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This paper proposes a novel hybrid algorithm which is mathematically modelled by amalgamating the superior features of recently developed Grey Wolf Optimizer (GWO), Sine Cosine Algorithm (SCA), and Crow Search Algorithm (CSA). Researchers have already implemented the aforementioned three algorithms and obtained superior quality results for solving diverse optimization problems. The novel hybrid Variegated GWO Algorithm (VGWO) developed in this proposed research work is initially realized and validated for solving IEEE CEC-C06 2019 benchmark functions. Thereafter, the proposed VGWO is utilized as an optimization tool to solve three emerging and complex power system optimization problems which includes energy management of microgrid systems operated in both islanded and grid-connected mode, dynamic economic emission dispatch and reactive power planning (RPP) problem. A comparative analysis of the proposed VGWO approach with other established metaheuristics is undertaken for each optimization problem. Numerical results show that the novel hybrid VGWO algorithm outperformed an ample number of optimization techniques in providing better quality solutions. The proposed hybrid algorithm yielded a 36.93% reduction in active power loss and 36.80% reduction in operating cost with respect to base case condition for RPP problem. Likewise while solving microgrid energy management problems 9–30% savings was realized in the generation cost compared to the ones mentioned in literature. The capability of handling many complex constraints within a minimum amount of computational time to provide consistently best solutions prioritize the proposed hybrid algorithm among its kinds. Statistical analysis validates the authenticity and viability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper develops a robust strategy based on integrating three mutation phases and adapted control parameters into the Adaptive Guided Differential Evolution algorithm called (mAGDE) to improve diversity and exploration of the original AGDE. The mAGDE performance is evaluated using IEEE CEC'2020 test suite. Furthermore, the mAGDE is employed to identify the solid oxide fuel cell (SOFC) model optimal parameters. Two modes of SOFC operation are investigated, steady and transient states. The results obtained from the proposed mAGDE are compared with a number of recent, well-established and reputed meta-heuristics, including Particle swarm optimization, Teaching learning-based optimization, Whale optimization algorithm, Harris hawks optimization, Marine predators algorithm, Archimedes optimization algorithm, Differential evolution, and the original AGDE. Additionally, the statistical parameters that measure the performance of the proposed optimizer and the other competitors are calculated. The main finding demonstrated the preference and robustness of the suggested mAGDE in constructing the SOFC circuit that closely converges to the actual one. During the steady-state operation, the best fitness value obtained via the suggested mAGDE for operation at 1273 K is 2.2995E−06, while in the transient-state operation, the best SMSE is 1.04. The average cost function is decreased by 43.33% compared to the one obtained by the original AGDE. From the aforementioned assessments, it can be concluded that the proposed mAGDE is outstanding and promising. • This paper introduces a modified mAGDE based on the integration of a modified three-phases AGDE with the DE_SPA algorithm. • A modified three-phases AGDE has been introduced to maintain diversity and convergence of the evolutionary process. • The CEC'2020 test suite problems are used to demonstrate the performance mAGDE against other competitors. • Applying for first time mAGDE to identify the optimal parameters of SOFC model. • The robustness of the proposed strategy-based mAGDE is proved. [ABSTRACT FROM AUTHOR]

This paper presents a new optimization algorithm called poor and rich optimization (PRO). This algorithm is inspired by the efforts of the two groups of the poor and the rich to achieve wealth and improve their economic situation. The rich always try to increase their class gap with the poor by gaining wealth from different ways. The rich are always trying to increase their class gap with the poor by acquiring wealth from different ways. On the other hand, the poor try to gain wealth and reduce their class gap with the rich. On the other hand, the poor try to gain wealth and reduce their class gap by modeling the rich. This struggle is always going on and should be mention that the poor may get rich and vice versa. The proposed algorithm is evaluated using 33 test functions and the simulation results are compared with a number of new and well-known optimization algorithms. The evaluation domain includes uni-modal, multi-modal, fixed dimension, hybrid and large scale functions. In addition, for more precise evaluation, Tension/compression spring design, pressure vessel design, Gear drain design, and three-bar truss design problems are solved by PRO algorithm. PRO algorithm has had better performance in these four problems by finding optimal values of parameters as compared to other algorithms. Finally, PRO algorithm was used to estimate software effort by UCP for more accurate evaluation. The obtained results confirmed the superiority of PRO in exploration, exploitation and convergence aspects, compared to other algorithms. [ABSTRACT FROM AUTHOR]

As the airline industry is ever expanding, companies are increasing their fleet sizes to obtain greater market shares. Moreover, as the airlines seek more growth, the complexity and size of the airline crew scheduling problem, which is one of the major planning problems in the industry, is also increasing. For this reason, companies dedicate resources to solve this problem, and lease software at great expense from external sources. Rigorous mathematical models and algorithms are used in solving these problems. This paper presents a survey of airline crew scheduling problems, and their proposed solutions from the literature. As a conclusion, prospective studies will be proposed and discussed with the aim of developing better solutions for airline crew scheduling problems in the future. [ABSTRACT FROM AUTHOR]

Abstract: Voltage regulation is an important task in electrical engineering for controlling node voltages in a power network. A widely used solution for the problem of voltage regulation is based on adjusting the taps in under load tap changers (ULTCs) power transformers and, in some cases, turning on Flexible Alternating Current Transmission Systems (FACTS), synchronous machines or capacitor banks in the substations. Most papers found in the literature dealing with this problem aim to avoid voltage drops in radial networks, but few of them consider power losses or meshed networks. The aim of this paper is to present and evaluate the performance of several multi-objective algorithms, including hybrid approaches, in order to minimize both voltage deviation and power losses by operating ULTCs located in high voltage substations. In particular, a well-known multi-objective algorithm, PAES, is used for this purpose. PAES finds a set of solutions according to Pareto-optimization concepts. Furthermore, this algorithm is hybridized with simulated annealing and tabu search to improve the quality of the solutions. The implemented algorithms are evaluated using two test networks, and the numerical results are analyzed with two metrics often used in the multi-objective field. The results obtained demonstrate the good performance of these algorithms. [Copyright &y& Elsevier]

Abstract: Updating individually the kernel radii of the neurons according to Van Hulle''s approach in the Fuzzy Labeled Self-Organizing Map (FLSOM) algorithm can produce a significant reduction of the mean quantization error as it is demonstrated in this paper using four datasets. The algorithm takes advantage of the available classification of the instances of the dataset since FLSOM is a version of SOM algorithm where the prototype vectors are influenced by the labeling data vectors that define the clusters of the dataset. In this work, the proposed modified version of the FLSOM is able to achieve a better approximation to the numerical variables by means of decreasing the mean quantization error using an individual adaptation of the kernel radii. The aim of this paper is to apply this idea to a pickling line of the steel industry to obtain a model trained with categorical and numerical process variables preserving the topological distribution of the output space in order to reach a visualization of the industrial process and estimate the optimum line speed that minimizes the pickling defects over the steel strip. [Copyright &y& Elsevier]

Abstract: In this paper, heuristic algorithms such as simulated annealing (SA), genetic algorithm (GA) and hybrid algorithm (hybrid-GASA) were applied to tool-path optimization problem for minimizing airtime during machining. Many forms of SA rely on random starting points that often give poor solutions. The problem of how to efficiently provide good initial estimates of solution sets automatically is still an ongoing research topic. This paper proposes a hybrid approach in which GA provides a good initial solution for SA runs. These three algorithms were tested on three-axis-cartesian robot during milling of wood materials. Their performances were compared based on minimum path and consequently minimum airtime. In order to make a comparison between these algorithms, two cases among the several milling operations were given here. According to results obtained from these examples, hybrid algorithm gives better results than other heuristic algorithms alone. Due to combined global search feature of GA and local search feature of SA, hybrid approach using GA and SA produces about 1.5% better minimum path solutions than standard GA and 47% better minimum path solutions than standard SA. [Copyright &y& Elsevier]

Particle filter (PF) is introduced to tackle the limitations of the Kalman filter which adopts Gaussian in the state and noise of the system. PFs have the problem of sample impoverishment and one approach to solve this problem is to optimize the proposal distribution shown by particles. This paper introduces a novel evolutionary PF based on Opposition based High Dimensional optimization Algorithm (OHDA) to reposition the particles of PF in high probable regions for estimation. OHDA will preserve the diversity of particles while emphasizing the more informative ones by information sharing and angular movement operators. Opposite particles are introduced in this paper to speed up the convergence of PF. Virtual forward movement by angular movement of OHDA is employed to better guide the search process. The optimized PF can improve the performance of the estimation algorithms in problems such as localization and SLAM. In robot localization problem, particles show the location of the robot in a known environment. For SLAM (Simultaneous Localization And Mapping), particles contain the location of the robot as well as estimated map of the environment. The application of the resulting evolutionary particle filter is tested in both localization and SLAM. Comparing the results of the proposed evolutionary particle filter with other algorithms confirms the efficiency of applying OHDA to PF in terms of improving estimation accuracy in the well-known Victoria park dataset and some other generated test environments. Comparing optimization algorithms on FASTSLAM and UFASTSLAM are PSO, FA, MVO, and MGWO. [ABSTRACT FROM AUTHOR]

Abstract: The problem of Systems Identification starts with a time-series of observed data and tries to determine the simplest model capable of exhibiting the observed behavior. This optimization problem searches the model from a space of possible models. In this paper, we present the theory and algorithms to perform Qualitative and Quantitative Systems Identification for Linear Time-Invariant Dynamic Systems. The methods described here are based on successive elimination of the components of the system''s response. Sinusoidals of high frequencies are eliminated first, then their carrying waves. We continue with the process until we obtain a non-oscillatory carrier. At this point, we determine the order of the carrier. This procedure allows us to determine how many sinusoidal components and exponential components are found in the impulse response of the system under study. The number of components determines the order of the system. The paper is composed of two important parts, the statement of some mathematical properties of the responses of Linear Time Invariant Dynamic Systems, and the proposal of a set of filters that allows us to implement the recognition algorithm. We present the application of the proposed methodology to analyze and model the electrical circuits and electrical power systems. [Copyright &y& Elsevier]

Solving multi-objective optimization problems plays an important role in several applications. Recently, the Marine Predator Algorithm (MPA) was introduced for solving single objective optimization problems inspired by the behaviour of marine predator in their search for a prey. This paper proposes a modified MPA based framework called Guided Multi-objective Marine Predator Algorithm (GMOMPA) to solve multi-objective optimization problems. The proposed GMOMPA incorporates an external archive to help store the optimal Pareto set solution and guide the particles during the exploitation of the search space. For obtaining non-dominated solutions, the Pareto dominance concept is utilized while the epsilon dominance is considered to update the archive's sorted solutions. In this context, the epsilon dominance concept extends the diversity and exploration of the solutions. Further, a fast non-dominated solution and crowding distance are introduced to update the particle's position, while maintaining the diversity and ensuring a fast convergence towards the Pareto optimal. The proposed GMOMPA is evaluated on several different benchmark test functions including multi-objective ZDT, DTLZ, UF, and WFG test functions as well as the recent multi-objective multimodal CEC 2020 test functions. Moreover, the performance of the proposed GMOMPA is compared with well-known multi-objective optimization algorithms. The obtained results show that the proposed GMOMPA is a good tool for multi-objective optimization and has significant advantages over several state-of-the-art algorithms in almost all of the test functions. [ABSTRACT FROM AUTHOR]

Accurate software development effort estimation is crucial to efficient planning of software projects. Due to complex nature of software projects, development effort estimation has become a challenging issue which must be seriously considered at the early stages of project. Insufficient information and uncertain requirements are the main reasons behind unreliable estimations in this area. Although numerous effort estimation models have been proposed during the last decade, accuracy level is not satisfying enough. This paper presents a new model based on a combination of adaptive neuro-fuzzy inference system (ANFIS) and satin bower bird optimization algorithm (SBO) to reach more accurate software development effort estimations. SBO is a novel optimization algorithm proposed to adjust the components of ANFIS through applying small and reasonable changes in variables. The proposed hybrid model is an optimized neuro-fuzzy based estimation model which is capable of producing accurate estimations in a wide range of software projects. The proposed optimization algorithm is compared against other bio inspired optimization algorithms using 13 standard test functions including unimodal and multimodal functions. Moreover, the proposed hybrid model is evaluated using three real data sets. Results show that the proposed model can significantly improve the performance metrics. [ABSTRACT FROM AUTHOR]

Software requirements selection is a problem which consists of choosing the set of new requirements which will be included in the next release of a software package. This NP-hard problem is an important issue involving several contradictory objectives which have to be tackled by software companies when developing new releases of software packages. Software projects have to stick to a budget, but they also have to satisfy the highest number of customer requirements. Furthermore, when managing real instances of the problem, the requirements tackled suffer interactions and other restrictions which make the problem even harder. In this paper, a novel multi-objective teaching learning based optimization (TLBO) algorithm has been successfully applied to several instances of the problem. For doing this, the software requirements selection problem has been formulated as a multiobjective optimization problem with two objectives: the total software development cost and the overall customer׳s satisfaction. In addition, three interaction constraints have been also managed. In this context, the original TLBO algorithm has been adapted to solve real instances of the problem generated from data provided by experts. Numerical experiments with case studies on software requirements selection have been carried out in order to prove the effectiveness of the multiobjective proposal. In fact, the obtained results show that the developed algorithm performs better than other relevant algorithms previously published in the literature. [ABSTRACT FROM AUTHOR]

Firefly algorithm (FA) is a meta-heuristic optimization algorithm inspired by the flickering behavior of fireflies. Due to its excellent performance, it has been widely used in engineering field.​ However, FA is a population-based algorithm, which needs to occupy a lot of running memory. It is adverse for some small wind turbines or scenarios with limited memory Therefore, this paper proposes an improved firefly algorithm, called parallel compact firefly algorithm (PCFA). The compact technique helps FA save operation memory, which is advantageous for some usage scenarios limited memory. And the parallel technique helps compact FA achieve better solutions and faster convergence. The proposed PCFA was tested on 28 benchmark functions and applied to the proportional–integral–derivative (PID) parameter tuning of the variable pitch wind turbine. Results demonstrate that (1) PCFA is superior to common compact optimization algorithms not only on less memory consumption, but also on more competitive solutions and faster convergence. (2) PCFA shows the better applicability in the PID parameter tuning of variable pitch wind turbine. It can availably smooth the power output of wind turbine under less memory consumption. [ABSTRACT FROM AUTHOR]

The Combined Heat and Power Economic Dispatch (CHPED) is a real-world optimization problem with several complex constraints that has been a topic of studies around energy systems and optimization processes. This paper attempts to conceptualize a potent algorithm by combining the Modified Grasshopper Optimization Algorithm (MGOA) and the Improved Harris Hawks Optimizer (IHHO) for attaining a better balance between the beginning stages of global search and the latter stages of global convergence. The proposed attempt is abbreviated as MGOA-IHHO. Firstly, the chaotic and Opposition-Based Learning (OBL) methods are invoked to generate the initial population. Second, the mathematical model of the conventional Grasshopper Optimization Algorithm (GOA) is modified using Sine–Cosine Acceleration Coefficients (SCAC) to simulate the global exploration at the initial iterations and graduating to the global convergence at the final stages of optimization. Hence, it is named MGOA. Finally, the adaptive search mechanism integrates the two improved search phases of HHO with a search phase of MGOA to improve the performance of the proposed optimization method. This mechanism investigates the best solution for the aging level of the individual during the optimal evaluation process for choosing an appropriate search phase in MGOA-IHHO. The intended effect of the proposed MGOA-IHHO method is verified with other nature-inspired methods on standard single-objective test functions including 23 benchmark problems, 30 test suits of IEEE Congress on Evolutionary Computation 2017 (CEC2017), and four CHPED problems. The statistical results ascertain that the proposed hybridized MGOA-IHHO is capable of providing promising results when compared with its variants and optimization algorithms introduced in the literature. [Display omitted] • A hybrid Grasshopper optimization algorithm and Harris Hawks optimizer is proposed. • Three mechanisms are applied in the proposed hybrid MGOA-IHHO algorithm. • The MGOA-IHHO algorithm is tested on benchmark functions and CHPED problems. • The results are evaluated based on search capability in cost-effectiveness analysis. • Non-parametrical tests are conducted to demonstrate the efficiency of the MGOA-IHHO. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel hybrid optimisation algorithm namely HBCSD, which synergises a bacterial foraging algorithm (BFA) and spiral dynamics algorithm (SDA). The main objective of this strategy is to develop an algorithm that is capable to reach a global optimum point at the end of the final solution with a faster convergence speed compared to its predecessor algorithms. The BFA is incorporated into the algorithm to act as a global search or exploration phase. The solutions from the exploration phase then feed into SDA, which acts as a local search or exploitation phase. The proposed algorithm is used in dynamic modelling of two types of flexible systems, namely a flexible robot manipulator and a twin rotor system. The results obtained show that the proposed algorithm outperforms its predecessor algorithms in terms of fitness accuracy, convergence speed, and time-domain and frequency-domain dynamic characterisation of the two flexible systems. [Copyright &y& Elsevier]

Grey wolf optimizer (GWO) is a widespread metaphor-based algorithm based on the enhanced variants of velocity-free particle swarm optimizer with proven defects and shortcomings in performance. Regardless of the proven defect and lack of novelty in this algorithm, the GWO has a simple algorithm and it may face considerable unbalanced exploration and exploitation trends. However, GWO is easy to be utilized, and it has a low capacity to deal with multi-modal functions, and it quickly falls into the optima trap or fails to find the global optimal solution. To improve the shortcomings of the basic GWO, this paper proposes an improved GWO called multi-stage grey wolf optimizer (MGWO). By dividing the search process into three stages and using different population updating strategies at each stage, the MGWO's optimization ability is improved while maintaining a certain convergence speed. The MGWO cannot easily fall into premature convergence and has a better ability to get rid of the local optima trap than GWO. Meanwhile, the MGWO achieves a better balance of exploration and exploitation and has a rough balance curve. Hence, the proposed MGWO can obtain a higher-quality solution. Based on verification on the thirty benchmark functions of IEEE CEC2017 as the objective functions, the simulation experiments in which MGWO compared with some swarm-based optimization algorithms and the balance and diversity analysis were conducted. The results verify the effectiveness and superiority of MGWO. Finally, the MGWO was applied to the multi-threshold image segmentation of Leaf Spot Diseases on Maize at four different threshold levels. The segmentation results were analysed by comparing each comparative algorithm's PSNR, SSIM, and FSIM. The results proved that the MGWO has noticeable competitiveness, and it can be used as an effective optimizer for multi-threshold image segmentation. • An improved multi-stage grey wolf optimizer (MGWO) is proposed. • The multi-stage strategy is used to balance exploration and exploitation. • A part of salp swarm algorithm strategy is introduced into GWO. • The greater performance of MGWO is verified over some advanced algorithms. • MGWO is tested on multi-threshold image segmentation of Leaf Spot Diseases on Maize. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new approach for solving short-term hydrothermal scheduling (HTS) using an integrated algorithm based on teaching learning based optimization (TLBO) and oppositional based learning (OBL). The practical hydrothermal system is highly complex and possesses nonlinear relationship of the problem variables, cascading nature of hydro reservoirs, water transport delay and scheduling time linkage that make the problem of optimization difficult using standard optimization methods. To overcome these problems, the proposed quasi-oppositional teaching learning based optimization (QOTLBO) is employed. To show its efficiency and robustness, the proposed QOTLBO algorithm is applied on two test systems. Numerical results of QOTLBO are compared with those obtained by two phase neural network, augmented Lagrange method, particle swarm optimization (PSO), improved self-adaptive PSO (ISAPSO), improved PSO (IPSO), differential evolution (DE), modified DE (MDE), fuzzy based evolutionary programming (Fuzzy EP), clonal selection algorithm (CSA) and TLBO approaches. The simulation results reveal that the proposed algorithm appears to be the best in terms of convergence speed, solution time and minimum cost when compared with other established methods. This method is considered to be a promising alternative approach for solving the short-term HTS problems in practical power system. [Copyright &y& Elsevier]

Sine Cosine Algorithm (SCA) that is one of the population-based metaheuristic optimization algorithms basically consists of the updating mechanism based on sine and cosine functions. In this algorithm, a few random and adaptive variables are also utilized for more effective motions of the candidate solutions. SCA has some drawbacks like other some metaheuristic algorithms. SCA tends to be stuck into the local regions in the search space and this affects negatively on the computational effort required to find the best solution point in the search space. This paper presents four different improved versions of SCA. The proposed improvements on original SCA are the innovations on the updating mechanism of SCA. To evaluate the performances of Improved Sine Cosine Algorithms (ImpSCAs), well-known numerical optimization problems including CEC 2014 test suite are used. Firstly, different analyses of the proposed ImpSCAs are dealt with such as the convergence analysis, search history analysis, trajectory analysis, average distance analysis, and computational complexity analysis. Secondly, the proposed four versions of ImpSCAs are compared with the original SCA for CEC 2014 benchmark problems with dimension sizes of 10D, 30D and 50D. Finally, original SCA and ImpSCAs are adapted to select optimal feature combination and they are tested for 10 feature selection datasets taken from the UCI machine learning repository. The benchmark results show that the performances of the ImpSCA 1 , ImpSCA 2 , and ImpSCA 4 are better than that of the original SCA. From the feature selection results, it is observed that three versions of ImpSCAs (except ImpSCA 3) outperform the original SCA in 80% of the datasets. Source codes of ImpSCAs are publicly available at https://github.com/uguryuzgec/ImpSCAs. • We focused to improve the exploration and exploitation ability of the original SCA. • The basic idea is based on the innovations on the update mechanism. • The ISCAs were evaluated using CEC2014 benchmark test suite. • The proposed ISCAs were tested for 10 popular UCI datasets. • Three versions of ISCAs (except ISCA 3) outperform the SCA in 80% of the datasets. [ABSTRACT FROM AUTHOR]

The three-parameter (3-p) Weibull distribution is an extremely important distribution to characterise the statistical behaviour of a large number of real world phenomenons. It is also useful as a failure model in analysing the reliability of different types of mechanical and electrical components/systems. Successful applications of the distribution rely on an accurate estimation of its three parameters because it directly affects the reliability and lifetime analysis. Due to the intricate system of nonlinear equations and the complexity of the likelihood function, derivative-based optimisation methods may fail to converge. Thus, an efficient and effective method for estimating the parameters of the model is important from the practical viewpoint. In this paper, an optimisation scheme based on an acceptance–rejection (AR) mechanism coupled with an elegant nested sampling (NS) technique is proposed to tackle this problem. The idea is to gradually approach the region of optimal solutions through an efficient sampling technique and a reweighting scheme. The AR-NS algorithm allows a good exploration of the parameter space and converges towards higher likelihood regions by decreasing progressively a pre-specified tolerance threshold. The proposed approach gives the entire distributions of the optimal estimates rather than a single point estimates. To demonstrate the practicality and the efficiency of the proposed approach, numerous numerical examples using simulated data and real-world engineering cases will be given. The obtained results show that the AR-NS algorithm is a suitable method for estimating the parameters of lifetime distributions using different distances. • An efficient algorithm for estimating the parameters of parametric lifetime distributions is proposed. • The optimisation scheme approaches gradually the optimal solutions by propagating "good" particles. • The proposed algorithm provides the entire distributions of the optimal estimates rather than a single point estimates. • The efficiency of the optimisation algorithm has been demonstrated through numerous examples. [ABSTRACT FROM AUTHOR]

Abstract: This paper deals with the preliminary design problem when the product is modeled as an analytic model. The analytic models based method aims to use mathematical equations to address both multi-physic and economic characteristics of a product. The proposed approach is to convert the preliminary design problem into a global constrained optimization problem. The objective is to develop powerful optimization methods enough to handle complex analytical models. We propose to adapt an approach to solve this problem based on interval analysis, constraint propagation and model reformulation. In order to understand the optimization algorithm used for engineering design problems, some basic definitions and properties of interval analysis are introduced. Then, the basic optimization algorithms for both unconstrained and constrained problems are introduced and illustrated. The next section introduces the reformulation technique as main accelerating device. An application of the reformulation device and its global optimization algorithm on the optimal design of electrical actuators is presented. [Copyright &y& Elsevier]

Abstract: Accidental or intentional drinking water contamination has long been and remains a major threat to water security throughout the world. An inverse problem can be constructed, given sensor measurements in a water distribution system (WDS), to identify the contaminant source characteristics by integrating a WDS simulation model with an optimization method. However, this approach requires numerous compute-intensive simulation runs to evaluate potential solutions; thus, determining the best source characteristic within a reasonable computational time is challenging. In this paper, we describe the development of a WDS contamination characterization algorithm by coupling a statistical model with a heuristic search method. The statistical model is used to identify potential source locations of contamination and a local search aims at further refining contaminant source characteristics. Application of the proposed approach to two illustrative example water distribution networks demonstrates its capability of adaptively discovering contaminant source characteristics as well as evaluating the degree of non-uniqueness of solutions. The results also showed that the local search as an optimizer has better performance than a standard evolutionary algorithm (EA). [Copyright &y& Elsevier]

Abstract: Selection of the optimal values of different operating parameters is of utmost importance for enhancing the performance of various non-traditional machining (NTM) processes. The performance measures (responses) of different NTM processes usually include metal removal rate, surface roughness, radial overcut, tool wear rate, heat affected zone, etc. In this paper, artificial bee colony (ABC) algorithm is employed to search out the optimal combinations of different operating parameters for three widely used NTM processes, i.e. electrochemical machining, electrochemical discharge machining and electrochemical micromachining processes. Both the single and multi-objective optimization problems for the considered NTM processes are solved using this algorithm. The results obtained while applying the ABC algorithm for parametric optimization of these three NTM processes are compared with those derived by the past researchers, which prove the applicability and suitability of the ABC algorithm in enhancing the performance measures of the considered NTM processes. [Copyright &y& Elsevier]

Abstract: Biogeography-based optimization (BBO) is a new evolutionary algorithm inspired by biogeography, which involves the study of the migration of biological species between habitats. Previous work has shown that various migration models of BBO result in significant changes in performance. Sinusoidal migration models have been shown to provide the best performance so far. Motivated by biogeography theory and previous results, in this paper a generalized sinusoidal migration model curve is proposed. A previously derived BBO Markov model is used to analyze the effect of migration models on optimization performance, and new theoretical results which are confirmed with simulation results are obtained. The results show that the generalized sinusoidal migration model is significantly better than other models for simple but representative problems, including a unimodal one-max problem, a multimodal problem, and a deceptive problem. In addition, performance comparison is further investigated through 23 benchmark functions with a wide range of dimensions and diverse complexities, to verify the superiority of the generalized sinusoidal migration model. [Copyright &y& Elsevier]

Abstract: In this paper, a Multi-Swarm Self-Adaptive and Cooperative Particle Swarm Optimization (MSCPSO) based on four sub-swarms is presented. In the proposed algorithm, several strategies are employed to avoid falling into local optimum, improve the diversity and achieve better solution. Particles in each sub-swarms share the only global historical best optimum to enhance the cooperative capability. Besides, the inertia weight of a particle in each sub-swarms is modified, which is subject to the fitness information of all particles, and the adaptive strategy is employed to control the influence of the historical information to create a more potential search ability. To effectively keep the balance between the global exploration and the local exploitation, the particle in each takes advantage of the shared information to maintain cooperation with each other and guides its own evaluation. On the other hand, in order to increase the diversity of the particles and avoid falling into a local optimum, a various diversity operation is adopted to guide the particles to jump out of the local optimum and achieve the global best position smoothly. The proposed method was applied to some well-known benchmarks; the results demonstrated good performances of MSCPSO in solving the complex multimodal functions. [Copyright &y& Elsevier]

Abstract: This paper presents a constrained Self-adaptive Differential Evolution (SaDE) algorithm for the design of robust optimal fixed structure controllers with uncertainties and disturbance. Almost all real world optimization problems have constraints which should be satisfied along with the best optimal solution for the problem. In evolutionary algorithms (EAs) the presence of constraints reduces the feasible region and complicates the search process. Therefore, a suitable method to handle the constraints must also be executed. In the SaDE algorithm, four mutation strategies and the control parameter CR are self-adapted. Self-adaptive Penalty (SP) method is introduced into the SaDE algorithm for constraint handling. The performance of SaDE algorithm is demonstrated on the design of robust optimal fixed structure controller of three systems, namely the linearized magnetic levitation system, F-8 aircraft linearized model and a SISO plant. For the comparison purpose, reported results of constrained PSO algorithm and five DE algorithms with different strategies and parameter values are taken into account. Statistical performance in 20 independent runs is considered to compare the performance of algorithms. From the obtained results, it is observed that SaDE algorithm is able to self-adapt the mutation strategy and the crossover rate and hence performs better than the other variants of DE and the constrained PSO algorithm. Better performance of SaDE is achieved by sustained maintenance of diversity throughout the evolutionary process thus producing better individuals consistently. This also aids the algorithm to escape from local optima thereby avoiding premature convergence. [Copyright &y& Elsevier]

Abstract: Parametric reconfiguration plays a key role in non-iterative concurrent design of mechatronic systems. This is because it allows the designer to select, among different competitive solutions, the most suitable without sacrificing sub-optimal characteristics. This paper presents a method based on an evolutionary algorithm to improve the parametric reconfiguration feature in the optimal design of a continuously variable transmission and a five-bar parallel robot. The approach considers a solution-diversity mechanism coupled with a memory of those sub-optimal solutions found during the process. Furthermore, a constraint-handling mechanism is added to bias the search to the feasible region of the search space. Differential Evolution is utilized as the search algorithm. The results obtained in a set of five experiments performed per each mechatronic system show the effectiveness of the proposed approach. [Copyright &y& Elsevier]

Abstract: Nonlinear model predictive control (NMPC) algorithms are based on various nonlinear models. A number of on-line optimization approaches for output-feedback NMPC based on various black-box models can be found in the literature. However, NMPC involving on-line optimization is computationally very demanding. On the other hand, an explicit solution to the NMPC problem would allow efficient on-line computations as well as verifiability of the implementation. This paper applies an approximate multi-parametric nonlinear programming approach to explicitly solve output-feedback NMPC problems for constrained nonlinear systems described by black-box models. In particular, neural network models are used and the optimal regulation problem is considered. A dual-mode control strategy is employed in order to achieve an offset-free closed-loop response in the presence of bounded disturbances and/or model errors. The approach is applied to design an explicit NMPC for regulation of a pH maintaining system. The verification of the NMPC controller performance is based on simulation experiments. [ABSTRACT FROM AUTHOR]

Abstract: As a powerful optimization algorithm, particle swarm optimization (PSO) has been widely applied to power system researches. However, most existing applications of PSO can only be implemented offline. The difficulties of online implementation mainly come from the unavoidable lengthy simulation time to evaluate a candidate solution. Recently, PSO was implemented online that can identify parameters in a motor control systems. In this paper, the real-time PSO (RT-PSO) based identification technique is applied to cancel current harmonics in power systems. By transforming the identification problem to optimization problem, RT-PSO can simultaneously identify four parameters associated with fundamental current from measurement. In this way, there is no need to identify the fundamental frequency separately or construct fundamental signal from identified harmonic information. The identification algorithm can be applied to three-phases independently, even for unbalanced system or single-phase system. The identified fundamental signal is then used as the reference for current harmonics cancellation. The RT-PSO based harmonic cancellation is realized with an active filter and used to compensate harmonic current created by a nonlinear load. Simulation results demonstrate that the RT-PSO algorithm can provide accurate identification of the fundamental current which in turn will result in good harmonic cancellation performance. As a capable online optimization technique, RT-PSO can be extensively applied to many optimization and control problems. [ABSTRACT FROM AUTHOR]

Abstract: The use of evolutionary algorithms (EAs) is beneficial for addressing optimization problems in dynamic environments. The objective function for such problems changes continually; thus, the optimal solutions likewise change. Such dynamic changes pose challenges to EAs due to the poor adaptability of EAs once they have converged. However, appropriate preservation of a sufficient level of individual diversity may help to increase the adaptive search capability of EAs. This paper proposes an EA-based Adaptive Dynamic OPtimization Technique (ADOPT) for solving time-dependent optimization problems. The purpose of this approach is to identify the current optimal solution as well as a set of alternatives that is not only widespread in the decision space, but also performs well with respect to the objective function. The resultant solutions may then serve as a basis solution for the subsequent search while change is occurring. Thus, such an algorithm avoids the clustering of individuals in the same region as well as adapts to changing environments by exploiting diverse promising regions in the solution space. Application of the algorithm to a test problem and a groundwater contaminant source identification problem demonstrates the effectiveness of ADOPT to adaptively identify solutions in dynamic environments. [Copyright &y& Elsevier]

Abstract: This paper systematically proposed a multi-population agent co-genetic algorithm with double chain-like agent structure (MPATCGA) to solve the problem of the low optimization precision and long optimization time of simple genetic algorithm in terms of two coding strategy. This algorithm adopted multi-population parallel searching mode, close chain-like agent structure, cycle chain-like agent structure, dynamic neighborhood competition, and improved crossover strategy to realize parallel optimization, and has the characteristics of high optimization precision and short optimization time. Besides, the size of each sub-population is adaptive. The characteristic is very competitive when dealing with imbalanced workload. In order to verify the optimization precision of this algorithm with binary coding, some popular benchmark test functions were used for comparing this algorithm and a popular agent genetic algorithm (MAGA). The experimental results show that MPATCGA has higher optimization precision and shorter optimization time than MAGA. Besides, in order to show the optimization performance of MPATCGA with real coding, the authors used it for feature selection problems as optimization algorithm and compared it with some other well-known GAs. The experimental results show that MPATCGA has higher optimization precision (feature selection precision). In order to show the performance of the adaptability of size of sub-populations, MPATCGA with sub-populations with same size and MPATCGA with sub-populations with different size are compared. The experimental results show that when the workload on different sub-populations becomes not same, the adaptability will adaptively change the size of different sub-population to obtain precision as high as possible. [Copyright &y& Elsevier]

Abstract: In this paper, a new multi-objective uniform-diversity genetic algorithm (MUGA) with a diversity preserving mechanism called the ε-elimination algorithm is used for Pareto optimization of a five-degree of freedom vehicle vibration model considering the five conflicting functions simultaneously. The important conflicting objective functions that have been considered in this work are, namely, seat acceleration, forward tire velocity, rear tire velocity, relative displacement between sprung mass and forward tire and relative displacement between sprung mass and rear tire. Further, different pairs of these objective functions have also been selected for 2-objective optimization processes. The comparison of the obtained results with those in the literature demonstrates the superiority of the results of this work. It is shown that the results of 5-objective optimization include those of 2-objective optimization and, therefore, provide more choices for optimal design of a vehicle vibration model. [Copyright &y& Elsevier]

Abstract: The paper presents an optimal fuzzy logic control algorithm for vibration mitigation of buildings using magneto-rheological (MR) dampers. MR dampers are semi-active devices and are monitored using external voltage supply. The voltage monitoring of MR damper is accomplished using evolutionary fuzzy system, where the fuzzy system is optimized using evolutionary algorithms (EAs). A micro-genetic algorithm (-GA) and a particle swarm optimization (PSO) are used to optimize the FLC parameters. Two cases of optimal FLCs are shown. One where FLC is optimized keeping the rule base predefined and in the other case, FLC rule base is also optimized along with other FLC parameters. The FLC rule base and membership function parameters are optimized using 10 variables. Fuzzy controllers with a predefined rule base and with an optimal rule base are applied to a single degree of freedom (SDOF) and a multi-degree of freedom (MDOF) system. Finally, the study evaluates the performance of the fuzzy controller optimized off-line, on a three storey building model under seismic excitations. The main advantage of using FLC to drive the MR damper voltage is that it provides a gradual and smooth change in voltage. Consequently, the present approach provides a better vibration control for structures under earthquake excitations. [Copyright &y& Elsevier]

As an efficient and simple optimization algorithm, particle swarm optimization (PSO) has been widely applied to solve various real optimization problems. However, avoiding premature convergence and balancing the global exploration and local exploitation capabilities of the PSO remains two crucial problems. To overcome these drawbacks of PSO, a hybrid particle swarm optimization with crisscross learning strategy (PSO-CL) algorithm is proposed in this paper. In PSO-CL, in order to well balance the global exploration and local exploitation capabilities of PSO, a search direction adjustment mechanism based on subpopulation division operation is proposed. Meantime, to avoid the premature convergence and enhance the global search ability, a crossover-based comprehensive learning strategy (CCL) is adopted. Additionally, a stochastic example learning strategy (SEL) is introduced, which can assist collective information to be spread among separate sub-swarms, improve the local exploitation ability of the algorithm. 15 classic benchmark functions, CEC2017 test suite and two real-world optimization problems are utilized to verify the promising performance of PSO-CL, experimental results and statistical analysis indicate that PSO-CL has competitive performance compared with state-of-the-art PSO variants. [Display omitted] • A search direction adjustment mechanism based on subpopulation division operation. • A crossover-based comprehensive learning strategy is presented, which can enhance the diversity of swarm. • A stochastic example learning strategy is introduced to further enhance the convergence precise. [ABSTRACT FROM AUTHOR]

This paper focuses on the scheduling problem of flexible assembly systems (FASs) without intermediate buffers. The main characteristic of the problem is that as no intermediate buffer exists between consecutive machines, blocking and deadlock constraints must be considered. Petri nets are used to model the considered FASs, and a novel hybrid particle swarm optimization (HPSO) algorithm is proposed to minimize the makespan. The proposed algorithm is the combination of the discrete PSO, particle repairing algorithm, particle improvement strategy, and local search method. First, each candidate solution for the problem is encoded as a permutation with repetition of part numbers, and can be uniquely decoded into a sequence of transitions. To ensure the feasibility of solutions, a repairing algorithm is developed, in which a deadlock avoidance policy is used. Then, a particle improvement policy is proposed to improve the performance of particles. Meanwhile, a local search method is designed and incorporated into HPSO to improve its search ability. Experiments are conducted to verify the effectiveness of the particle improvement policy and local search method. Comparisons between HPSO and ten other algorithms are performed. The comparison results and analysis show that our proposed algorithm can find feasible solutions for all tested instances, and is superior to other scheduling algorithms in terms of finding better solutions and performance stability. [ABSTRACT FROM AUTHOR]

Tree-Seed Algorithm (TSA) is a meta-heuristic optimization algorithm with good performance in solving continuous optimization problems. However, there is an imbalance between its exploration and exploitation when solving complex problems, mainly lack exploration. To overcome this problem, this paper proposes two tree migration mechanisms: triple-learning-based migration mechanism and sine-random-distribution migration mechanism. The target tree position is migrated by learning from the first three trees in the current iteration. The sine function is added to the tree migration formula to enhance the randomness of tree distribution. In order to verify these migration mechanisms, Triple Tree-Seed Algorithm (TriTSA) has been proposed and compared with TSA on 30 well-known test functions from IEEE CEC 2014. In addition, STSA, SCA, PSO, ABC, Jaya, and TLBO are adopted in some comparative experiments on different dimensions. The experiments show that the tree migration mechanism can improve the optimization capability of the original algorithm effectively. On all 30 benchmark test functions, TriTSA outperforms TSA on 10, 30, 50, and 100 dimensions by 70%, 90%, 90%, and 97% respectively. Finally, the proposed TriTSA is compared with TSA, ABC, PSO, and SCA on solving two classical engineering design problems. It is proved that the proposed algorithm is more applicable in solving practical problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper characterizes general optimization problems into four categories based on the solution representation schemes, as they have been the key to the design of various evolutionary algorithms (EAs). Four EAs have been designed for different formulations with the aim of utilizing similar and generalized strategies for all of them. Several modifications to the existing EAs have been proposed and studied. First, a new tradeoff function-based mutation has been proposed that takes advantages of Cauchy, Gaussian, random as well as chaotic mutations. In addition, a generalized learning rule has also been proposed to ensure more thorough and explorative search. A theoretical analysis has been performed to establish the convergence of the learning rule. A theoretical study has also been performed in order to investigate the various aspects of the search strategy employed by the new tradeoff-based mutations. A more logical parameter tuning has been done by introducing the concept of orthogonal arrays in the EA experimentation. The use of noise-based tuning ensures the robust parameter tuning that enables the EAs to perform remarkably well in the further experimentations. The performance of the proposed EAs has been analyzed for different problems of varying complexities. The results prove the supremacy of the proposed EAs over other well-established strategies given in the literature. [Copyright &y& Elsevier]

Abstract: In this paper a new iterative construction algorithm for local model networks is presented. The algorithm is focussed on building models with sparsely distributed data as they occur in engine optimization processes. The validity function of each local model is fitted to the available data using statistical criteria along with regularization and thus allowing an arbitrary orientation and extent in the input space. Local models are consecutively placed into those regions of the input space where the model error is still large thus guaranteeing maximal improvement through each new local model. The orientation and extent of each validity function are also adapted to the available training data such that the determination of the local regression parameters is a well-posed problem. The regularization of the model can be controlled in a distinct manner using only two user-defined parameters. In order to assess the quality of the obtained model, the algorithm also provides accurate model statistics. Different examples illustrate the efficiency of the proposed algorithm. One illustrative example shows how local models are adapted to the shape of the target function in the presence of noise. A second example shows results obtained with measurement databases of IC-engines. [Copyright &y& Elsevier]

Genetic algorithms are mostly considered to represent the primary class of evolutionary methods that operate by combining solutions to produce better ones. In this paper, a very efficient method based on the concept of the genetic algorithms metaheuristic technique is developed for providing an efficient solution for observing a surveying network using space-based satellites systems. These systems are used to determine the geographical positions of unknown points on and above the earth and its oceans using suitable satellite receiving equipment. When related to satellite technology, a surveying network can be defined as a number of points which are co-ordinated by a series of observation sessions. These sessions are formed by placing receivers on the points of the network. An observation session can be defined as a period of time during which two or more receivers simultaneously record satellite signals. Thus, the schedule of receivers is a sequence of sessions to be observed consecutively. The goal is to select the best order in which these sessions can be organised to give the best possible solution at minimal cost. Several real space-based satellites surveying networks have been used to assess the performance of the proposed technique in terms of the solution quality and computational effort. [Copyright &y& Elsevier]

An architecture for the operation of a recuperative-type glass furnace is introduced in this paper. It is based on a hierarchical scheme, with two main parts: process optimisation and process modelling. Process optimisation is carried out by an expert controller, and uses genetic algorithms to solve a multiobjective optimisation problem. Process modelling is performed by a learning system, based on a fuzzy learning-by-examples algorithm. Results of real and simulated experiments with the glass manufacturing process are presented. [Copyright &y& Elsevier]

In practical applications, solving multimodal multiobjective optimization problems (MMOPs), which have multiple Pareto optimal sets (PSs) in the decision space mapping to the same Pareto front (PF) in the objective space, has great significance for decision makers. The issue of how to maintain diversity in both decision space and objective space remains a key problem for existing multimodal multiobjective evolutionary algorithms. To address this issue, a novel grey prediction evolution algorithm for multimodal multiobjective optimization, termed MMGPE, is proposed in this paper. This is the first time that the grey prediction evolution algorithm (GPE), which is a recently proposed competitive optimization algorithm with strong exploration capability, is improved for MMOPs. These improvements are conducted in the following four aspects: (1) an initialization operator based on particle swarm optimization, (2) an adaptive parameter setting strategy depending on the domain of decision variables of MMOPs, (3) an accelerating convergence mechanism inspired by the niche principle, and (4) an environmental selection operator based on a nondominated sorting mechanism and a special crowding distance approach. The performance of MMGPE is compared with two state-of-the-art multiobjective evolutionary algorithms and four multimodal multiobjective evolutionary algorithms on 11 multimodal multiobjective test functions. MMGPE is also applied to solve a practical problem. The results show the MMGPE's effectiveness and superiority in achieving the goal of finding multiple PSs while obtaining a well-distributed PF. [ABSTRACT FROM AUTHOR]

Feature selection is the problem of finding the optimal subset of features for predicting class labels by removing irrelevant or redundant features. S-shaped Binary Butterfly Optimization Algorithm (S-bBOA) is a nature-inspired algorithm for solving the feature selection problems. The evidence shows that S-bBOA has a better performance in exploration, exploitation, convergence, and avoidance of getting stuck in local optimal compared to other optimization algorithms. However, S-bBOA does not consider redundancy and relevancy of features. This paper proposes Information Gain binary Butterfly Optimization Algorithm (IG-bBOA), to overcome the S-bBOA constraints firstly. IG-bBOA maximizes both the classification accuracy and the mean of the mutual information between features and class labels. In addition, IG-bBOA also tries to minimize the number of selected features and is used within a three-phase proposed method called Ensemble Information Theory based binary Butterfly Optimization Algorithm (EIT-bBOA). In the first phase, 80% of irrelevant and redundant features are removed using Minimal Redundancy-Maximal New Classification Information (MR-MNCI) feature selection. In the second phase, the best feature subset is selected using IG-bBOA. Finally, a similarity based ranking method is used to select the final features subset. The experimental results are conducted using six standard datasets from UCI repository. The findings confirm the efficiency of the proposed method in improving the classification accuracy and selecting the best optimal features subset with minimum number of feature in most cases. • Minimizing two type of feature redundancy and maximizing relevancy between features and class label, before solution optimization. • Using a three-objective function to determine the fitness of each solution in the binary butterfly optimization algorithm. • Using an ensemble similarity-based ranking method in final phase for selection of the best subset. [ABSTRACT FROM AUTHOR]

Crow search algorithm is one of bio-inspired optimization algorithms which is essentially derived for solving continuous based optimization problems. Although many main-frame discrete optimizers are available, they still have some performance challenges. This paper proposes three discrete crow inspired algorithms for enhancing the performance of the original crow search algorithm when it is applied for solving discrete traveling salesman problems. The proposed algorithms are derived based on modular arithmetic, basic operators and dissimilar solutions techniques. Each technique guarantees switching from continuous spaces into discrete spaces without losing information. Such algorithms are called Modular Arithmetic, Basic Operators, and Dissimilar Solutions algorithms. For evaluating their performance, the proposed algorithms are compared with the most state-of-the-art discrete optimizers for solving 111 instances of traveling salesman problems. Simulation results illustrate that, the performance of the proposed algorithms is much better than the performance of most state-of-the-art discrete optimizers in terms of the average optimal solutions accuracy, the average errors from the optimal solutions and the average of computational time. [ABSTRACT FROM AUTHOR]

This paper proposes a novel, reliable, and effective hybrid approach based on the integration of the firefly algorithm (FA) and the adaptive particularly tunable fuzzy particle swarm optimization (APT-FPSO) method to address reactive power dispatch (RPD) problem, a crucial optimization problem in the operation of power systems. Similar to many other original meta-heuristic optimization techniques, the standard FA suffers from some severe drawbacks, most importantly being easily trapped into a locally optimal solution. In order to tackle these difficulties, in the current study, an improved version of fuzzy-based particle swarm optimization is utilized in the internal structure of the original FA. The developed hybrid approach, which is capable of avoiding premature convergence of the original FA by enhancing exploration and exploitation procedures, is employed to determine the optimum control variables (i.e., the voltage of generation buses, tap positions of tap-changer transformers, and reactive power output of shunt compensators) through optimizing three distinct objective functions consisting of total transmission real power loss, the voltage magnitude deviations as well as voltage stability index. To validate the accuracy and competency of the proposed hybrid approach, it is firstly used for solving several benchmark optimization functions and then applied to three test systems at different scales, consisting of IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus power systems, for solving the RPD problem. Eventually, the results of the presented hybrid method will be compared to those obtained by other implemented swarm intelligence-based approaches. The statistical analysis of this research substantiates the robustness and effectiveness of the developed algorithm to handle sophisticated optimization problems, particularly the RPD problem. • Introducing a novel hybrid algorithm based on FA and APT-FPSO for the RPD problem. • Investigating the proposed hybrid method performance by using benchmark functions. • Applying the presented model to IEEE 30-bus, 57-bus, and 118-bus test systems. • Proposed hybrid method outperforms other implemented techniques. [ABSTRACT FROM AUTHOR]

In this article, a new optimization technique known as Kho-Kho optimization (KKO) algorithm is presented. This proposed technique is a population based meta-heuristic method which is inspired from the strategies used by players in a well known tag-team game played in India, i.e. Kho-Kho. The performance and superiority of the proposed method with respect to other existing methods is evaluated using twenty nine benchmark functions and real-time optimization problems related to power system i.e. combined emission economic dispatch and combined heat and power economic dispatch problem. • This paper presents a new Kho-Kho optimization algorithm (KKO). • KKO is inspired by a well-known tag-team game played in India known as Kho-Kho. • KKO mimics the strategies used by a chasing team to catch the runners of a running team. • Twenty-nine benchmark functions are used to test the performance of the proposed algorithm. • Further, KKO is used to solve real-time optimization problems of power system. [ABSTRACT FROM AUTHOR]

This paper introduces a bio-inspired metaheuristic optimization algorithm named Tunicate Swarm Algorithm (TSA). The proposed algorithm imitates jet propulsion and swarm behaviors of tunicates during the navigation and foraging process. The performance of TSA is evaluated on seventy-four benchmark test problems employing sensitivity, convergence and scalability analysis along with ANOVA test. The efficacy of this algorithm is further compared with several well-regarded metaheuristic approaches based on the generated optimal solutions. In addition, we also executed the proposed algorithm on six constrained and one unconstrained engineering design problems to further verify its robustness. The simulation results demonstrate that TSA generates better optimal solutions in comparison to other competitive algorithms and is capable of solving real case studies having unknown search spaces. Note that the source codes of the proposed TSA algorithm are available at [ABSTRACT FROM AUTHOR]

Abstract: 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. [Copyright &y& Elsevier]