Design of optimal digital IIR filters by using a Bandwidth Adaptive Harmony Search algorithm

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

In the recent years, the digital IIR filter design as a single objective optimization problem using evolutionary algorithms has gained much attention. In this paper, the digital IIR filter design is treated as a multiobjective problem by minimizing the magnitude response error, linear phase response error and optimal order simultaneously along with meeting the stability criterion. Hybrid gravitational search algorithm (HGSA) has been applied to design the digital IIR filter. GSA technique is hybridized with binary successive approximation (BSA) based evolutionary search method for exploring the search space locally. The relative performance of GSA and hybrid GSA has been evaluated by applying these techniques to standard mathematical test functions. The above proposed hybrid search techniques have been applied effectively to solve the multiparameter and multiobjective optimization problem of low-pass (LP), high-pass (HP), band-pass (BP), and band-stop (BS) digital IIR filter design. The obtained results reveal that the proposed technique performs better than other algorithms applied by other researchers for the design of digital IIR filter with conflicting objectives.

In this chapter an improved version of harmony search algorithm called an adaptive harmony search algorithm is presented. The harmony memory considering rate and pitch adjusting rate are conceived as the two main parameters of the technique for generating new solution vectors. In the standard implementation of the technique, appropriate constant values are assigned to these parameters following a sensitivity analysis for each problem considered. The success of the optimization process is directly related to a chosen parameter value set. The adaptive harmony search algorithm proposed here incorporates a novel approach for adjusting these parameters automatically during the search for the most efficient optimization process. The efficiency of the proposed algorithm is numerically investigated using number of steel frameworks that are designed for minimum weight according to the provisions of various international steel design code specifications. The solutions obtained are compared with those of the standard algorithm as well as those of the other meta-heuristic search techniques. It is shown that the proposed algorithm improves performance of the technique and it renders unnecessary the initial selection of the harmony search parameters.

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.

In recent decades, evolutionary optimisation algorithms have been used successfully for a wide variety of water resources engineering problems and their applications are still increasing. In this research work, a hybrid harmony search algorithm, ‘Non‐dominated Sorting Harmony Search’ algorithm is developed and compared with two state‐of‐the‐art multi‐objective evolutionary algorithms – the non‐dominated sorting genetic algorithm (NSGA)‐IIand multi‐objective particle swarm optimisation (MOPSO) algorithms – for assigning optimal rehabilitation plans for sewer pipe networks. The algorithms considered were validated using some standard test functions reported in the literature and compared with each other in terms of several metrics. These algorithms were then linked to theSWMM‐EPAhydraulic model and applied to a storm sewer pipe network case study in Seoul, South Korea, to obtain the best rehabilitation plans for pipe replacements. The results showed that the algorithms considered have different behaviours in solving the benchmark tests and rehabilitation problem. The proposed hybrid multi‐objective harmony search algorithm provides better optimal solutions in terms of different metrics and clearly outperforms the other two algorithms for the rehabilitation of the storm sewer pipe networks.

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.

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.

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.

Basic IIR and FIR digital filters design techniques are reviewed, with emphasis on various analog-to-digital conversion methods for deriving IIR filter transfer functions, as well as windowing and frequency sampling methods for FIR filters design. The computational algorithm of filtering is then realized in recursive and nonrecursive network structures for hardware implementation. The recently developed INTEL 2920 signal processor is used for demonstrating the implementation of the four basic operations of digital filtering: input/output, add/subtract, multiply and unit delay. Key features of other similar processors are also listed.

Segmentation is one of the most important tasks in image processing that endeavors to classify pixels into two or more groups according to their intensity levels and a threshold value. Since traditional image processing techniques exhibit several difficulties when they are employed to segment images, the use of evolutionary algorithms has been extended to segmentation tasks in last years. The Harmony Search Algorithm (HSA) is an evolutionary method which is inspired in musicians improvising new harmonies while playing. Different to other evolutionary algorithms, HSA exhibits interesting search capabilities still keeping a low computational overhead. In this chapter, a multilevel thresholding (MT) algorithm based on the HSA is presented. The approach combines the good search capabilities of HSA with objective functions suggested by the popular MT methods of Otsu and Kapur. The presented algorithm takes random samples from a feasible search space inside the image histogram. Such samples build each harmony (candidate solution) in the HSA context whereas its quality is evaluated considering the objective function that is employed by the Otsu’s or Kapur’s method. Guided by these objective values, the set of candidate solutions are evolved through HSA operators until an optimal solution is found. The approach generates a multilevel segmentation algorithm which can effectively identify threshold values of a digital image in a reduced number of iterations. Experimental results show a high performance of the presented method for the segmentation of digital images.

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.

A dynamical search space harmony search (DSHS) algorithm in order to improve the efficiency of standard harmony search algorithm. The DSHS employs two strategies which are dynamically changing the search space and ancillary harmony-memory to increase the diversity of harmonies and the global search ability. First the ratio of twin-harmony is defined which is an index of identifying the diversity of harmonies in the Harmony Memory (HM). Then the search space is dynamically changed according to the max ratio of twin-harmony. Finally, ancillary harmony-memories are introduced to replace worse harmonies in the HM, which can keep the main HM from getting into troubles of HM diversity lacking and the local minimum point. Various benchmarks and PID tuning problem are performed to demonstrate the effectiveness of proposed algorithm.

An improved harmony search algorithm for power economic load dispatch

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.

This paper proposes a conceptual modification of the interpolator used by the extended window design (EWD) of IIR and fractional delay filters. The original EWD digitizes analog filters by performing a trigonometric polynomial interpolation along an extended window that ends at the current sampling time. The proposed changes increase the flexibility and the degrees of freedom of the interpolator in two ways. First, the interpolation space is expanded from the space spanned by a restricted set of sinusoidal functions to the space spanned by any set of linearly independent functions. Second, the Hermite interpolation (which processes the values of both the signal and some of its derivatives at sampling times) is considered in order to smoothen the interpolated signal. Since the input derivatives are not available, related parameters are estimated and updated recursively. The increased accuracy of the proposed recursive EWD relatively to nonrecursive EWD and WLS optimal filter designs is illustrated with an example.