Durbadal Mandal

Cat Swarm Optimization algorithm for optimal linear phase FIR filter design.

In this paper a new meta-heuristic search method, called Cat Swarm Optimization (CSO) algorithm is applied to determine the best optimal impulse response coefficients of FIR low pass, high pass, band pass and band stop filters, trying to meet the respective ideal frequency response characteristics. CSO is generated by observing the behaviour of cats and composed of two sub-models. In CSO, one can decide how many cats are used in the iteration. Every cat has its own position composed of M dimensions, velocities for each dimension, a fitness value which represents the accommodation of the cat to the fitness function, and a flag to identify whether the cat is in seeking mode or tracing mode. The final solution would be the best position of one of the cats. CSO keeps the best solution until it reaches the end of the iteration. The results of the proposed CSO based approach have been compared to those of other well-known optimization methods such as Real Coded Genetic Algorithm (RGA), standard Particle Swarm Optimization (PSO) and Differential Evolution (DE). The CSO based results confirm the superiority of the proposed CSO for solving FIR filter design problems. The performances of the CSO based designed FIR filters have proven to be superior as compared to those obtained by RGA, conventional PSO and DE. The simulation results also demonstrate that the CSO is the best optimizer among other relevant techniques, not only in the convergence speed but also in the optimal performances of the designed filters.

A new design method using opposition-based BAT algorithm for IIR system identification problem

BAT algorithm BA is a meta-heuristic algorithm, based on the echolocation behaviour of bats. In this paper, optimal set of filter coefficients is searched by the modified optimisation methodology called opposition-based BAT algorithm OBA for infinite impulse response IIR system identification problem. Opposition based numbering concept is embedded into the primary foundation of BA metaphorically to enhance the convergence speed and performance for finding better near-global optimal solution. Detailed and balanced search in multidimensional problem space is accomplished with judiciously chosen control parameters of OBA technique. When tested against standard benchmark examples, for same and reduced order models, the simulation results establish the OBA as a more competent candidate to other evolutionary algorithms as real coded genetic algorithm RGA, differential evolution DE and particle swarm optimisation PSO in terms of accuracy and convergence speed.

Design and simulation of FIR band pass and band stop filters using gravitational search algorithm

In this paper, a new optimization method named gravitational search algorithm (GSA) is adopted for designing optimal linear phase finite impulse response band pass (BP) and band stop (BS) digital filters. Other various population based evolutionary algorithms like real coded genetic algorithm, conventional particle swarm optimization, differential evolution (DE), bee swarm optimization have also been applied for the sake of comparative study of the same optimal designs. In GSA, particles are considered as objects and their performances are measured by their masses. All these objects attract each other by gravity forces, and these forces produce global movements of all objects towards the objects with heavier masses. GSA guarantees the exploitation step of the algorithm and it is apparently free from premature convergence. Extensive simulation results justify superior optimization capability of GSA over the afore-mentioned optimization techniques for the solution of the multimodal, non-differentiable, highly non-linear, and constrained filter design problems.

Efficient and accurate optimal linear phase FIR filter design using opposition-based harmony search algorithm.

In this paper, opposition-based harmony search has been applied for the optimal design of linear phase FIR filters. RGA, PSO, and DE have also been adopted for the sake of comparison. The original harmony search algorithm is chosen as the parent one, and opposition-based approach is applied. During the initialization, randomly generated population of solutions is chosen, opposite solutions are also considered, and the fitter one is selected as a priori guess. In harmony memory, each such solution passes through memory consideration rule, pitch adjustment rule, and then opposition-based reinitialization generation jumping, which gives the optimum result corresponding to the least error fitness in multidimensional search space of FIR filter design. Incorporation of different control parameters in the basic HS algorithm results in the balancing of exploration and exploitation of search space. Low pass, high pass, band pass, and band stop FIR filters are designed with the proposed OHS and other aforementioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the OHS over the other optimization techniques for the solution of the multimodal, nondifferentiable, nonlinear, and constrained FIR filter design problems.

Harmony search algorithm for infinite impulse response system identification

In this paper, optimal sets of filter coefficients are searched by a meta-heuristic optimization technique called Harmony Search (HS) algorithm for infinite impulse response (IIR) system identification problem. For different optimization problems, HS algorithm undergoes three basic rules; namely Random Selection (RS), Harmony Memory Consideration (HMC), and Pitch Adjustment (PA) rules, which are inspired from the process that the musicians use to improvise a perfect state of harmony with the consummate skill of blending notes in tune. With the help of the properly selected control parameters, a perfect balance is achieved in exploration and exploitation in searching phases. The detailed analysis of simulation results emphasizes the strength of HS algorithm to find the near-global optimal solution, quality of convergence profile and the speed of convergence while tested against standard benchmark examples for same and reduced order models.

Optimal and accurate design of fractional-order digital differentiator – an evolutionary approach

This study deals with the implementation of highly accurate, stable, minimum phase, and wideband fractional-order digital differentiators (FODDs) in terms of infinite impulse response filters using an efficient evolutionary optimisation algorithm called adaptive Gbest-guided gravitational search algorithm (GGSA). Performance evaluation of GGSA as compared with real coded genetic algorithm (RGA), particle swarm optimisation (PSO), and differential evolution (DE) based designs are carried out in terms of different magnitude and phase response error metrics, solution quality reliability, and convergence speed. Simulation results clearly demonstrate that GGSA significantly outperforms RGA, PSO, and DE in consistently achieving the most accurate FODDs in a computationally efficient manner. The proposed FODDs also significantly outperform all state-of-the-art designs in terms of magnitude responses.

An Efficient Craziness Based Particle Swarm Optimization Technique for Optimal IIR Filter Design

In this paper an improved version of Particle Swarm Optimization (PSO) called Craziness based PSO (CRPSO) is considered as an efficient optimization tool for designing digital Infinite Impulse Response (IIR) filters. Apart from gaining better control on cognitive and social components of conventional PSO, the CRPSO dictates better performance due to incorporation of craziness parameter in the velocity equation of PSO. This modification in the velocity equation not only ensures the faster searching in the multidimensional search space but also the solution produced is very close to the global optimal solution. The effectiveness of this algorithm is justified with a comparative study of some well established algorithms, namely, Real coded Genetic Algorithm (RGA) and conventional Particle Swarm Optimization (PSO) with a superior CRPSO based outcome for the designed 8th order IIR low pass (LP), high pass (HP), band pass (BP) and band stop (BS) filters. Simulation results affirm that the proposed CRPSO algorithm outperforms its counterparts not only in terms of quality output, i.e., sharpness at cut-off, pass band ripple and stop band attenuation but also in convergence speed with assured stability.

Optimal design of wideband digital integrators and differentiators using hybrid flower pollination algorithm

In this paper, a recently proposed metaheuristic optimization technique called hybrid flower pollination algorithm (HFPA) is applied to design wideband infinite impulse response digital differentiators (DDs) and digital integrators (DIs). In recent years, benchmark nature-inspired optimization algorithms such as particle swarm optimization (PSO), simulated annealing, and genetic algorithm have been employed for the design of wideband DDs and DIs. However, individually, these algorithms show major drawbacks such as premature convergence, thus leading to a sub-optimal solution. HFPA, however, is a hybrid approach which combines the efficient exploitation and exploration capabilities of two different metaheuristics, namely PSO and flower pollination algorithm (FPA), respectively. The HFPA-based designs have been compared with real-coded genetic algorithm, PSO, differential evolution, success-history-based adaptive differential evolution with linear population size reduction (L-SHADE), self-adaptive differential evolution (jDE), and FPA-based designs with respect to the solution quality, robustness, convergence, and optimization time. Simulation results demonstrate that among all the algorithms, the HFPA-based designs consistently achieve superior performances in the least number of function evaluations. Exhaustive experimentations are conducted to determine the best values of the control parameters of HFPA for the optimal design of DDs and DIs. The proposed designs also outperform the recently reported designs based on non-optimal, classical, and nature-inspired optimization approaches in terms of magnitude response. The lower orders of the proposed designs render them suitable for real-time applications.

Improved Particle Swarm Optimization with wavelet mutation: Application to linear phase FIR filter design

In this paper, various swarm based algorithms like conventional Particle Swarm Optimization PSO, Improved Particle Swarm Optimization IPSO and another novel Improved Particle Swarm Optimization with Wavelet Mutation IPSOWM have been applied for the optimal design of linear phase FIR filters. Real coded genetic algorithm RGA has also been adopted for the sake of comparison. IPSO uses new definition for the velocity vector. Whereas in addition to the above-mentioned new definition added in IPSO, IPSOWM incorporates a new definition of swarm updating with the help of wavelet mutation based on wavelet theory. Wavelet mutation enhances the PSO to explore the solution space more effectively compared to the other optimization methods. IPSOWM is apparently free from getting trapped at local optima and premature convergence. Low pass LP, high pass HP, band pass BP and band stop BS FIR filters are designed with the proposed IPSOWM and other afore-mentioned algorithms individually for comparative optimization performance. A comparison of simulation results reveals the optimization efficacy of the IPSOWM over the other optimization techniques for the solution of the multimodal, non-differentiable, highly non-linear, and constrained FIR filter design problems.

Optimal design of fractional order low pass Butterworth filter with accurate magnitude response

Abstract The design of ( 1 + α ) order, 0 α 1 , low pass Butterworth filter approximated in terms of an integer order continuous-time transfer function using a nature-inspired optimization technique called Gravitational Search Algorithm (GSA) is presented in this paper. While approximations of the non-integer order Laplacian operator s α in terms of second order rational function using the continued fraction expansion method for the design of fractional order low pass Butterworth filters (FOLBFs) is recently reported in literature, however, such a design technique is non-optimal. In this work, the metaheuristic global search process of GSA efficiently explores and intensely exploits the nonlinear, non-uniform, multidimensional, and multimodal FOLBF design problem error landscape. At the end of the iterative search routine of GSA, the optimal values of the coefficients in terms of the third order rational approximations are achieved which accurately approximate the magnitude response of the ideal FOLBF. The proposed GSA based FOLBFs consistently achieve the best solution quality with the fastest convergence rate as compared with the designs based on Real coded Genetic Algorithm (RGA) and Particle Swarm Optimization (PSO). Comparison with the recent literature also demonstrates the superiority of the proposed designs. SPICE simulations justify the design feasibility of the proposed FOLBF models.