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Harmony Search (HS) is a metaheuristic optimisation algorithm inspired by musical improvisation. So far it has been applied to various optimisation problems, and there are several application-oriented review papers. However, this review paper tries to focus on the historical development of algorithm structure instead of applications. This paper explains the original HS algorithm along with a selection of modified and hybrid HS methods: adaption of original operators of the basic harmony search, parameter adaption, hybrid methods, handling multi-objective optimisation problems and constraint handling.

This paper proposes a novel scalable multimodal multiobjective test problem suite. The proposed test problems have various properties, such as presence of local Pareto optimal set (PS), scalable number of PSs, nonuniformly distributed PSs, discrete Pareto front (PF), and scalable number of variables and objectives. All of the test problems proposed in this paper are continuous optimization problems. Therefore, they can be used to measure different capacities of multimodal multiobjective continuous optimization algorithms. Moreover, a landscape visualization method for multiobjective problems is proposed to show the properties of the multimodal multiobjective test problems. Based on the landscapes, the characteristics of these problems are analyzed and characterized. Furthermore, the existing multimodal multiobjective optimization algorithms and several popular multiobjective algorithms are tested and compared with the novel test problem suite. Then, a discussion on the desired properties of multimodal multiobjective optimization algorithms and future works on multimodal multiobjective optimization are presented.

Whale Optimization Algorithm (WOA) is an optimization algorithm developed by Mirjalili and Lewis in 2016. An overview of WOA is described in this paper, rooted from the bubble-net hunting strategy, besides an overview of WOA applications that are used to solve optimization problems in various categories. The best solution has been determined to make something as functional and effective as possible through the optimization process by minimizing or maximizing the parameters involved in the problems. Research and engineering attention have been paid to Meta-heuristics for purposes of decision-making given the growing complexity of models and the needs for quick decision making in the engineering. An updated review of research of WOA is provided in this paper for hybridization, improved, and variants. The categories included in the reviews are Engineering, Clustering, Classification, Robot Path, Image Processing, Networks, Task Scheduling, and other engineering applications. According to the reviewed literature, WOA is mostly used in the engineering area to solve optimization problems. Providing an overview and summarizing the review of WOA applications are the aims of this paper.

This paper investigates a hypothesis that in case of hard optimization problems, selection of the proper search space is more relevant than the choice of the solving algorithm. Dynamic Vehicle Routing Problem is used as a test problem and the hypothesis is verified experimentally on the well-known set of benchmark instances. The paper compares Particle Swarm Optimization (PSO) and Differential Evolution (DE) operating in two continuous search spaces (giving in total four distinctive approaches) and a state-of-the art discrete encoding utilizing Genetic Algorithm (GA). The advantage of selected continuous search space over a discrete one is verified on the basis of quality of the final solution and stability of intermediate partial solutions. During stability analysis it has been observed that practical level of uncertainty, resulting from the dynamic nature of the problem, is lower than could be expected from a popular degree of dynamism measure. In order to challenge that issue, benchmark problems have been solved also with a higher level of dynamism and an empirical degree of dynamism has been proposed as an additional measure of the amount of uncertainty of the problem. The results obtained by both continuous algorithms outperform those of state-of-the-art algorithms utilizing discrete problem representation, while the performance differences between them (PSO and DE) are minute. Apart from higher numerical efficiency in solving DVRP, the use of continuous problem encoding proved its advantage over discrete encoding also in terms of intermediate solutions stability. Requests-to-vehicles assignment sequences generated by the proposed approach were approximately 40% more accurate with respect to the final solution than their counterparts generated with a discrete encoding. Analysis of these sequences of intermediate solutions for several benchmark sets resulted in designing a penalty term taking into account a specific dynamic nature of the optimized problem. An addition of this penalty term improved the above-mentioned stability of partial solutions by another 10%.

One of the main current applications of Intelligent Systems are Recommender systems (RS). RS can help users to find relevant items in huge information spaces in a personalized way. Several techniques have been investigated for the development of RS. One of them are Swarm Intelligence (SI) techniques, which are an emerging trend with various application areas. Although the interest in using Computational Intelligence in web personalization and information retrieval fostered the publication of some survey papers, these surveys so far focused on different application domains, e.g., clustering, or were too broadly focused and incorporated only a handful of SI approaches. This study provides a comprehensive review of 77 research publications applying SI in RS. The study focus on five aspects we consider relevant for such: the recommendation technique used, the datasets and the evaluation methods adopted in their experimental parts, the baselines employed in the experimental comparison of proposed approaches and the reproducibility of the reported results. At the end of this review, we discuss negative and positive aspects of these papers, as well as point out opportunities, challenges and possible future research directions. To the best of our knowledge, this survey is the most comprehensive review of approaches using SI in RS. Therefore, we believe this review will be a relevant material for researchers interested in either of the domains.

In this paper, we propose a multi-agent based art production framework. In existing artwork creation systems, images were generated using artificial life and evolutionary computation approaches. In artificial life, swarm intelligence or Boids model, and in evolutionary computation, genetic algorithm or genetic programming are commonly used to create images. These automated artwork creation systems make it easy to create artistic images even if the users are not professional artists. Despite the high possibility of these creation systems, however, much research has not been done so far. In this paper, we propose an art production framework that generates images using multi-agents with chaotic dynamics features. Agents act on the canvas following the three rules of Boids model. In addition, each agent possesses a chaotic neural network which trained by differential evolution algorithm, so that colors can be evolved to represent a better style. As a result, we propose an art production framework for generating processing artworks that contain highly complex dynamics. Finally, we created the glitch artworks using the proposed framework, which shows a new glitch style.

It makes great economic losses and bad social influence for our country about some accidental drinking water contamination and vicious attacks to water distribution networks. In terms of solving the problems of drinking water contamination caused by accidental contaminant event in water supply network, used the techniques just like sensor network which could determinate the source location to isolate the contaminated area and minimized its hazards. Previous studies have shown that the contamination source determination problem model can be utilized to convert the contamination source determination problem to an unimodal function optimization problem. However, we notice that it is a multimodal function optimization problem in essence and the number of its solution has non-uniqueness feature. In this paper, we first modified the problem model with formulate the threshold value based on the previous works and proposed the niching genetic algorithm calculate multiple contamination sources, and provide the possibility for screening the true contamination source. Furthermore, this paper applies different distribution networks verify the validity after the threshold formulation as well as the effectiveness of algorithm from various aspects.

This paper proposes a novel decomposition method based on user-preference and developed a variation of the decomposition based multi-objective optimization algorithm (MOEA/D) targeting only solutions in a small region of the Pareto-front defined by the preference information supplied by the decision maker (DM). This is particularly advantageous for solving multi-objective optimization problems (MOPs) with more than 3 objectives, i.e., many-objective optimization problems (MaOPs). As the number of objectives increases, the ability of an EMO algorithm to approximate the entire Pareto front ( PF ) is rapidly diminishing. In this paper, we first propose a novel scalarizing function making use of a series of new reference points derived from a reference point specified by the DM in the preference model. Based on this scalarizing function, we then develop a user-preference-based EMO algorithm, namely R-MOEA/D. One key merit of R-MOEA/D is that it does not rely on an estimation of the ideal point, which may impact significantly the performances of state-of-the-art decomposition based EMO algorithms. Our experimental results on multi-objective and many-objective benchmark problems have shown that R-MOEA/D provides a more direct and efficient search towards the preferred PF region, resulting in competitive performances. In an interactive setting when the DM changes the reference point during optimization, R-MOEA/D has a faster response speed and performance than the compared algorithms, showing its robustness and adaptability to changes of the preference model. Furthermore, the effectiveness of R-MOEA/D is verified on a real-world problem of reservoir flood control operations.

The nonlinear behavior of present day power electronic based equipments generates harmonics that lead to overheating, efficiency reduction and malfunctioning of the utility equipments. Shunt active power filters (SAPF), comprising of a three phase voltage source inverter (VSI) and a dc capacitor, are commonly used to eliminate the harmonics at source side. The design of these filters is very important in obtaining satisfactory performances. The classical design methods and the tuning of controller gain parameters may not yield optimal performances. This paper formulates the design of SAPF as an optimization problem with an objective of minimizing the total harmonic distortion (THD) and solves it using predator-prey based firefly optimization (PPFO). The PPFO inherits the features of predator-prey concept and firefly optimization (FO) and helps to get away from the suboptimal traps, thereby ensuring global optimal design. The paper also includes the simulation results of a few test cases representing different types of harmonic loads and illustrates the superior performances of the proposed design philosophy.

A new model and solution for the multi-objective heterogeneous vehicle routing and scheduling problem, with energy minimizing, is presented in this paper. The concept of heterogeneities is concerned with the ownership of fleets. Ownership heterogeneities occur when the private fleet is not sufficient and the company has to rent some vehicles from external carriers to complete the shipments. A new mathematical formulation for vehicle routing problem with time windows (VRPTW) is also presented using the proposed concept of heterogeneities. Moreover, unlike prior attempts to minimize cost by minimizing overall traveling distance, the model also incorporates energy minimizing which meets the latest requirements of green logistics. This paper considers the customers' priority for servicing as well. The proposed model is interpreted as multi-objective optimization and used in two scenarios where, in the first scenario (I), the energy consumed and the total number of vehicles are minimized and the total satisfaction rate of customers is maximized. In the second scenario (II) the distance traveled by the vehicles, the total number of rental vehicles and the fuel consumed by the private vehicles are minimized and the total satisfaction is maximized. A new solution based on an evolutionary algorithm is proposed and its performance on several completely random instances is compared to the non-dominated sorting genetic algorithm II (NSGA II) and CPLEX Solver. The efficiency and effectiveness of the proposed approach is further demonstrated through several computational experiments.

Multi-population based nature-inspired optimization algorithms have attracted wide research interests in the last decade, and become one of the frequently used methods to handle real-world optimization problems. Considering the importance and value of multi-population methods and its applications, we believe it is the right time to provide a comprehensive survey of the published work, and also to discuss several aspects for the future research. The purpose of this paper is to summarize the published techniques related to the multi-population methods in nature-inspired optimization algorithms. Beginning with the concept of multi-population optimization, we review basic and important issues in the multi-population methods and discuss their applications in science and engineering. Finally, this paper presents several interesting open problems with future research directions for multi-population optimization methods.

Grey Wolf Optimizer (GWO) algorithm is a relatively new algorithm in the field of swarm intelligence for solving continuous optimization problems as well as real world optimization problems. The Grey Wolf Optimizer is the only algorithm in the category of swam intelligence which is based on leadership hierarchy. This paper has three important aspects- Firstly, for improving the search ability by grey wolf a modified algorithm RW-GWO based on random walk has been proposed. Secondly, its performance is exhibited in comparison with GWO and state of art algorithms GSA, CS, BBO and SOS on IEEE CEC 2014 benchmark problems. A non-parametric test Wilcoxon and Performance Index Analysis has been performed to observe the impact of improving the leaders in the proposed algorithm. The results presented in this paper demonstrate that the proposed algorithm provide a better leadership to search a prey by grey wolves. The third aspect of the paper is to use the proposed algorithm and GWO on real life application problems. It is concluded from this article that RW-GWO algorithm is an efficient and reliable algorithm for solving not only continuous optimization problems but also for real life optimization problems.

Robust optimisation refers to the process of finding optimal solutions that have the lowest sensitivity to possible perturbations. In a multi-objective search space the robust optimal solutions should have the least dispersion on all of the objectives, making it a more challenging problem than in a single-objective search space. This paper establishes a novel and cheap technique for finding robust optimal solutions called confidence-based robust multi-objective optimisation. This approach uses a novel, modified Pareto dominance operator to differentiate search agents of meta-heuristics based on both levels of robustness and confidence. The proposed confidence-based Pareto dominance allows us to design different confidence-based robust optimisation variants of meta-heuristics based on different methods. As a case study, robust Multi-Objective Particle Swarm Optimisation is equipped with the proposed operator to produce Confidence-based Robust Multi-Objective Particle Swarm Optimisation. A set of specific test functions and performance indicators is employed for benchmarking the Confidence-based Robust Multi-Objective Particle Swarm Optimisation. The results show that the proposed method is able to confidently and reliably find robust optimal solutions without significant extra computational burden. The paper also considers finding the robust Pareto optimal front for a marine propeller design problem to demonstrate the applicability of the approach proposed in solving computationally expensive real-world problems with unknown true robust Pareto optimal fronts.

This paper has solved the transformer design optimization problem using Multi-Objective Evolutionary Algorithms based on Decomposition with Dynamical Resource Allocation (MOEA/D-DRA). For lesser computation burden, the existing design techniques merely employ few Standard Design Variables (SDV), satisfying only a few performance constraints, resulting in an approximated design, without any focus on an energy efficient transformer. The proposed methodology minimizes four sets of conflicting design bi-objectives, subjected to 27 constraints, incorporating three crucial design variables with SDV to ensure energy efficient transformer design with lesser losses, total life time cost (TLTC), green house gas emission, and failure rate. Different cases are analysed on a sample 1500kVA transformer, which is designed by existing technique and the proposed multi objective optimization problem formulation approach and the performances of the competing transformers are compared. To prove the effectiveness of Iterative Chaotic map with infinite collapses assisted MOEA/D-DRA (ICMDRA), NSGA-II has also been successfully applied to solve the problem. When tested in all three different rating transformers, the simulation results have proved that the proposed methodology saves energy, cost, and material, with ICMDRA rather than NSGA-II. This paper identifies ICMDRA as a superior algorithm for transformer design, in terms of diversity and convergence. Also, the core loss calculation of the transformer designed using the proposed methodology is validated by 3D-FEM assessment and experimental prototype setup for a 200kVA transformer.

Bakurov, I., Castelli, M., Fontanella, F., Scotto Di Freca, A., & Vanneschi, L. (2022). A novel binary classification approach based on geometric semantic genetic programming. Swarm and Evolutionary Computation, 69(March), 1-12. [101028]. https://doi.org/10.1016/j.swevo.2021.101028 ------Funding Information: This work was supported by national funds through the FCT (Fundação para a Ciência e a Tecnologia) by the projects GADgET (DSAIPA/DS/0022/2018), BINDER (PTDC/CCIINF/29168/2017), and AICE (DSAIPA/DS/0113/2019). Mauro Castelli acknowledges the financial support from the Slovenian Research Agency (research core funding no. P5-0410). Geometric semantic genetic programming (GSGP) is a recent variant of genetic programming. GSGP allows the landscape of any supervised regression problem to be transformed into a unimodal error surface, thus it has been applied only to this kind of problem. In a previous paper, we presented a novel variant of GSGP for binary classification problems that, taking inspiration from perceptron neural networks, uses a logistic-based activation function to constrain the output value of a GSGP tree in the interval [0,1]. This simple approach allowed us to use the standard RMSE function to evaluate the train classification error on binary classification problems and, consequently, to preserve the intrinsic properties of the geometric semantic operators. The results encouraged us to investigate this approach further. To this aim, in this paper, we present the results from 18 test problems, which we compared with those achieved by eleven well-known and widely classification schemes. We also studied how the parameter settings affect the classification performance and the use of the -score function to deal with imbalanced data. The results confirmed the effectiveness of the proposed approach. authorsversion published

Population-based algorithms are among the most successful approaches to optimization. These algorithms require high computational capacities such as memory storage. During the last decade, an alternative approach, called compact optimization, was developed. In real-valued compact algorithms, the population is represented by a probabilistic distribution function. Real-valued compact genetic algorithm was first developed and then the idea was extended to other population-based algorithms, like differential evolution, particle swarm optimization and teaching-learning-based optimization. In this paper, we introduce a set of new compact firefly algorithms (cFAs) with minimal computational costs. Our primary aim is to reduce the computational capacity and storage required by the classical variants of FA. The proposed approaches lead to the reduction of the complexity of the attraction model used in FA. The proposed cFAs achieve the optimization with a minimal number of attractions. Several propositions are investigated and reported; such as: elitism strategies, Levy movements, and opposition-based learning. The proposed algorithms consist of: permanent elitism-based compact firefly algorithm (pe-cFA), non-permanent elitism-based compact firefly algorithms (ne-cFA), permanent elitism-based compact Levy-flight firefly algorithms (pe-cLFA), non-permanent elitism-based compact Levy-flight firefly algorithms (ne-cLFA), opposition-based compact firefly algorithms (OBcFA) and opposition-based compact Levy-flight firefly algorithms (OBcLFA). All the known compact algorithms use normal probability of density function (NPDF) to represent the population. In this paper, a new way is investigated. The alternative solution proposed here is based on uniform PDF (UPDF). Thus, two categories of cFAs are presented: NPDF-based cFAs and UPDF-based cFAs. Hence, for each proposed algorithm, two versions are presented and analyzed. The proposed set of twelve algorithms are tested on the IEEE CEC2014 benchmark functions and compared to the state-of-art of compact evolutionary algorithms (cEAs), swarm intelligent algorithms (SIAs), and the most advanced evolutionary algorithms (EAs). The obtained results show that the proposed cFAs are very competitive and that the uniform distribution is very efficient. The case study of this paper concerns the optimal swing-up control of a gymnastic humanoid robot hanging on a bar.

Differential Evolution (DE) is a state-of-the art evolutionary algorithm that solves global optimization problems in a real domain. The algorithm adapts the mutation range and direction by basing these on the differences between individuals in the current population. In this paper, we provide formulas for the expectation vectors and covariance matrices of the mutants' distribution for several operators of differential mutation. The covariance matrices are proportional to each other, which means that the main difference between the analyzed DE operators is the mutation range. This can be conveniently described using a generalized scaling factor g ( F ) , introduced in this paper. Next, we propose transformations of the scaling factors that make the expectation vectors and covariance matrices of the expected mutants' distributions equal to the respective statistics of DE/best/1 or DE/rand/1. These transformations establish a framework for a synthetic investigation of various differential mutation operators and for generalizing the results of parameter tuning. A simulation study based on the CEC′13 benchmark in 10, 30 and 50 dimensions confirms that the transformations do not influence the performance much, especially in the case of DE operators with two difference vectors.

The objective of image contrast enhancement is to improve the contrast level of images, which are degraded during image acquisition. Image contrast enhancement is considered as an optimization problem in this paper and the artificial bee colony (ABC) algorithm is utilized to find the optimal solution for this optimization problem. The contribution of the proposed approach is two-fold. First, in view of that the fitness function is indispensable to evaluate the quality of the enhanced image, a new objective fitness function is proposed in this paper. Second, the image transformation function is critical to generate new pixel intensities for the enhanced image from the original input image; more importantly, it guides the searching movements of the artificial bees. For that, a parametric image transformation function is utilized in this paper so that only the optimal parameters used in the transformation function need to be searched by the ABC algorithm. This is in contrast to that the whole space of image intensity levels is used in the conventional ABC-based image enhancement approaches. Extensive experiments are conducted to demonstrate that the proposed approach outperforms conventional image contrast enhancement approaches to achieve both better visual image quality and higher objective performance measures.

The population initialization step is a common step in the majority (or even all) of evolutionary algorithms (EAs). There are many population initialization techniques. Due to the limited population size and the high dimensionality of many problems, there is little chance to cover the promising regions in the search space. From different perspectives, this paper compares the stochastic and deterministic population initialization techniques through comparing five of the well-known population initializers: Random number generator (RNG), Latin Hypercube, Sobol, Halton, and Kronecker. Due to the presence of many constraints in real-world applications, in this paper, we are focusing only on single-objective constrained optimization problems. Specifically, the goal is to investigate if there is a significant difference between these population initialization methods. In this paper, we explain theoretically and mathematically these different population initialization techniques. Moreover, different illustrative examples and visualizations are introduced to explain the behavior of each technique and compare different techniques from different perspectives. The results show that due to the high uniformity of the low-discrepancy sequences such as the Halton and Sobol sequences, the generated points using these sequences are more evenly distributed over the space than RNG, which is the commonly used technique for initializing the populations in EAs. Practically, using a set of benchmark functions, we investigate the use of each population initialization technique for initializing different population-based evolutionary algorithms. The results of our experiments prove that with sufficient numbers of iterations, the EAs are not sensitive to the initialization methods and there are no significant differences between the mentioned population initialization methods. Further, the low discrepancy methods enhance the exploration ability of EAs in early iterations.

Evolutionary algorithms rely on the population initialization strategy to determine a set of candidate solutions, which provide the preliminary knowledge of the problem landscape for the subsequent evolutionary process. However, the distribution of the initial population is rarely concerned in the multimodal evolutionary community. Moreover, a large initial population has not been attractive enough for evolutionary multimodal optimization, because it is difficult and challenging to achieve a balance between diversity and convergence within limited computing resources. As an extended version of our previous conference paper, this paper focuses on the construction of a large initial population that is beneficial for evolutionary multimodal optimization. First, we propose an improved density-based population initialization strategy to generate a uniform initial population with a certain degree of randomness. Then, after acquiring the raw fitness landscape of the problem, a fitness-weighted density-based population initialization strategy is proposed to explore potential global peaks. Finally, we design a multi-species cooperative coevolution algorithm for multimodal optimization, which balances the exploration and exploitation of such a population in the evolutionary process. Experimental results demonstrate that the proposed algorithm is better than the mainstream algorithms on the CEC2013 multimodal optimization benchmark.

This paper is concerned with an interesting variant of the traveling salesman problem (TSP) called a profitable tour problem (PTP). Unlike TSP, in PTP there is no need to visit all the cities, and each city is associated with a profit which the salesman gets in case he visits that city. Like TSP, a travel cost is incurred in visiting a city that depends on the city visited last before visiting the city in consideration. The goal of the problem is to maximize the total profit minus total travel cost. In this paper, we have proposed three methods, viz. a multi-start hyper-heuristic (MSHH), a multi-start iterated local search (MS-ILS) and a multi-start general variable neighborhood search (MS-GVNS) to solve the PTP. MSHH uses eight different low level heuristics, whereas MS-ILS and MS-GVNS utilize variable neighborhood descent search over five different neighborhoods for local search. To evaluate the performance of the proposed approaches, a set of benchmark instances is generated based on the publicly available TSPLIB instances. Computational results on these instances show the effectiveness of our proposed approaches.

Recent advances in swarm inspired optimization algorithms have shown its extensive acceptance in solving a wide range of different real-world problems. Particle Swarm Optimization (PSO) is one of the most explored nature-inspired population-based stochastic optimization algorithm. In this paper, a Multi-level Particle Swarm Optimization (MPSO) algorithm is proposed to find the architecture and hyperparameters of the Convolutional Neural Network (CNN) simultaneously. This automated learning will reduce the overhead of human experts to find these parameters through manual analysis and experiments. The proposed solution uses multiple swarms at two levels. The initial swarm at level-1 optimizes architecture and multiple swarms at level-2 optimize hyperparameters. The proposed method has used sigmoid like inertia weight to adjust the exploration and exploitation property of particles and avoid the PSO algorithm to prematurely converge into a local optimum solution. In this paper, we have explored an approach to suggest the best well-conditioned CNN architecture and its hyperparameters using MPSO in a specified search space. The complexity and performance of MPSO-CNN will depend on the dimension of the search space. The experimental results on 5 benchmark datasets of MNIST, CIFAR-10, CIFAR-100, Convex Sets, and MDRBI have demonstrated one more effective application of PSO in learning a deep neural architecture.

This paper presents an investigation of mutual coupling effect among the array elements in a symmetric linear array antenna with the aim of reducing the side lobe level and the null control for the radiation pattern synthesis using BAT Algorithm. PSO and DE optimization techniques are also adopted for the sake of comparison and to prove the superiority of BAT algorithm based design. Reduced side lobe level and null control, with and without considering the mutual coupling effect in the cost function have been achieved by an optimum perturbation of the array elements' current excitation amplitude weights and the inter-element spacing among the array elements. The results are also compared with those of a uniform reference array having equal number of elements with λ 2 inter-element spacing. The approach proposed in this paper is a generic one and can be easily applied to any type of symmetrical linear arrays having any number of elements. Five different design examples are presented and their performances are studied to illustrate the capability of BAT algorithm based approach over those of PSO and DE.

A structural damage detection approach based on bird mating optimizer (BMO) in time-frequency domain is proposed in this paper. A hybrid objective function is introduced by minimizing the discrepancies between the measured and calculated natural frequencies and correlation function vector of acceleration of damaged and intact structures. Then the BMO algorithm with a disturbance procedure is developed to solve the objective function. Benefited from the hybrid objective function, only a few number of natural frequencies are needed in the detection process. And the disturbance procedure designed in this paper can enhance the precision of identification. The efficiency and robustness of the proposed method are verified by a planar truss and a frame, a three connected shear buildings and an experimental work. The studies in numerical simulations validate that the proposed objective function and disturbance procedure are helpful to improve the precision of identification. The experimental work shows that the proposed method has the potential of practical application. In addition, comparison among the proposed method and other optimization algorithms, i.e. GA, ABC, L-SHADE and HCLPSO, reveals the superiority of the proposed method in structural damage detection.

This paper describes an application of quasi-oppositional harmony search (QOHS) algorithm to design the scaling factor (SF) based fuzzy-classical controller (such as PI/PD/PID) for frequency and power control of an isolated hybrid power system (IHPS). The considered IHPS model is comprised of a wind turbine generator, a diesel engine generator and an energy storage device (such as superconducting magnetic energy storage (SMES), in this case). Traditionally, SF, membership functions and control rules are obtained in fuzzy logic controllers (FLCs) by trial and error method or are obtained based on the experiences of the designers or are optimized by some traditional optimization techniques with some extra computational cost. To overcome all these problems of FLCs, classical controllers have been integrated in this paper with the FLC. QOHS algorithm is applied to simultaneously tune the SFs (the only tunable parameter of FLC), the gains of the classical controllers and the tunable parameters of the SMES device to minimize frequency and power deviations of the studied IHPS system against various load demand and wind change. Different considered controller configurations of the IHPS are SF based FLC (termed as Fuzzy-only), SF based FLC with proportional-integral (PI) (named as Fuzzy-PI) controller, SF based FLC with proportional-derivative (PD) (abbreviated as Fuzzy-PD) controller and SF based FLC with proportional-integral-derivative (PID) (designated as Fuzzy-PID) controller. Simulation results, explicitly, show that the performance of the Fuzzy-PID controller based IHPS is superior to Fuzzy-only, Fuzzy-PI and Fuzzy-PD controller based IHPS configuration in terms of overshoot, settling time and the proposed Fuzzy-PID controller is robust against various wide range of load changes.

In this paper, a new meta-heuristic method is proposed by combining Particle Swarm Optimization (PSO) and gravitational search in a coherent way. The advantage of swarm intelligence and the idea of a force of attraction between two particles are employed collectively to propose an improved meta-heuristic method for constrained optimization problems. Excellent constraint handling is always required for the success of any constrained optimizer. In view of this, an improved constraint-handling method is proposed which was designed in alignment with the constitutional mechanism of the proposed algorithm. The design of the algorithm is analyzed in many ways and the theoretical convergence of the algorithm is also established in the paper. The efficiency of the proposed technique was assessed by solving a set of 24 constrained problems and 15 unconstrained problems which have been proposed in IEEE-CEC sessions 2006 and 2015, respectively. The results are compared with 11 state-of-the-art algorithms for constrained problems and 6 state-of-the-art algorithms for unconstrained problems. A variety of ways are considered to examine the ability of the proposed algorithm in terms of its converging ability, success, and statistical behavior. The performance of the proposed constraint-handling method is judged by analyzing its ability to produce a feasible population. It was concluded that the proposed algorithm performs efficiently with good results as a constrained optimizer.

In this paper, a genetic algorithm with minimum description length (GAWMDL) is proposed for grammatical inference. The primary challenge of identifying a language of infinite cardinality from a finite set of examples should know when to generalize and specialize the training data. The minimum description length principle that has been incorporated addresses this issue is discussed in this paper. Previously, the e-GRIDS learning model was proposed, which enjoyed the merits of the minimum description length principle, but it is limited to positive examples only. The proposed GAWMDL, which incorporates a traditional genetic algorithm and has a powerful global exploration capability that can exploit an optimum offspring. This is an effective approach to handle a problem which has a large search space such the grammatical inference problem. The computational capability, the genetic algorithm poses is not questionable, but it still suffers from premature convergence mainly arising due to lack of population diversity. The proposed GAWMDL incorporates a bit mask oriented data structure that performs the reproduction operations, creating the mask, then Boolean based procedure is applied to create an offspring in a generative manner. The Boolean based procedure is capable of introducing diversity into the population, hence alleviating premature convergence. The proposed GAWMDL is applied in the context free as well as regular languages of varying complexities. The computational experiments show that the GAWMDL finds an optimal or close-to-optimal grammar. Two fold performance analysis have been performed. First, the GAWMDL has been evaluated against the elite mating pool genetic algorithm which was proposed to introduce diversity and to address premature convergence. GAWMDL is also tested against the improved tabular representation algorithm. In addition, the authors evaluate the performance of the GAWMDL against a genetic algorithm not using the minimum description length principle. Statistical tests demonstrate the superiority of the proposed algorithm. Overall, the proposed GAWMDL algorithm greatly improves the performance in three main aspects: maintains regularity of the data, alleviates premature convergence and is capable in grammatical inference from both positive and negative corpora.

This paper presents a novel optimization algorithm based on competitive behavior of various creatures such as birds, cats, bees and ants to survive in nature. In the proposed method, a competition is designed among all aforementioned creatures according to their performances. Every optimization algorithm can be appropriate for some objective functions and may not be appropriate for another. Due to the interaction between different optimization algorithms proposed in this paper, the algorithms acting based on the behavior of these creatures can compete each other for the best. The rules of competition between the optimization methods are based on imperialist competitive algorithm. Imperialist competitive algorithm decides which of the algorithms can survive and which of them must be extinct. In order to have a comparison to well-known heuristic global optimization methods, some simulations are carried out on some benchmark test functions with different and high dimensions. The obtained results shows that the proposed competition based optimization algorithm is an efficient method in finding the solution of optimization problems.

In this paper, a novel prediction based mean-variance (PBMV) model has been proposed, as an alternative to the conventional Markowitz mean-variance model, to solve the constrained portfolio optimization problem. In the Markowitz mean-variance model, the expected future return is taken as the mean of the past returns, which is incorrect. In the proposed model, first the expected future returns are predicted, using a low complexity heuristic functional link artificial neural network (HFLANN) model and the portfolio optimization task is carried out by using multi-objective evolutionary algorithms (MOEAs). In this paper, swarm intelligence based, multiobjective optimization algorithm, namely self-regulating multiobjective particle swarm optimization (SR-MOPSO) has also been proposed and employed efficiently to solve this important problem. The Pareto solutions obtained by applying two other competitive MOEAs and using the proposed PBMV models and Markowitz mean-variance model have been compared, considering six performance metrics and the Pareto fronts. Moreover, in the present study, the nonparametric statistical analysis using the Sign test and Wilcoxon rank test are also carried out, to compare the performance of the algorithms pair wise. It is observed that, the proposed PBMV model based approach provides better Pareto solutions, maintaining adequate diversity, and also quite comparable to the Markowitz model. From the simulation result, it is observed that the self regulating multiobjective particle swarm optimization (SR-MOPSO) algorithm based on PBMV model, provides the best Pareto solutions amongst those offered by other MOEAs.

This paper provides three innovations. Firstly, a new Laplacian BBO is presented which introduces a Laplacian migration operator based on the Laplace Crossover of Real Coded Genetic Algorithms. Secondly, the performance of the Laplacian BBO and Blended BBO is exhibited on the latest benchmark collection of CEC 2014. (To the best of the knowledge of the authors, the complete CEC 2014 benchmarks have not been solved by Blended BBO). On the basis of the criteria laid down in CEC 2014 as well as popular evaluation criteria called Performance Index, It is shown that Laplacian BBO outperforms Blended BBO in terms of error value defined in CEC 2014 benchmark collection. T-Test has also been employed to strengthen the fact that Laplacian BBO performs better than Blended BBO. The third innovation of the paper is the use of the proposed Laplacian BBO and Blended BBO to solve a real life problem from the field of Computer Vision. It is concluded that proposed Laplacian BBO is an efficient and reliable algorithm for solving not only the continuous functions but also real life problems like camera calibration.

Differential Evolution (DE) is arguably one of the most powerful and versatile evolutionary optimizers for the continuous parameter spaces in recent times. Almost 5 years have passed since the first comprehensive survey article was published on DE by Das and Suganthan in 2011. Several developments have been reported on various aspects of the algorithm in these 5 years and the research on and with DE have now reached an impressive state. Considering the huge progress of research with DE and its applications in diverse domains of science and technology, we find that it is a high time to provide a critical review of the latest literatures published and also to point out some important future avenues of research. The purpose of this paper is to summarize and organize the information on these current developments on DE. Beginning with a comprehensive foundation of the basic DE family of algorithms, we proceed through the recent proposals on parameter adaptation of DE, DE-based single-objective global optimizers, DE adopted for various optimization scenarios including constrained, large-scale, multi-objective, multi-modal and dynamic optimization, hybridization of DE with other optimizers, and also the multi-faceted literature on applications of DE. The paper also presents a dozen of interesting open problems and future research issues on DE.

This paper describes the performance of the Brain Project, a distributed software tool for the formal modeling of numerical data using a hybrid neural-genetic programming technique. One of the most interesting characteristics of the Brain Project is its distributed implementation. Unlike many other parallel and/or distributed solutions the only requirement of the Brain Project is that the collaborating personal computers must be 64-bit Linux machines connected to Internet via the transmission control protocol/internet protocol. The performance of the Brain Project is clearly enhanced with the very simple parallelization scheme illustrated in the paper. Although the Brain Project presents many innovative solutions for the genetic programming research, this paper focuses mainly on its behavior in the distributed environment.

In this paper, the considered hybrid power system (HPS) is having a wind turbine generator, a diesel engine generator (DEG) and a storage device (such as capacitive energy storage). This paper presents a comparative study of frequency and power control for the studied isolated wind–diesel HPS with four different classical controllers for the pitch control of wind turbines and the speed governor control of DEG The classical controllers considered are integral, proportional-integral, integral-derivative and proportional-integral-derivative (PID) controller. A quasi-oppositional harmony search (QOHS) algorithm is proposed for the tuning of the controller gains. The comparative dynamic simulation response results indicate that better performance may be achieved with choosing PID controller among the considered classical controllers, when subjected to different perturbation. Stability and sensitivity analysis, presented in this paper, reveals that the optimized PID controller gains offered by the proposed QOHS algorithm are quite robust and need not be reset for wide changes in system perturbations.

Graphs in computer science are widely used in social network analysis, computer networks, transportation networks, and many other areas. In general, they can visualize relationships between objects. However, fast drawing of graphs and other structures containing large numbers of data points with readable layouts is still a challenge. This paper describes a novel variant of the Fruchterman–Reingold graph layout algorithm which is adapted to GPU parallel architecture. A new approach based on space-filling curves and a new way of repulsive forces computation on GPU are described. The paper contains both performance and quality tests of the new algorithm.

Swarm and evolutionary based algorithms represent a class of search methods that can be used for solving optimization problems. They mimic natural principles of evolution and swarm based societies like ants, bees, by employing a population-based approach in mutual communication and information sharing and processing, including randomness. In this paper, history of swarm and evolutionary algorithms are discussed in general as well as their dynamics, structure and behavior. The core of this paper is an overview of an alternative way how dynamics of arbitrary swarm and evolutionary algorithms can be visualized, analyzed and controlled. Also selected representative applications are discussed at the end. Both subtopics are based on interdisciplinary intersection of two interesting research areas: swarm and evolutionary algorithms and complex dynamics of nonlinear systems that usually exhibit very complex behavior.

This paper presents a new model and solution for the multi-objective Vehicle Routing Problem with Soft Time Windows ( VRPSTW ) using a hybrid metaheuristic technique. The proposed methodology is developed on the basics of a new swarm based Artificial Bee Colony ( ABC ) algorithm combined with two-step constrained local search for neighborhood selection. VRPSTW involves computing the routes of a set of vehicles with fixed capacity from a central depot to a set of geographically dispersed customers with known demands and predefined time windows. Here, the time window constraints are relaxed into “soft”, that is penalty terms are added to the solution cost whenever a vehicle serves a customer outside of his time window. The solution of routing problems with soft time windows has valuable practical applications. This paper uses a direct interpretation of the VRPSTW as a multi-objective optimization problem where the total traveling distance, number of window violations and number of required vehicles are minimized while capacity and time window constraints are met. Our work aims at using ABC inspired foraging behavior of honey bees which balances exploration and exploitation to avoid local optima and reach the global optima. The algorithm is applied to solve the well known benchmark Solomon׳s problem instances. Experimental results show that our suggested approach is quite effective, as it provides solutions that are competitive with the best known results in the literature. Finally, we present an analysis of our proposed algorithm in terms of computational time.

This paper analyses the mixed no-idle flowshop scheduling problem by adding the sequence-dependent setup times constraint and focusing on minimising the total tardiness criterion. In the mixed no-idle flowshop environment, machines that allow idleness, and also those that do not, coexist. In this paper, an extension of this problem in which dependent setup times are included in machines that permit idleness is studied. In order to do so, a mixed integer linear programming (MILP) model is developed. Furthermore, a method to assess the total tardiness of a permutation sequence is provided. Moreover, a partial acceleration method is devised so as to compute the total tardiness in an insertion neighbourhood. Since this problem has not yet been studied in the literature, this research adapted the best known heuristics and metaheuristics available from related problems. Moreover, a new heuristic was developed in order to provide an efficient solving mechanism for the problem. The proposed heuristic was incorporated in the best metaheuristics found in the literature. The adapted methods, as well as our proposal, were tested and compared through statistical and computational experimentation in an extensive benchmark. The MILP was also evaluated and the optimal solutions were compared to those found by the new proposed heuristic. The results show that the proposed heuristic perform extremely well in terms of solution quality and computational efficiency, providing near optimal solutions in some cases.

Despite the successful application of an extension of the Multi-Objective Evolution Algorithm based on Decomposition (MOEA/D-M2M) to solve unbalanced multi-objective optimization problems (UMOPs), its use in constrained unbalanced multi-objective optimization problems has not been fully explored. In an earlier paper, a definition of UMOPs was suggested that had two necessary conditions: 1) finding a favored subset of the Pareto set is easier than finding an unfavored subset, and 2) the favored subset of the Pareto set dominates a large part of the feasible space. The second condition strongly reduces the fraction of MOPs that are considered UMOPs. In this paper, we eliminate that second condition and consider a broader class of UMOPs. We design an unbalanced constrained multi-objective test suite with three different types of biased constraints, yielding three different types of constrained test problems in which the degree of imbalance is scalable via a set of parameters introduced for each problem. We analyse the characteristics of three types of constraints and the difficulties they present for potential solution algorithms–i.e., NSGA-II, MOEA/D and MOEA/D-M2M, with four constraint-handling techniques. MOEA/D-M2M is shown to significantly outperform the other algorithms on these problems due to its decomposition strategy.

In this paper, a new version of the aggregation-based evolutionary algorithm Global WASF-GA (GWASF-GA) for many-objective optimization is proposed, called Adaptive Global WASF-GA (A-GWASF-GA). The fitness function of GWASF-GA is defined by an achievement scalarizing function (ASF) based on the Tchebychev distance, which considers two reference points (the nadir and utopian points) and a set of weight vectors. Despite of the benefits of using these two reference points simultaneously and a well-distributed set of weight vectors, it is necessary to go a step further to get better approximations in problems with complicated Pareto optimal fronts. For this, in A-GWASF-GA, some of the weight vectors are re-calculated during the optimization process based on the sparsity of the solutions found so far, and taking into account some theoretical results demonstrated in this paper regarding the ASF considered. Different strategies are carried out to accelerate the convergence and to maintain the diversity. The computational results, carried out in comparison with RVEA, NSGA-III, and different versions of MOEA/D, show the potential of A-GWASF-GA in well-known but also in novel many-objective optimization benchmark problems.

The plant disease classification based on using digital images is very challenging. In the last decade, machine learning techniques and plant images classification tools such as deep learning can be used for recognizing, detecting and diagnosing plant diseases. Currently, deep learning technology has been used for plant disease detection and classification. In this paper, an ensemble model of two pre-trained convolutional neural networks (CNNs) namely VGG16 and VGG19 have been developed for the task plant disease diagnosis by classifying the leaves images of healthy and unhealthy. In this context, CNNs are used due to its capability of overcoming the technical problems which are associated with the classification problem of plant diseases. However, CNNs suffer from a great variety of hyperparameters with specific architectures which is considered as a challenge to identify manually the optimal hyperparameters. Therefore, orthogonal learning particle swarm optimization (OLPSO) algorithm is utilized in this paper to optimize a number of these hyperparameters by finding optimal values for these hyperparameters rather than using traditional methods such as the manual trial and error method. In this paper, to prevent CNNs from falling into the local minimum and to train efficiently, an exponentially decaying learning rate (EDLR) schema is used. In this paper, the problem of the imbalanced used dataset has been solved by using random minority oversampling and random majority undersampling methods, and some restrictions in terms of both the number and diversity of samples have been overcome. The obtained results of this work show that the accuracy of the proposed model is very competitive. The experimental results are compared with the performance of other pre-trained CNN models namely InceptionV3 and Xception, whose hyperparameters were selected using a non-evolutionary method. The comparison results demonstrated that the proposed diagnostic approach has achieved higher performance than the other models.

In this paper, the convergence issue of the Particle Swarm Optimization (PSO) algorithm is investigated. Most of the models of PSO algorithms are time-invariant linear models with the assumption the local and global best solutions do not change, i.e., the stagnation assumption. However, in this paper, a discrete-time switched linear model is introduced to study the stability and convergence of the PSO algorithm without the stagnation assumption. By considering the updates of local best positions and global best solutions, a sequence of state transform matrixes is generated during the searching process. The semistability of the proposed switched linear system is studied. The conditions of the convergence in mean and convergence in probability are derived by using the recently developed results in paracontraction. Moreover, numerical examples are provided to verify the results proposed in this paper.

A majority of existing works dealing with redundancy allocation problems are based on traditional series-parallel structures. While in many real-life scenarios, the way of connecting subsystems is not limited to a series-only configuration. This paper considers a generalized redundancy allocation problem (GRAP), where the system structure is a more general network. Since the reliability evaluation in GRAPs is a NP-hard problem and the traditional exact symbolic reliability calculation is not suitable, a cellular automata based monte carlo simulation method is implemented in this paper to estimate the system reliability. It is a relatively simple but effective method without knowing the MPs/MCs. Moreover, to deal with GRAPs, a novel discrete bat algorithm is proposed in this paper with a goal of determining an optimal system structure that achieves the minimum cost under several constraints by using redundant components in parallel. Computational complexity of the proposed algorithm is also calculated in this paper. In the end, three experiments are carried out based on ten networks to set parameters, measure the effectiveness of the modifications, and compare with other state-of-the-art algorithms, separately. The reported computational results show that the proposed algorithm is powerful, which is more superior on this sort of problems.

Two-sided robotic assembly lines are employed to assemble large-sized high-volume products, where robots are allocated to the workstations to perform the tasks and human workers are replaced for achieving lower cost and greater flexibility in production. In the two-sided robotic assembly lines, setup times are unavoidable and it has been ignored in most of the reported works. There has been limited attention on this till date. This paper focusses on the robotic two-sided assembly line with consideration of sequence-dependent setup times and robot setup times. A new mixed integer linear programming model is developed with the objective of optimizing the cycle time. Due to the NP-hard nature of the considered problem, this paper proposes a set of metaheuristics to solve this considered problem, where two main scenarios with low and high setup time’s variability are considered. Computational results verify that this new model is capable to achieve the optimal solutions for small-size instances whereas the simple adoption of the published mathematical model might produce wrong solutions for the considered problem. A comprehensive study with 13 algorithms demonstrates that the two variants of artificial bee colony algorithm and migrating bird optimization algorithm are capable to achieve the optimality for small-size instances and to obtain promising results for large-size instances.

This paper gives a review of recent extensions of the Differential Evolution (DE) algorithm for use in Large-Scale Global Optimization (LSGO) and presents an empirical analysis of DE-based and some other state-of-the-art algorithms for LSGO on the CEC 2013 LSGO benchmark suite. Since witnessing the first successful applications of DE for a wide variety of optimization problems in the early nineties, researchers have developed several new algorithms in this field. In this paper, we are especially interested in algorithms for solving LSGO. As LSGO is one of the most active research lines, not only in DE, but in many evolutionary and meta-heuristic algorithms, we discuss general approaches for dealing with LSGO first. The main focus of the paper is DE. We review its basic algorithm and discuss several extensions used for coping with large-scale problems. This paper has two main objectives: (1) To propose, from a theoretical point of view, the grouping of DE mechanisms for dealing with LSGO into nine groups, and (2) To evaluate sixteen recently proposed algorithms for LSGO empirically. Many benchmark suites were designed with the aim of providing a suitable evaluation platform for testing and comparing large-scale optimization algorithms. In this paper, the CEC 2013 LSGO benchmark suite was chosen for comparison, because it resembles the following features of real-world problems: Non-uniform subcomponent sizes; imbalance in the contribution of subcomponents; and functions with interdependent overlapping subcomponents. The performances of state-of-the-art algorithms are compared, and the algorithms are ranked using three different metrics, which evaluate the performance from different perspectives. The conducted research shows that DE is among the best algorithms for LSGO on the CEC 2013 LSGO benchmark suite, especially when used with other mechanisms for dealing with large numbers of variables. Finally, the analysis has shown that there is still some room for further improvements in DE towards the solution of LSGO problems.

This paper proposes a hybrid of genetic algorithm (GA) and differential evolution (DE), termed hGADE, to solve one of the most important power system optimization problems known as the unit commitment (UC) scheduling. The UC problem is a nonlinear mixed-integer combinatorial high-dimensional and highly constrained optimization problem consisting of both binary UC variables and continuous power dispatch variables. Although GA is more capable of efficiently handling binary variables, the performance of DE is more remarkable in real parameter optimization. Thus, in the proposed algorithm hGADE, the binary UC variables are evolved using GA while the continuous power dispatch variables are evolved using DE. Two different variants of hGADE are presented by hybridizing GA with two classical variants of DE algorithm. Additionally, in this paper a problem specific heuristic initial population generation method and a replacement strategy based on preservation of infeasible solutions in the population are incorporated to enhance the search capability of the hybridized variants on the UC problem. The scalability of the proposed algorithm hGADE is demonstrated by testing on systems with generating units in the range of 10 up to 100 in one-day scheduling period and the simulation results demonstrate that hGADE algorithm can provide a system operator with remarkable cost savings as compared to the best approaches in the literature. Finally, an ensemble optimizer based on combination of hGADE variants is implemented to further amplify the performance of the presented algorithm.

In this study, coordination of directional overcurrent relays in power systems is formulated as an optimization problem. The objective is to find out an optimum setting of relays in order to minimize the operating time of relays for faults at their primary protection zone, while coordinating the relays properly. The coordination is performed using Improved Group Search Optimization algorithm. This paper introduces IGSO by applying some modifications to the original GSO in order to improve its searching ability. In order to validate the efficiency of the proposed IGSO, comprehensive simulation studies are carried out. The simulation studies include some benchmark test functions and test power systems. The results are compared with some existing analytic and evolutionary methods. Numerical results confirm efficiency of the proposed method in comparison with some recently published papers.

In this paper, we propose a genetic algorithm for unconstrained multi-objective optimization. Multi-objective genetic algorithm (MOGA) is a direct method for multi-objective optimization problems. Compared to the traditional multi-objective optimization method whose aim is to find a single Pareto solution, MOGA tends to find a representation of the whole Pareto frontier. During the process of solving multi-objective optimization problems using genetic algorithm, one needs to synthetically consider the fitness, diversity and elitism of solutions. In this paper, more specifically, the optimal sequence method is altered to evaluate the fitness; cell-based density and Pareto-based ranking are combined to achieve diversity; and the elitism of solutions is maintained by greedy selection. To compare the proposed method with others, a numerical performance evaluation system is developed. We test the proposed method by some well known multi-objective benchmarks and compare its results with other MOGASs׳; the result show that the proposed method is robust and efficient.

In this paper, design of a new algorithm and a framework for retiming the DSP blocks based on evolutionary computation process is explained. Optimal DSP blocks such as digital filter design is a high level synthesis problem which includes optimally mapping digital filter specifications on to FPGA (Field Programmable Gate Array) architecture. Retiming is the considered optimization method in this paper which gives optimality in terms of algorithm processing speed and digital filter operating frequency with register count as a constraint. The designed novel algorithm is for the synthesis of high speed digital filters for different signal processing applications based on nature inspired evolutionary computation method. The classical retiming algorithms such as clock period minimization and register minimization that are addressed in the literature provide a single heuristic solution based on the chosen optimization parameter such as clock period. However, for retiming which is multi-objective optimization, evolutionary approach can lead to better results. Using the designed evolutionary computation based retiming method, retimed solution database is generated with higher frequency and different output register counts by searching the digital block solution space. Depending on the clock period and register count constraint, designer can take a design decision. Here, various signal processing designs are used to facilitate the design analysis. Results also show that the CPU processing time needed to compute multiple solutions using the designed algorithm for filter circuits is reduced for designs whose maximum feasible solutions are less than 50. If the circuit is very big with the possible solution space greater than 50 solutions, then algorithm performs slower. A comparison is also provided in the Simulations section with respect to all the existing classical retiming methods in the literature such as clock period and register minimization retiming to prove the concept. Multi-objective genetic algorithms are the considered evolutionary computation method in this paper.

Optimization based pattern discovery has emerged as an important field in knowledge discovery and data mining (KDD), and has been used to enhance the efficiency and accuracy of clustering, classification, association rules and outlier detection. Cluster analysis, which identifies groups of similar data items in large datasets, is one of its recent beneficiaries. The increasing complexity and large amounts of data in the datasets have seen data clustering emerge as a popular focus for the application of optimization based techniques. Different optimization techniques have been applied to investigate the optimal solution for clustering problems. Swarm intelligence (SI) is one such optimization technique whose algorithms have successfully been demonstrated as solutions for different data clustering domains. In this paper we investigate the growth of literature in SI and its algorithms, particularly Particle Swarm Optimization (PSO). This paper makes two major contributions. Firstly, it provides a thorough literature overview focusing on some of the most cited techniques that have been used for PSO-based data clustering. Secondly, we analyze the reported results and highlight the performance of different techniques against contemporary clustering techniques. We also provide an brief overview of our PSO-based hierarchical clustering approach (HPSO-clustering) and compare the results with traditional hierarchical agglomerative clustering (HAC), K-means, and PSO clustering.

Teaching–Learning-Based Optimization (TLBO) is recently being used as a new, reliable, accurate and robust optimization technique for global optimization over continuous spaces. Few variants of TLBO have been proposed by researchers to improve the performance of the basic TLBO algorithm. In this paper the authors investigate the performance of a new variant of TLBO called modified TLBO ( m TLBO) for global function optimization problems. The performance of m TLBO is compared with the state-of-the art forms of Particle Swarm Optimization (PSO), Differential Evolution (DE) and Artificial Bee Colony (ABC) algorithms. Several advanced variants of PSO, DE and ABC are considered for the comparison purpose. The suite of benchmark functions are chosen from the competition and special session on real parameter optimization under IEEE Congress on Evolutionary Computation (CEC) 2005. Statistical hypothesis testing is undertaken to demonstrate the significance of m TLBO over other investigated algorithms. Finally, the paper investigates the data clustering performance of m TLBO over other evolutionary algorithms on a few standard synthetic and artificial datasets. Results of our work reveal that m TLBO performs better than many other algorithms investigated in this work.