results show that the algorithm avoids the premature problem of the algorithm and enhances the global search ability of the algorithm, with obvious improvement in convergence speed and stability, and has good optimize performance.

Harmony search (HS) algorithm is an emerging population oriented stochastic metaheuristic algorithm, which is inspired by the music improvisation process. This paper introduces an Amended harmony search (AHS) algorithm for solving optimization problems. In AHS, an enhanced approach is employed for generating better solution that improves accuracy and convergence speed of harmony search (HS). The effects of various parameters on harmony search algorithm are analyzed in this paper. The proposed approach performs fine tuning of two parameters bandwidth and pitch adjustment rate. The proposed algorithm is demonstrated on complex benchmark functions and results are compared with two recent variants of HS optimization algorithms, improved harmony search (IHS) and highly reliable harmony search (HRHS). Results suggested that the AHS method has strong convergence and has better balance capacity of exploration and exploitation.

Evolutionary optimization algorithms have been recently applied to optimal digital IIR filter design. In this paper, we apply a Bandwidth Adaptive Harmony Search (BAHS) algorithm to the design of 1-dimensional IIR filters. Harmony Search is an evolutionary algorithm, which emulates the improvisation process of musicians. We have modified the algorithm by setting the bandwidth equal to the standard deviation of the vectors in the harmony memory, and by introducing a penalty function to ensure IIR filter stability. The proposed variant has been applied to the design of low-pass, high-pass, band pass and band stop filters, by minimizing the L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> and L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> norm approximation errors and the maximum pass band and stop band ripples. The algorithm has been compared with the TIA approach. The harmony search variant has been found to outperform the TIA approach in designing IIR filters having near-desired frequency responses.

In this study, a truss system is optimized with the Harmony Search Algorithm (HS) inspired by the process of searching for the best harmony. It is compared with the Adaptive Harmony Search Algorithm whose initial values of parameters are defined and gradually decrease. The optimization process is aimed to optimize the volume by calculating the optimum volume of the elements of the truss system. In design, the effect of design factors specific to the harmony search algorithm on optimization was investigated. For this purpose, optimization was performed with different harmony memory consideration ratio (HMCR) values. By adapting the harmony search algorithm, optimum results are obtained for the values that gradually decrease according to the HMCR and fret width (FW) values. Optimum volume function with the lowest standard deviation values was obtained with adaptive harmony search optimization in the mean of the optimum value found for both optimizations.KeywordsTruss systemHarmony searchAdaptive harmony searchStructural engineeringOptimization

Integer programming and minimax problems are essential tools in solving various problems that arise in data mining and machine learning such as multi-class data classification and feature selection problems. In this paper, we propose a new hybrid harmony search algorithm by combining the harmony search algorithm with the multidirectional search method in order to solve the integer programming and minimax problems. The proposed algorithm is called multidirectional harmony search algorithm (MDHSA). MDHSA starts the search by applying the standard harmony search for numbers of iteration then the best-obtained solution is passing to the multidirectional search method as an intensification process in order to accelerate the search and overcome the slow convergence of the standard harmony search algorithm. The proposed algorithm is balancing between the global exploration of the harmony search algorithm and the deep exploitation of the multidirectional search method. MDHSA algorithm is tested on seven integer programming problems and 15 minimax problems and compared against 12 algorithms for solving integer programming problems and 11 algorithms for solving minimax problems. The experiments results show the efficiency of the proposed algorithm and its ability to solve integer programming and minimax problems in reasonable time.

To enhance the performance of harmony search (HS) algorithm on solving the discrete optimization problems, this paper proposes a novel harmony search algorithm based on teaching-learning (HSTL) strategies to solve 0-1 knapsack problems. In the HSTL algorithm, firstly, a method is presented to adjust dimension dynamically for selected harmony vector in optimization procedure. In addition, four strategies (harmony memory consideration, teaching-learning strategy, local pitch adjusting, and random mutation) are employed to improve the performance of HS algorithm. Another improvement in HSTL method is that the dynamic strategies are adopted to change the parameters, which maintains the proper balance effectively between global exploration power and local exploitation power. Finally, simulation experiments with 13 knapsack problems show that the HSTL algorithm can be an efficient alternative for solving 0-1 knapsack problems.

A method based on harmony search (HS) algorithm for designing an optical comb generator with excellent flatness is proposed. The comb generator with simple structure consists of four phase modulators with a single laser as the input, single radio frequency (RF) bias with different amplitudes, and DC bias for each modulator. No RF phase shifter, filter, or fiber loop is needed. Instead of following a classic mathematical model for finding the values of RF amplitudes and DC voltages for generating an optical comb, HS algorithm is implemented, which is an intelligent algorithm inspired from the improvisation of music players and seeks for the most harmonized answers corresponding to flat optical combs. The simulation results of generating two sets of optical combs by HS algorithm with 43 and 53 lines with flatness of 0.51 and 0.59 dB and then after inclusion of power conversion efficiency in the objective function of HS algorithm, two other sets of combs with 47 and 55 lines, flatness of 1.64 and 1.77 dB, and power conversion efficiency of 28% and 32% are presented. Such a device can be used in wavelength-division multiplexing systems and many other applications.

Hybrid harmony search and artificial bee colony algorithm for global optimization problems

This work presents the development of multi-objective harmony search (MOHS) algorithm for optimization problem using self-adaptive improved harmony search (SIHS) algorithm which is a variant of recently developed harmony search algorithm (HS) for single objective optimization. The approach used in this work is decomposing of multiple objectives into several single objective functions which are simultaneously optimized in such a way that a nearly uniform distribution of the solutions along the pareto-front is followed. The algorithm upon testing for standard test functions has shown promising results.KeywordsHarmony SearchMulti-objective optimizationPareto front

An improved harmony search algorithm for power economic load dispatch