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The optimization of industrial processes is a critical task for leveraging profitability and sustainability. To ensure the selection of optimum process parameter levels in any industrial process, numerous metaheuristic algorithms have been proposed so far. However, many algorithms are either computationally too expensive or become trapped in the pit of local optima. To counter these challenges, in this paper, a hybrid metaheuristic called PSO-GSA is employed that works by combining the iterative improvement capability of particle swarm optimization (PSO) and gravitational search algorithm (GSA). A binary PSO is also fused with GSA to develop a BPSO-GSA algorithm. Both the hybrid algorithms i.e., PSO-GSA and BPSO-GSA, are compared against traditional algorithms, such as tabu search (TS), genetic algorithm (GA), differential evolution (DE), GSA and PSO algorithms. Moreover, another popular hybrid algorithm DE-GA is also used for comparison. Since earlier works have already studied the performance of these algorithms on mathematical benchmark functions, in this paper, two real-world-applicable independent case studies on biodiesel production are considered. Based on the extensive comparisons, significantly better solutions are observed in the PSO-GSA algorithm as compared to the traditional algorithms. The outcomes of this work will be beneficial to similar studies that rely on polynomial models. [ABSTRACT FROM AUTHOR]

This paper presents characteristics of model-based optimization methods utilized within the Generalized Self-Adapting Particle Swarm Optimization (GA– PSO) – a hybrid global optimization framework proposed by the authors. GAPSO has been designed as a generalization of a Particle Swarm Optimization (PSO) algorithm on the foundations of a large degree of independence of individual particles. GAPSO serves as a platform for studying optimization algorithms in the context of the following research hypothesis: (1) it is possible to improve the performance of an optimization algorithm through utilization of more function samples than standard PSO sample-based memory, (2) combining specialized sampling methods (i.e. PSO, Differential Evolution, model-based optimization) will result in a better algorithm performance than using each of them separately. The inclusion of model-based enhancements resulted in the necessity of extending the GAPSO framework by means of an external samples memory - this enhanced model is referred to as M-GAPSO in the paper. We investigate the features of two model-based optimizers: one utilizing a quadratic function and the other one utilizing a polynomial function. We analyze the conditions under which those model-based approaches provide an effective sampling strategy. Proposed model-based optimizers are evaluated on the functions from the COCO BBOB benchmark set. [ABSTRACT FROM AUTHOR]

Four-bar linkages are one of the most widely used mechanisms in industries. This paper presents a comparative study on the accuracy and efficiency of the optimum synthesis of path-generating four-bar linkages using five metaheuristic optimization algorithms. The utilized metaheuristic methods included two swarm intelligence-based algorithms, i.e., particle swarm optimization and hybrid particle swarm optimization, and three evolutionary-based algorithms, i.e., differential evolution, ensemble of parameters and mutation strategies in differential evolution, and linearly ensemble of parameters and mutation strategies in differential evolution. The objective function to be minimized is the sum of squares of the distance between the generated points and the precision points of a coupler point. The optimal design of four-bar linkages must meet the Grashof's criteria and exhibit sequential constraints that can prevent the occurrence of order defect. This study investigated five representative cases of the dimensional synthesis of four-bar path generators with and without prescribed timing and compared the optimal solutions of the utilized five metaheuristic methods to those of previously reported algorithms in literature. The improved metaheuristic methods exhibited superior optimal solution and enhanced reliability compared to the original methods. Moreover, three improved metaheuristic methods were not only easy implemented, but also more efficient for solving the optimal synthesis problems, particularly for high dimensional problems. [ABSTRACT FROM AUTHOR]

In this paper, six metaheuristic algorithms, in the form of artificial bee colony optimization, ant colony optimization, particle swarm optimization, differential evolution, firefly algorithm and teaching-learning-based optimization techniques are applied for parametric optimization of a multi-pass face milling process. Using those algorithms, the optimal values of cutting speed, feed rate and depth of cut for both roughing and finishing operations are determined for having minimum total production time and total production cost. It is observed that the teaching-learning-based optimization algorithm outperforms the others with respect to accuracy and consistency of the derived solutions as well as computational speed. Two statistical tests, i.e. paired t-test and Wilcoxson signed rank test also confirm its superiority over the remaining algorithms. Finally, these metaheuristics are employed for multi-objective optimization of the considered multi-pass milling process while concurrently minimizing both the objectives. [ABSTRACT FROM AUTHOR]

The soil water retention curve (SWRC) has a significant role in determining the unsaturated properties of soil. A stochastic optimisation algorithm named Rao-1 algorithm is employed to estimate the parameters of the SWRC model in this paper. The Rao-1 algorithm is a simple heuristic search algorithm containing only addition and multiplication operations. This paper introduces the method and its application in determining soil water retention this model parameters in detail. In this study, the van Genuchten model is used to depict the SWRC for its good fitting capacity, and the van Genuchten model parameters are determined using Rao-1 algorithm. The feasibility and efficiency of the proposed method are validated via the experimental results of 24 soil samples of 12 soil textural classes. Besides, the performance of Rao-1 algorithm is compared with that of salp swarm algorithm, the particle swarm optimization algorithm, differential evolution algorithm, and RETC program. Through comparative analysis, Rao-1 algorithm outperforms other methods in determining SWRC parameters. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Engineering Research (2307-1877) is the property of Kuwait University, Academic Publication Council and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper presents the evolution of combinational logic circuits by a new hybrid algorithm known as the Differential Evolution Particle Swarm Optimization (DEPSO), formulated from the concepts of a modified particle swarm and differential evolution. The particle swarm in the hybrid algorithm is represented by a discrete 3-integer approach. A hybrid multi-objective fitness function is coined to achieve two goals for the evolution of circuits. The first goal is to evolve combinational logic circuits with 100% functionality, called the feasible circuits. The second goal is to minimize the number of logic gates needed to realize the feasible circuits. In addition, the paper presents modifications to enhance performance and robustness of particle swarm and evolutionary techniques for discrete optimization problems. Comparison of the performance of the hybrid algorithm to the conventional Karnaugh map and evolvable hardware techniques such as genetic algorithm, modified particle swarm, and differential evolution are presented on a number of case studies. Results show that feasible circuits are always achieved by the DEPSO algorithm unlike with other algorithms and the percentage of best solutions (minimal logic gates) is higher. [ABSTRACT FROM AUTHOR]

Copyright of Informatica (03505596) is the property of Slovene Society Informatika and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

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]

Abstract: This paper presents combination of differential evolution (DE) and biogeography-based optimization (BBO) algorithm to solve complex economic emission load dispatch (EELD) problems of thermal generators of power systems. Emission substances like NO X , SO X , COX, Power demand equality constraint and operating limit constraint are considered here. Differential evolution (DE) is one of the very fast and robust, accurate evolutionary algorithms for global optimization and solution of EELD problems. Biogeography-based optimization (BBO) is another new biogeography inspired algorithm. Biogeography deals with the geographical distribution of different biological species. This algorithm searches for the global optimum mainly through two steps: migration and mutation. In this paper combination of DE and BBO (DE/BBO) is proposed to accelerate the convergence speed of both the algorithm and to improve solution quality. To show the advantages of the proposed algorithm, it has been applied for solving multi-objective EELD problems in a 3-generator system with NO X and SO X emission, in a 6-generators system considering NO X emission, in a 6-generator system addressing both valve-point loading and NO X emission. The current proposal is found better in terms of quality of the compromising and individual solution obtained. [Copyright &y& Elsevier]

Wireless sensor networks are appealing, largely because they do not need wired infrastructure, but it is precisely this feature that renders them energy-constrained. The duty cycle scheduling is perceived as a contributor to the energy efficiency of sensing. This paper developed a novel paradigm for modeling wireless sensor networks; in this context, an adaptive sensing scheduling strategy is proposed depending on event occurrence behavior, and the scheduling problem is framed as an optimization problem. The optimization objectives include reducing energy depletion and optimizing detection accuracy. We determine the explicit form of the objective function by numerical fitting and found that the objective function aggregated by the fitting functions is a bivariate multimodal function that favors the Fibonacci tree optimization algorithm. Then, with the optimal parameters optimized by the Fibonacci tree optimization algorithm, the scheduling scheme can be easily deployed, and it behaves consistently in the coming hours. The proposed "Fibonacci Tree Optimization Strategy" ("FTOS") outperforms lightweight deployment-aware scheduling (LDAS), balanced-energy scheduling (BS), distributed self-spreading algorithm (DSS) and probing environment and collaborating adaptive sleeping (PECAS) in achieving the aforementioned scheduling objectives. The Fibonacci tree optimization algorithm has attained a better optimistic effect than the artificial bee colony (ABC) algorithm, differential evolution (DE) algorithm, genetic algorithm (GA) algorithm, particle swarm optimization (PSO) algorithm, and comprehensive learning particle swarm optimization (CLPSO) algorithm in multiple runs. [ABSTRACT FROM AUTHOR]

In this study, the PID tuning method (controller design scheme) is proposed for a linear quarter model of active suspension system installed on the vehicles. The PID tuning scheme is considered as a multiobjective problem which is solved by converting this multiobjective problem into single objective problem with the aid of scalarization approaches. In the study, three different scalarization approaches are used and compared to each other. These approaches are called linear scalarization (weighted sum), epsilon-constraint and Bensons methods. The objectives of multiobjective optimization are selected from the time-domain properties of the transient response of the system which are over-shoot, rise time, peak time and error (in total there are four objectives). The aim of each objective is to minimize the corresponding property of the time response of the system. First, these four objective is applied to the scalarization functions and then single objective problem is obtained. Finally, these single objective problems are solved with the aid of heuristic optimization algorithms. For this purpose, four optimization algorithms are selected, which are called Particle Swarm Optimization, Differential Evolution, Firefly, and Cultural Algorithms. In total, twelve implementations are evaluated with the same number of iterations. In this study, the aim is to compare the scalarization approaches and optimization algorithm on active suspension control problem. The performance of the corresponding cases (implementations) are numerically and graphically demonstrated on transient responses of the system. [ABSTRACT FROM AUTHOR]

Driver pathways have been acknowledged to play critical roles in the initiation and progression of cancers►hence it is essential for precision medicine related studies to develop accurate and efficient methods to identify them. Although previous approaches have shown promising results by integrating multi-omics data, their preset artificial parameters may decrease the convenience to use and limit the application scalability. In this paper, a novel integration approach is proposed to incorporate four omics data, i.e., construct a weighted non-binary mutation matrix without presetting artificial parameters. A parameter-free identification model is put forward based on it. It takes advantage of the association between genes in the PPI network as well as balances the contribution of coverage and mutual exclusivity with the harmonic mean. Furthermore, a cooperative co-evolution algorithm is proposed for solving this model. In the algorithm, a particle swarm optimization algorithm suitable for solving combinatorial problems is presented. Three cooperative operators are devised to construct the cooperation among the populations and the swarm to increase the population diversity. Both real biological datasets and simulated ones were exerted to perform experimental comparisons among the proposed method and six other state-of-the-art ones. The gene sets identified by the presented method generally contain more genes involved in known signaling pathways than those obtained by the other methods. Simultaneously, both high accuracy and high efficiency of the proposed method were verified in experiments, making it practical in realistic applications and an effective supplementary tool to identify driver pathways. • A non-binary mutation matrix is constructed without artificial adjustable parameters. • The model incorporates gene association and balances coverage and mutual exclusivity. • A PSO algorithm suitable for solving combinatorial problems is presented. • A co-operative co-evolution algorithm is put forward for solving the presented model. • The performance is compared among the proposed method and seven state of the art ones. [ABSTRACT FROM AUTHOR]

Intelligent optimization algorithms are widely utilized to deal with complex optimization problems in various areas. However, a single intelligent optimization algorithm cannot handle well more and more complex optimization problems. The ensemble strategy can integrate several different operators and algorithms by using some appropriate strategies and maybe obtain better optimization performance. In this paper, a new ensemble multi-swarm method based on teaching–learning-based optimization (EMTLBO) was proposed by integrating three different algorithms including the original teaching–learning-based optimization algorithm, its variant with neighborhood search and the variant with differential evolution. In EMTLBO, a new evaluating mechanism based on the fitness-based and diversity-based metrics (FDEM) for each sub-swarm was proposed to evaluate the optimization performance after a continuous generation interval. Moreover, an algorithm matching mechanism based on ranking for sub-swarms (AMM) is adapted to re-divide the population into three sub-swarms and match a suitable algorithm for each sub-swarm so as to increase the whole optimization performance. Furthermore, the experimental results on CEC2014 and CEC2017 test suits verify the feasibility and optimization performance of EMTLBO. Finally, the proposed algorithm is extended to optimize the segmentation thresholds of images and the segmentation performances on different benchmark images show that EMTLBO has good performance in most cases. • A new evaluating mechanism was proposed to evaluate the optimization performance. • Algorithm matching mechanism is adopted to match a suitable algorithm for each sub-swarm. • The experimental results on CEC2014 and CEC2017 test suits verify EMTLBO. • The proposed EMTLBO algorithm is extended to deal with image segmentation problems. [ABSTRACT FROM AUTHOR]

To address the problems of uneven distribution and low coverage of wireless sensor network (WSN) nodes in random deployment, a node coverage optimization strategy with an improved COOT bird algorithm (COOTCLCO) is proposed. Firstly, the chaotic tent map is used to initialize the population, increase the diversity of the population, and lay the foundation for the global search for the optimal solutions. Secondly, the Lévy flight strategy is used to perturb the individual positions to improve the search range of the population. Thirdly, Cauchy mutation and an opposition-based learning strategy are fused to perturb the optimal solutions to generate new solutions and enhance the ability of the algorithm to jump out of the local optimum. Finally, the COOTCLCO algorithm is applied to WSN coverage optimization problems. Simulation results show that COOTCLCO has a faster convergence speed and better search accuracy than several other typical algorithms on 23 benchmark test functions; meanwhile, the coverage rate of the COOTCLCO algorithm is increased by 9.654%, 13.888%, 6.188%, 5.39%, 1.31%, and 2.012% compared to particle swarm optimization (PSO), butterfly optimization algorithm (BOA), seagull optimization algorithm (SOA), whale optimization algorithm (WOA), Harris hawks optimization (HHO), and bald eagle search (BES), respectively. This means that in terms of coverage optimization effect, COOTCLCO can obtain a higher coverage rate compared to these algorithms. The experimental results demonstrate that COOTCLCO can effectively improve the coverage rate of sensor nodes and improve the distribution of nodes in WSN coverage optimization problems. [ABSTRACT FROM AUTHOR]

Taking the full network observability of power system and the least number of PMU as objective, to appearing fault situation in the grid, this paper proposes Differential Evolution and Particle Swarm Optimization (DEPSO) algorithm in view of the system failure rate. The improved DEPSO algorithm is global optimization, the algorithm takes the constraint condition of fault rate into account during the course of seeking optimal solutions. At the end, through the examples show that the algorithm compares with the existing optimization methods, which can reduce the number of PMU configuration and achieve completely observability of the system, at the same time, and stable operation of the system, through the simulation results verify feasibility and valibity of the algorithm. [ABSTRACT FROM AUTHOR]

Unmanned aerial vehicles (UAVs) have shown their superiority in military and civilian missions. In the face of complex tasks, many UAVs are usually needed to cooperate with each other. Therefore, multi-UAV cooperative target search has attracted more and more scholars' attention. At present, there are many bionic algorithms for solving the cooperative search problem of multi-UAVs, including particle swarm optimization algorithm (PSO) and differential evolution (DE). Pigeon-inspired optimization (PIO) is a new swarm intelligence optimization algorithm proposed in recent years. It has great advantages over other algorithms in convergence, robustness, and accuracy, and has few parameters to be adjusted. Aiming at the shortcomings of the standard pigeon colony algorithm, such as poor population diversity, slow convergence speed, and the ease of falling into local optimum, we have proposed chaotic disturbance pigeon-inspired optimization (CDPIO) algorithm. The improved tent chaotic map was used to initialize the population and increase the diversity of the population. The disturbance factor is introduced in the iterative update stage of the algorithm to generate new individuals, replace the individuals with poor performance, and carry out disturbance to increase the optimization accuracy. Benchmark functions and UAV target search model were used to test the algorithm performance. The results show that the CDPIO had faster convergence speed, better optimization precision, better robustness, and better performance than PIO. [ABSTRACT FROM AUTHOR]

The optimal resource allocation in the large-scale intelligent device-to-device (D2D) communication system is of great importance for improving system spectrum efficiency and ensuring communication quality. In this study, the D2D resource allocation is modelled as an ultrahigh-dimensional optimization (UHDO) problem with thousands of binary dimensionalities. Then, for efficiently optimizing this UHDO problem, the coupling relationships among those dimensionalities are comprehensively analysed, and several efficient variable-grouping strategies are developed, i.e., cellular user grouping (CU-grouping), D2D pair grouping (DP-grouping), and random grouping (R-grouping). In addition, a novel evolutionary algorithm called the cooperatively coevolving particle swarm optimization with variable-grouping (VGCC-PSO) is developed, in which a novel mutation operation is introduced for ensuring fast satisfaction of constraints. Finally, the proposed UHDO-based allocation model and VGCC-PSO algorithm as well as the grouping and mutation strategies are verified by a comprehensive set of case studies. Simulation results show that the developed VGCC-PSO algorithm performs the best in optimizing the UHDO model with up to 6000 dimensionalities. According to our study, the proposed methodology can effectively overcome the "curse of dimensionality" and optimally allocate the resources with high accuracy and robustness. [ABSTRACT FROM AUTHOR]

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]

In order to solve the shortcomings of particle swarm optimization (PSO) in solving multiobjective optimization problems, an improved multiobjective particle swarm optimization (IMOPSO) algorithm is proposed. In this study, the competitive strategy was introduced into the construction process of Pareto external archives to speed up the search process of nondominated solutions, thereby increasing the speed of the establishment of Pareto external archives. In addition, the descending order of crowding distance method is used to limit the size of external archives and dynamically adjust particle parameters; in order to solve the problem of insufficient population diversity in the later stage of algorithm iteration, time-varying Gaussian mutation strategy is used to mutate the particles in external archives to improve diversity. The simulation experiment results show that the improved algorithm has better convergence and stability than the other compared algorithms. [ABSTRACT FROM AUTHOR]

Aiming at the problems of low search efficiency and inaccurate optimization of existing service composition optimization methods, a new multiobjective optimization model of cloud manufacturing service composition was constructed, which took service matching degree, composition synergy degree, cloud entropy, execution time, and execution cost as optimization objectives, and an improved particle swarm optimization algorithm (IPSOA) was proposed. In the IPSOA, the integer encoding method was used for particle encoding. The inertia coefficient and two acceleration coefficients were improved by introducing the normal cloud model, sine function, and cosine function. The global search ability of IPSOA in the early stage was improved, and its prematurity was restrained to form a more comprehensive solution space. In the later stage, IPSOA focused on the local fine search and improved the optimization precision. Taking automatic guided forklift manufacturing task as an example, the correctness of the proposed multiobjective optimization model of cloud manufacturing service composition and the effectiveness of its solution algorithm were verified. The performance of IPSOA was analyzed and compared with standard genetic algorithm (SGA) and traditional particle swarm optimization (PSO). Under the same conditions, IPSOA had a faster convergence speed than PSO and SGA and had better performance than PSO. [ABSTRACT FROM AUTHOR]

Graphic processing units (GPUs) emerged recently as an exciting new hardware environment for a truly parallel implementation and execution of Nature and Bio-inspired Algorithms with excellent price-to-power ratio. In contrast to common multicore CPUs that contain up to tens of independent cores, the GPUs represent a massively parallel single-instruction multiple-data devices that can nowadays reach peak performance of hundreds and thousands of giga floating-point operations per second. Nature and Bio-inspired Algorithms implement parallel optimization strategies in which a single candidate solution, a group of candidate solutions (population), or multiple populations seek for optimal solution or set of solutions of given problem. Genetic algorithms (GA) constitute a family of traditional and very well-known nature-inspired populational meta-heuristic algorithms that have proved its usefulness on a plethora of tasks through the years. Differential evolution (DE) is another efficient populational meta-heuristic algorithm for real-parameter optimization. Particle swarm optimization (PSO) can be seen as nature-inspired multiagent method in which the interaction of simple independent agents yields intelligent collective behavior. Simulated annealing (SA) is global optimization algorithm which combines statistical mechanics and combinatorial optimization with inspiration in metallurgy. This survey provides a brief overview of the latest state-of-the-art research on the design, implementation, and applications of parallel GA, DE, PSO, and SA-based methods on the GPUs. [ABSTRACT FROM AUTHOR]

With the advancement of technology, the need of antenna arrays with shaped power patterns increases day by day for the purpose of improvement of communication. In this article, we represent a new method for designing optimized linear array with shaped beam radiation pattern of desired specifications. The main objective is to obtain suitable current excitation amplitude and phase distribution for the linear array elements so that it can produce the desired custom shaped radiation pattern as the user demands. The design procedure utilizes an improved variant of a prominent and efficient metaheuristics of current interest, namely the Differential Evolution (DE). In our modified DE algorithm, denoted as DE rBM 2SX, new mutation and crossover strategies are employed. These modifications help to overcome some drawbacks of classical DE. Two examples of linear array with shaped radiation pattern design problem are considered to illustrate the effectiveness of our algorithm. Our results are also compared with two state-of-the-art variants of DE and Particle Swarm Optimization (PSO) -- namely JADE and CLPSO (Comprehensive Learning Particle Swarm Optimization). The comparison clearly reveals that our optimization algorithm is more efficient than JADE or CLPSO in finding optimum element excitation amplitude and phase distribution for the desired shaped pattern. [ABSTRACT FROM AUTHOR]