Millie Pant

Particle swarm optimization: Hybridization perspectives and experimental illustrations

Metaheuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods. In the present study an attempt is made to review the hybrid optimization techniques in which one main algorithm is a well known metaheuristic; particle swarm optimization or PSO. Hybridization is a method of combining two (or more) techniques in a judicious manner such that the resulting algorithm contains the positive features of both (or all) the algorithms. Depending on the algorithm/s used we made three classifications as (i) Hybridization of PSO and genetic algorithms (ii) Hybridization of PSO with differential evolution and (iii) Hybridization of PSO with other techniques. Where, other techniques include various local and global search methods. Besides giving the review we also show a comparison of three hybrid PSO algorithms; hybrid differential evolution particle swarm optimization (DE-PSO), adaptive mutation particle swarm optimization (AMPSO) and hybrid genetic algorithm particle swarm optimization (GA-PSO) on a test suite of nine conventional benchmark problems.

An efficient Differential Evolution based algorithm for solving multi-objective optimization problems

In the present study, a modified variant of Differential Evolution (DE) algorithm for solving multi-objective optimization problems is presented. The proposed algorithm, named Multi-Objective Differential Evolution Algorithm (MODEA) utilizes the advantages of Opposition-Based Learning for generating an initial population of potential candidates and the concept of random localization in mutation step. Finally, it introduces a new selection mechanism for generating a well distributed Pareto optimal front. The performance of proposed algorithm is investigated on a set of nine bi-objective and five tri-objective benchmark test functions and the results are compared with some recently modified versions of DE for MOPs and some other Multi Objective Evolutionary Algorithms (MOEAs). The empirical analysis of the numerical results shows the efficiency of the proposed algorithm.

Optimal coordination of over-current relays using modified differential evolution algorithms

Optimization of directional over-current relay (DOCR) settings is an important problem in electrical engineering. The optimization model of the problem turns out to be non-linear and highly constrained in which two settings namely time dial setting (TDS) and plug setting (PS) of each relay are considered as decision variables; the sum of the operating times of all the primary relays, which are expected to operate in order to clear the faults of their corresponding zones, is considered as an objective function. In the present study, three models are considered namely IEEE 3-bus model, IEEE 4-bus model and IEEE 6-bus model. To solve the problem, we have applied five newly developed versions of differential evolution (DE) called modified DE versions (MDE1, MDE2, MDE3, MDE4, and MDE5). The results are compared with the classical DE algorithm and with five more algorithms available in the literature; the numerical results show that the modified DE algorithms outperforms or perform at par with the other algorithms.

A Simple Diversity Guided Particle Swarm Optimization

In this paper we have proposed a new diversity guided particle swarm optimizer (PSO), namely ATRE-PSO, which is a modification of attractive and repulsive PSO (ARPSO), suggested by Riget and Vesterstorm [1]. Depending on the diversity of the population the ATRE-PSO switches alternately between three phases of attraction, repulsion and a combination of attraction and repulsion, called the phase of positive conflict [2]. The performance of ATRE-PSO is compared with basic PSO (BPSO) and ARPSO. The numerical results show that besides preserving the rapid convergence of the BPSO, ATRE-PSO also maintains a good diversity in the population. Under most of the test cases, simulations show that ATRE-PSO finds a better solution than BPSO as well as ARPSO.

Improving the performance of differential evolution algorithm using Cauchy mutation

Differential evolution (DE) is a powerful yet simple evolutionary algorithm for optimization of real-valued, multimodal functions. DE is generally considered as a reliable, accurate and robust optimization technique. However, the algorithm suffers from premature convergence and/or slow convergence rate resulting in poor solution quality and/or larger number of function evaluation resulting in large CPU time for optimizing the computationally expensive objective functions. Therefore, an attempt to speed up DE is considered necessary. This research introduces a modified differential evolution (MDE) that enhances the convergence rate without compromising with the solution quality. The proposed MDE algorithm maintains a failure_counter (FC) to keep a tab on the performance of the algorithm by scanning or monitoring the individuals. Finally, the individuals that fail to show any improvement in the function value for a successive number of generations are subject to Cauchy mutation with the hope of pulling them out of a local attractor which may be the cause of their deteriorating performance. The performance of proposed MDE is investigated on a comprehensive set of 15 standard benchmark problems with varying degrees of complexities and 7 nontraditional problems suggested in the special session of CEC2008. Numerical results and statistical analysis show that the proposed modifications help in locating the global optimal solution in lesser numbers of function evaluation in comparison with basic DE and several other contemporary optimization algorithms.

An image watermarking scheme in wavelet domain with optimized compensation of singular value decomposition via artificial bee colony

Digital image watermarking is the process of authenticating a digital image by embedding a watermark into it and thereby protecting the image from copyright infringement. This paper proposes a novel robust image watermarking scheme developed in the wavelet domain based on the singular value decomposition (SVD) and artificial bee colony (ABC) algorithm. The host image is transformed into an invariant wavelet domain by applying redistributed invariant wavelet transform, subsequently the low frequency sub-band of wavelet transformed image is segmented into non-overlapping blocks. The most suitable embedding blocks are selected using the human visual system for the watermark embedding. The watermark bits are embedded into the target blocks by modifying the first column coefficients of the left singular vector matrix of SVD decomposition with the help of a threshold and the visible distortion caused by the embedding is compensated by modifying the coefficients of the right singular vector matrix employing compensation parameters. Furthermore, ABC is employed to obtain the optimized threshold and compensation parameters. Experimental results, compared with the related existing schemes, demonstrated that the proposed scheme not only possesses the strong robustness against image manipulation attacks, but also, is comparable to other schemes in term of visual quality.

Enhancing the food locations in an artificial bee colony algorithm

Artificial bee colony or ABC is one of the newest additions to the class of population based Nature Inspired Algorithms. In the present study we suggest some modifications in the structure of basic ABC to further improve its performance. The corresponding algorithms proposed in the present study are named Intermediate ABC (I-ABC) and I-ABC greedy. In I-ABC, the potential food sources are generated by using the intermediate positions between the uniformly generated random numbers and random numbers generated by opposition based learning (OBL). I-ABC greedy is a variation of I-ABC, where the search is always forced to move towards the solution vector having the best fitness value in the population. While the use of OBL provides a priori information about the search space, the component of greediness improves the convergence rate. The performance of proposed I-ABC and I-ABC greedy are investigated on a comprehensive set of 13 classical benchmark functions, 25 composite functions included in the special session of CEC 2005 and eleven shifted functions proposed in the special session of CEC 2008, ISDA 2009, CEC 2010 and SOCO 2010. Also, the efficiency of the proposed algorithms is validated on two real life problems; frequency modulation sound parameter estimation and to estimate the software cost model parameters. Numerical results and statistical analysis demonstrates that the proposed algorithms are quite competent in dealing with different types of problems.

Particle Swarm Optimization Using Adaptive Mutation

Two new variants of particle swarm optimization (PSO) called AMPSO1 and AMPSO2 are proposed for global optimization problems. Both the algorithms use adaptive mutation using beta distribution. AMPSO1 mutates the personal best position of the swarm and AMPSO2, mutates the global best swarm position. The performance of proposed algorithms is evaluated on twelve unconstrained test problems and three real life constrained problems taken from the field of electrical engineering. The numerical results show the competence of the proposed algorithms with respect some other contemporary techniques.

Multi-level image thresholding by synergetic differential evolution

The multi-level image thresholding is often treated as a problem of optimization. Typically, finding the parameters of these problems leads to a nonlinear optimization problem, for which obtaining the solution is computationally expensive and time-consuming. In this paper a new multi-level image thresholding technique using synergetic differential evolution (SDE), an advanced version of differential evolution (DE), is proposed. SDE is a fusion of three algorithmic concepts proposed in modified versions of DE. It utilizes two criteria (1) entropy and (2) approximation of normalized histogram of an image by a mixture of Gaussian distribution to find the optimal thresholds. The experimental results show that SDE can make optimal thresholding applicable in case of multi-level thresholding and the performance is better than some other multi-level thresholding methods.

Optimal gain tuning of PI speed controller in induction motor drives using particle swarm optimization

This article presents particle swarm optimization (PSO)-based optimal gain tuning of proportional integral (PI) speed controller in an induction motor (IM) drive (30 hp) with mine hoist load diagram. Optimization considers the load and speed variations, and provides appropriate gains to the speed controller to obtain good dynamic performance of the motor. IM performance is checked with the optimal gains through the simulation studies in MATLAB/SIMULINK environment. Results are compared with hand tuning (fixed gains) and fuzzy logic (FL) speed controller. Hybrid of FL and PSO-based PI controller for the speed control of given motor is also performed to eliminate the drawbacks of PI controller (overshoot and undershoot) and FL controller (steady-state error). From the simulation studies, hybrid controller produces better performance in terms of rise time, overshoot and settling time.