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High-utility itemsets mining (HUIM) is an important research topic in data mining that consists of extracting efficient itemsets that generate high profit in databases. Metaheuristic algorithms are good candidates for finding some sufficiently good high-utility itemsets (HUIs) while reducing the prohibitive computational cost incurred by such mining. However, metaheuristic algorithms suffer from crucial issues: runtime and memory consumption, entailing scalability issues. To contribute in alleviating these drawbacks, we explore a hybrid approach combining metaheuristics with an optimization technique, and experimentally show the obtainment of better quality solutions. The exploration component in our approach relies on the crow search algorithm (CSA) which is a method that presents a strong capacity in the global search process. The exploitation component is based on the particle swarm optimization (PSO) which is an established stochastic optimization technique known to have a good convergence capability. This article proposes the HUIM-ICSO algorithm, coupling CSA and PSO, as a hybrid method for mining HUIs. In addition to the proposed main CSA-based algorithm, two additional novel enhanced variants are incorporated and integrated with PSO. Experiments are undertaken on 12 publicly available datasets and compared with state-of-the-art algorithms, such as mHUIMiner, HUIM-SPSO and HUIM-AF. Experiments show that, as the number of transactions or items grows, the suggested approach remains scalable and delivers favorable outcomes in terms of runtime, memory usage, and the quantity of HUIs mined, all while maintaining a good convergence rate. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is a population-based metaheuristic search algorithm that exhibits excellent performance. However, it is sensitive to mutation strategies and control parameters.To mitigate the impact of these factors, this paper proposes refining differential evolution with mutation rate and neighborhood weight local search(MRNLDE). The algorithm guides individuals in selecting an appropriate mutation mode through the mutation rate, effectively utilizing the evolutionary information inherent in the individuals themselves, thereby enhancing the search efficiency of the algorithm. Furthermore, the neighborhood individual information is utilized to re-explore the solution space, allowing for a comprehensive exploration of individual evolutionary potential and enhancing the algorithm's diversity. The performance of MRNLDE was validated under two sets of benchmark problems at the Institute of Electrical and Electronics Engineers (IEEE) Conference on Computing in Evolution (CEC), and the results show that MRNLDE performs well overall. [ABSTRACT FROM AUTHOR]

Arithmetic optimization algorithm (AOA) is a meta-heuristic optimization method based on mathematical operators proposed in recent years. Although it has good performance, it can also lead to insufficient local search ability and falling into local optima when solving complex optimization problems. In order to make up for the above shortcomings, the optimization performance of AOA is further improved. This paper proposes a hybrid algorithm based on AOA and particle swarm optimization (PSO) called HAOAPSO. Firstly, a compound opposition-based learning (COBL) strategy is introduced to broaden the scope of finding optimal solutions to help the algorithm better jump out of local optima. Secondly, PSO is combined with AOA that integrates COBL to improve the algorithm's local search ability, so as to improve the overall search efficiency of the algorithm. In addition, experiments are performed on 23 classical benchmark functions with different characteristics and five engineering design optimization problems, and the experimental results of HAOAPSO are compared with those of other well-known optimization algorithms to comprehensively evaluate the performance of the proposed algorithm. The simulation results show that HAOAPSO can provide better solutions in most cases when solving global optimization problems such as engineering, with better convergence speed and accuracy. [ABSTRACT FROM AUTHOR]

The stochastic fractal search (SFS) algorithm, among population-based metaheuristic automation algorithms, is a robust optimization algorithm for solving optimization problems in different fields of science, inspired by the diffusion feature and natural growth phenomenon seen regularly in random fractals. However, as in population-based optimization algorithms, it is a great challenge to effectively design the selection process in the SFS method. To imitate the selection process in nature effectively and accurately, the dynamic-fitness-distance-balance (dFDB) selection method has been used in the SFS algorithm in six different versions. In this way, the dFDB-SFS algorithm has been developed, which more effectively mimics nature with exploitation, exploration, and balanced search capabilities. Firstly, the performance of the proposed dFDB-SFS algorithm was investigated in CEC 2020 benchmark test functions. Wilcoxon and Friedman statistical analyses of the results obtained from the test functions were made and according to these analysis results, the best version of the proposed approach was determined. Secondly, the performance of the proposed algorithm was investigated in determining photovoltaic module parameters, which is one of the real-world engineering problems. In this article, the dFDB-SFS algorithm uses the root mean square error (RMSE) as the objective function to estimate the unknown parameters of the single diode model (SDM), double diode model (DDM), and PV module models. In terms of a quantitative and qualitative performance evaluation, it reveals that the proposed algorithm provides better results than other proposed algorithms in terms of accuracy and robustness when obtaining PV parameters. [ABSTRACT FROM AUTHOR]

UWB positioning can be modeled as an optimization problem for a fitness function, which is resolved through the conventional whale optimization algorithm. The fitness function used in the conventional whale positioning algorithm does not use the range measurement data between labels, and the range measurement data is incomplete, which leads to a limited improvement in its positioning accuracy. Consequently, a novel whale cooperative positioning algorithm that can increase positioning accuracy is presented in this paper. First, a fitness function is established during the positioning process that contains the range measurement data between the labels to improve positioning accuracy. Then, the conventional whale positioning method provides a good initial position for the labels, enabling the proposed algorithm to quickly search for the optimal position. Finally, Levy flight mode is adopted to prevent the positioning result from converging to the local optimal solution. According to simulation results, the proposed algorithm can provide better positioning accuracy than the conventional whale positioning algorithm while realizing simultaneous positioning of all the labels. [ABSTRACT FROM AUTHOR]

Jaya is a metaheuristic algorithm that uses a pair of random internal parameters to adjust its exploration and exploitation search behaviors. Such a random setting can negatively affect the search performance of the algorithm by causing inappropriate search behavior in some iterations. To tackle this issue, the present study deals with developing a new fuzzy decision-making mechanism for dynamic adjusting the trade-off between the exploration and exploitation search behaviors of the Jaya method. The new algorithm is named Fuzzy Reinforced Jaya (FRJ) method. The search capability of the FRJ is evaluated in solving a suite of unconstrained mathematical benchmarks and constrained mechanical and structural optimization problems with buckling and natural frequency constraints. Also, the relevant decision variables are selected from both continuous and discrete domains. To provide a deeper insight into the effect of the defined auxiliary fuzzy module, the performance of the algorithm is evaluated and discussed using normalized diversity concept and behavioral diagrams. Also, employing different statistical analyses (e.g., Q–Q diagrams, Wilcoxson and Friedman tests), the significance of the outcomes is evaluated. Also, the numeric achievements are compared with six other well-stablished techniques. Attained outcomes indicate that the proposed FRJ, as a self-adaptive and parameter-free method, provides superior and promising results in the terms of stability, accuracy, and computational cost in solving mathematical and structural optimization problems. [ABSTRACT FROM AUTHOR]

Directional sensor networks (DSNs) are ad-hoc networks which are utilized in different industrial applications. Their usual engagements are to monitor and to perform the coverage of all specific targets in the observing fields permanently. These kinds of networks include numerous configurable directional sensors in which they can be utilized in one of the possible directions along with the one of their adjustable ranges. Although the energy harvesting methodology is being applied for these battery-hungry applications, the battery management and network lifetime maximization are still prominent challenges. In this paper, the network lifetime extension is formulated to a discrete optimization problem which is a famous non-deterministic polynomial time hardness (NP-Hard) problem. To solve this combinatorial problem, a discrete cuckoo search algorithm (D-CSA) is designed and is called in several rounds. A cover is a sub set of configured sensors capable of monitoring all targets in the observing field. In each round, the most efficient cover is constituted along with its activation time. In the determined activation time, the sensors in the cover are scheduled in wakeup mode whereas others are set in sleep mode to save energy. Despite other meta-heuristic algorithms, this proposed algorithm utilizes the novel defined discrete walking around procedures that makes to reach a good balance between exploration and exploitation in this complex search space. The proposed algorithm has been tested in different scenarios to be evaluated. The simulation results in the variety circumstances prove the superiority of the proposed algorithm is about 20.29%, 19.55%, 14.40%, 14.51%, 7.70% and 8.03% in term of average lifespan improvement against H-MNLAR, Hm-LifMax-BC, GA, ACOSC, H-GATS, and HDPSO algorithms, respectively. The results also show the high potential scalability of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper presents an effective approach for solving economic load dispatch problems contemplating the scheduling a set of thermal generating units to produce a specific power at low consumption costs. These problems can be thought of as nonlinear, non-convex, and highly constrained optimization problems with a large number of local minima. To cope with the above issues in solving such problems, a new meta-heuristic named capuchin search algorithm was adopted. To boost the search performance of this algorithm as well as to mitigate its early convergence and regression to the local optimum, it was hybridized with another algorithm and improved using several positive amendments. First, a memory element was added to this algorithm to ameliorate its position and velocity update mechanisms in order to exploit the most encouraging candidate solutions. Second, two adaptive parametric functions were used to manage the exploration and exploitation features of this algorithm and balance them appropriately. Finally, the hybridization was made using the gradient-based optimizer to strengthen the intensification ability of this algorithm and balance its searching ability to fulfill sensible search performance. The proficiency of the proposed algorithm was divulged by assessing it on computationally difficult economic load dispatch problems under 6 different tests with a generator of 3, 13, 40, 80, and 140 units, each with different constraints and load conditions. The proposed algorithm provided the best performance among many other competitors. Its superiority and practicality were revealed by obtaining optimal solutions for large-scale test cases such as 40-unit and 140-unit test systems. [ABSTRACT FROM AUTHOR]

The Harris hawks optimization (HHO) algorithm is a new metaheuristic algorithm proposed in recent years. Due to the shortcomings of this algorithm in solving complex high-dimensional optimization problems with a slow convergence speed, low accuracy, and the high likelihood to fall into local optimum, a mixed Harris hawks optimization (MHHO) algorithm based on the pinhole imaging strategy is proposed, including four strategies to improve the optimization performance. Firstly, the pinhole imaging strategy is used to enable the Harris' hawks to approach the optimal solution faster and accelerate convergence. Secondly, the spiral parameter is introduced into the exploration phase to help the searching paths of the Harris' hawks more diverse and improve the global search ability of the algorithm. Finally, the greedy strategy of the aquila optimization algorithm and the position update strategy of the flower pollination optimization algorithm are embedded in the exploitation stage to make the algorithm jump out of local optimum effectively. To verify the effectiveness of the proposed MHHO algorithm, it is compared with the classical HHO algorithm and 16 other state-of-the-art algorithms, and extensively tested on 23 well-known benchmark functions, the IEEE CEC2017 test sets, and three complex constrained engineering optimization problems. The test results show that MHHO achieves the top ranking on both the benchmark functions and the CEC2017 test sets, demonstrating its superior performance in terms of faster convergence speed and higher accuracy. [ABSTRACT FROM AUTHOR]

Back propagation (BP) is widely used for parameter search of fully-connected layers in many neural networks. Although BP has the potential of quickly converging to a solution, due to its gradient-based nature, it tends to fall into a local optimum. Metaheuristics such as evolutionary computation (EC) techniques, as gradient-free methods, may have excellent global search capability due to their stochastic nature. However, these techniques tend to perform worse than BP in terms of convergence speed. In this paper, a hybrid gradient descent search algorithm (HGDSA) is proposed for training the parameters in fully-connected neural networks. HGDSA initially searches the space extensively by means of an ensemble of gradient descent strategies in the early stage and then uses BP as an exploitative local search operator. Moreover, a self-adaptive method which selects strategies and updates the learning rates of strategies has been designed and embedded in the global search operators to prevent stagnation in local optima. To verify the effectiveness of HGDSA, experiments were performed on eleven classification datasets. Experimental results demonstrate that the proposed HGDSA possesses both powerful global and local search abilities. Furthermore, the proposed approach appears to be promising also on high-dimensional datasets. [ABSTRACT FROM AUTHOR]

Cooperation search algorithm (CSA) is a new metaheuristic algorithm inspired from the team cooperation behaviors in modern enterprises and is characterized by fast convergence. However, for complex multimodal problems, it may get trapped into local optima and suffer from premature convergence for the shortcoming of population updating guided only by leading individuals. In this paper, the issue of low convergence efficiency and convergence accuracy of the CSA algorithm on complex multimodal problems is dramatically alleviated by integrating the mutation and crossover operators in DE algorithm. Experimental results demonstrate the better performance of CCSA on convergence speed and accuracy as compared to other existing optimizers. Furthermore, aiming at the problem that there is no universal approach for the multi-degree reduction in Ball Bézier surfaces under different interpolation constrains, we propose a new method to solve this problem by introducing metaheuristic methods, where the change of interpolation constrains is treated as the change of decision variables. The modeling examples show that the proposed method is effective and easy to implement under different interpolation constrains, which can achieve the multi-degree reduction in Ball Bézier surfaces at one time and can simplify the degree reduction procedure significantly. [ABSTRACT FROM AUTHOR]

The marine predators algorithm (MPA) is a metaheuristic algorithm for solving optimization problems. MPA divides the whole optimization process into three phases evenly, and each phase corresponds to a different search agent update strategy. Such a setup makes MPA inflexible when facing different optimization problems, which affects the optimization performance. In this paper, we propose a novel modified MPA hybridizing by Q-learning (QMPA), which applies reinforcement learning to the selection of update strategy, and selects the most appropriate position update strategy for search agents in different iteration stages and states. It can effectively compensate for the deficiency of MPA's adaptive ability when facing different optimization problems. The performance of QMPA is tested on classical benchmark functions, the CEC2014 test suite, and engineering problems. In the classical benchmark functions test, QMPA is compared with MPA in 10, 30, and 50 dimensions. QMPA performs better than MPA for seven of the ten functions when the dimension is 10 and 30. The results of dimension 50 show that QMPA outperforms MPA in 5 functions and is close to it in 4 functions. Then, comparing QMPA with algorithms such as grey wolf optimizer, particle swarm optimization, slime mould algorithm, sine cosine algorithm, reptile search algorithm, and aquila optimizer, the results show that QMPA has the best performance on 22 of the total 30 functions in the CEC2014 test suite. Finally, QMPA is tested on two commonly used real-world engineering problems and gives the most optimal results. In general, the adaptive update strategy proposed in this paper improves the optimization performance of the MPA algorithm in terms of convergence and stability. [ABSTRACT FROM AUTHOR]

This paper introduces a novel population-based vortex search algorithm (PVS) to improve the weakness of the global search capability of the original Vortex Search (VS) algorithm which is a simple and efficient physics-based metaheuristic and originally has a single-solution-based structure. Single-solution-based metaheuristics perform a local search in the neighborhood of a single solution, whereas population-based metaheuristics conduct the search process by creating several candidate solutions at different points in the search space. The fast-running structures of single-solution-based algorithms may cause the search process to get stuck in the local optimum in some cases. The proposed algorithm transforms VS into a population-based structure with a location update operator and the polynomial mutation operator. Also, the strategy of generating solutions based on the radius reduction mechanism around a center is maintained. Furthermore, two variants of PVS, called PVS_a and PVS_b, are presented in this study. The performance of the proposed approach is investigated by applying a set of experimental series. Three different benchmark sets involving (i) 20 classical benchmark functions, (ii) 29 CEC2017 test functions, and (iii) 10 CEC2019 test functions are employed in experiments. In addition, four real-world-constrained optimization problems are used to evaluate the effectiveness of PVS. Considering the experimental results obtained from the comparison of the proposed algorithm with both state-of-the-art and recent metaheuristics, the developed PVS_a algorithm provides highly quite promising and superior outcomes in solution quality and robustness. [ABSTRACT FROM AUTHOR]

The minimum vertex cover problem (MVCP) is one of the well-known NP-complete problems that can be used to formulate numerous real-life applications. The MVCP has been solved using different approaches, exact, heuristic, and metaheuristic. Chemical reaction optimization (CRO) is a population-based metaheuristic algorithm that simulates what happens in chemical reactions to solve many problems. In this paper, the MVCP is solved using hybridization of a modified version of the CRO algorithm and the best-first search (BFS) algorithm. This hybridization is symbolized by MCROA-BFS. The BFS algorithm is exploited to generate initial populations with high-quality initial solutions in comparison with the random bit-vector (RBV) approach as a traditional approach for generating initial populations for several population-based metaheuristic algorithms. At first, the MCROA is evaluated analytically in terms of run time complexity. Then the performance of the MCROA is evaluated experimentally to show the effectiveness of exploiting the BFS in terms of quality of gained solutions and run time. The most valuable player algorithm (MVPA), genetic algorithm (GA), and hybrid CRO algorithm (HCROA) are metaheuristic algorithms that used the RBV approach to generate the initial population. MCROA-BFS is compared, under the selected performance metrics, with these metaheuristic algorithms in addition to MCROA with the RBV approach (MCROA-RBV). The conducted experiments were carried out using 18 instances of DIMACS and BHOSLIB benchmarks. The experimental results revealed the superiority of MCROA-BFS over MVPA, GA, and MCROA-RBV in terms of both performance metrics. Although HCROA has the smallest run time, it failed to obtain high-quality solutions in comparison with MCROA. [ABSTRACT FROM AUTHOR]

The rapid growing number of web services has posed new challenges for service composition computing. How to combine services that meet the needs of users in the least amount of time from a huge number of candidate services is a hot topic of research today. As a meta-heuristic algorithm for solving optimization problems, salp swarm algorithm (SSA) has been widely applied to case scenarios in different fields due to its simple structure and high performance. However, QoS-aware service composition is a discrete problem and existing methods are not suitable for it. Therefore, in this paper, we propose an improved SSA integrating chaotic mapping method for QoS service composition selection, named CSSA. Through the randomness and ergodicity of chaos, reducing the possibility of falling into local optimum and strengthening the exploitation capability of the algorithm. In addition, a fuzzy continuous neighborhood search method is used to enhance the local search capability of the algorithm which makes the discrete space of service composition in a way similar to continuous space. Finally, two well-known datasets are used to verify the effectiveness of CSSA compared to three advanced algorithms and original SSA. The test results demonstrate that CSSA has significant advantages and it also has satisfactory performance in large scale scenarios. [ABSTRACT FROM AUTHOR]

The Fixed Set Search (FSS) is a novel metaheuristic that adds a learning mechanism to the Greedy Randomized Adaptive Search Procedure (GRASP). In recent publications, its efficiency has been shown on different types of combinatorial optimization problems like routing, machine scheduling and covering. In this paper the FSS is adapted to multi-objective problems for finding Pareto Front approximations. This adaptation is illustrated for the bi-objective Minimum Weighted Vertex Cover Problem (MWVCP). In this work, a simple and effective bi-objective GRASP algorithm for the MWVCP is developed in the first stage. One important characteristic of the proposed GRASP is that it avoids the use of weighted sums of objective functions in the local search and the greedy algorithm. In the second stage, the bi-objective GRASP is extended to the FSS by adding a learning mechanism adapted to multi-objective problems. The conducted computational experiments show that the proposed FSS and GRASP algorithm significantly outperforms existing methods for the bi-objective MWVCP. To fully evaluate the learning mechanism of the FSS, it is compared to the underlying GRASP algorithm on a wide range of performance indicators related to convergence, distribution, spread and cardinality. [ABSTRACT FROM AUTHOR]

Over the last decade, the size and complexity of real-world problems have grown dramatically, necessitating more effective tools. Nature-inspired metaheuristic algorithms have proven to be a promising tool for solving such problems due to their performance in a variety of fields. JAYA algorithm is a novel population-based algorithm which could have been able to present reliable results. This is because it does not need any parameters to be set other than the population size and the maximum number of iteration. Despite its positive feedbacks, this algorithm should be modified to witness more efficiency. This paper aims to amend the original version of Jaya to present a high-efficiency version named Powerful Enhanced Jaya (PEJAYA). In other words, the methodology of updating position in Jaya is modified to enhance the convergence and search capabilities. This approach is assessed according to solve 20 well-known benchmark functions, feature selection, and statistical tests. The output results of proposed optimization algorithm are then evaluated by comparing it with other recent algorithms including crow search algorithm (CSA), standard version of JAYA, particle swarm optimization (PSO), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), moth-flame optimization (MFO) and sine–cosine algorithm (SCA). Solving a real-world problem is another way of checking the efficiency of this approach with other published works. Prompt escape from local minima, superior convergence, and stability demonstrate that the suggested approach is a very powerful instrument that may be employed in a variety of optimization situations. [ABSTRACT FROM AUTHOR]

Power system stabilizers (PSSs) are extensively used in generator units to enhance the transient stability of the power system. Hence, optimal tuning and placement of the parameters of PSS are crucial for the efficiency of the stabilizer. Researchers have been proposed many methods for optimizing such parameters. In this paper, the Crow search algorithm (CSA), which is based on the intelligence of crows, was employed in a single-machine infinite-bus (SMIB) system to determine the optimum parameters of the PSS. Modeling and simulation of the SMIB and designing of PSS were made by MATLAB/Simulink. PSSs are designed to minimize low-frequency oscillations such as power angle, rotor speed, and field current deviation following a large disturbance. Our objective in this study is the minimization of the rotor speed deviation. The results of the simulations proved the effectiveness and robustness of the optimization process compared to other metaheuristic algorithms such as particle swarm optimization (PSO) and genetic algorithm (GA). When compared to the performance attained by the GA-based and PSO-based PSS controller designs, the simulations show that the CSA-based PSS delivers a far better dynamic response when the system is disrupted. The CSA-based PSS settles 48.1% faster than the PSO-based PSS and 55.7% faster than the GA-based PSS. CSA has just 2 parameters to adjust, making it much easier to implement than other methods. These parameters for PSO and GA are 4 and 6. When CSA-based PSS is used in the SMIB system, overshoot and low-frequency oscillations are also significantly reduced compared to other methods. [ABSTRACT FROM AUTHOR]

Crow search algorithm (CSA) is a novel meta-heuristic optimization algorithm based on the intelligent behavior of the crow population. Although the algorithm has the characteristics of few parameters, simple structure, and easy application, it has the shortcomings of low convergence accuracy and imbalance between exploration and exploitation capabilities. The occurrence of these issues is originated from crow learning from only one goal. In this paper, an improved crow search algorithm based on oppositional forgetting learning (OFLCSA) is proposed. In order to solve the shortcomings of CSA, the forgetting mechanism is introduced to help the algorithm jump out of the local optimum. Moreover, the opposition-based learning (OBL) strategy is combined with the forgetting mechanism to increase the probability of approaching the optimal solution. In addition, the elite crow and adaptive flight length are used to improve the convergence accuracy. To verify the performance of OFLCSA, experiments were conducted on the Congress on Evolutionary Computation (CEC) 2014 and CEC 2019 benchmark functions. OFLCSA is compared with the ten state-of-the-art meta-heuristic optimization algorithms. Moreover, OFLCSA is evaluated by four real-world engineering applications. Experimental results and analysis show that OFLCSA is a competitive meta-heuristic optimization algorithm. [ABSTRACT FROM AUTHOR]

In today’s data-centric world, the significance of generated data has increased manifold. Clustering the data into a similar group is one of the dynamic research areas among other data practices. Several algorithms’ proposals exist for clustering. Apart from the traditional algorithms, researchers worldwide have successfully employed some metaheuristic approaches for clustering. The crow search algorithm (CSA) is a recently introduced swarm-based algorithm that imitates the performance of the crow. An effective crow search algorithm (ECSA) has been proposed in the present work, which dynamically attunes its parameter to sustain the search balance and perform an oppositional-based random initialization. The ECSA is evaluated over CEC2019 Benchmark Functions and simulated for data clustering tasks compared with well-known metaheuristic approaches and famous partition-based K-means algorithm over benchmark datasets. The results reveal that the ECSA performs better than other algorithms in the context of external cluster quality metrics and convergence rate. [ABSTRACT FROM AUTHOR]

Marine predators algorithm (MPA) is one of the recently proposed metaheuristic algorithms. In the MPA, position update mechanisms are implemented, emphasizing global search in the first part of the search process, balanced search in the middle, and local search in the last part. This may adversely affect the local search capability of the algorithm in the first part of the search process and the global search capability in the last part of the search process. To overcome these issues, an algorithm called MultiPopMPA with a multi-population and multi-search strategy is proposed in this study. Thanks to the proposed algorithm, local, balanced, and global search strategies of the original MPA were utilized from the beginning to the end of the search process. Thus, it is aimed to contribute to a more detailed search of the parameter space. In this study, the proposed algorithm has been applied in training artificial neural networks for 21 different classification datasets. The success of the algorithm has been scored on precision, sensitivity, specificity, and F1-score metrics and compared with eight different metaheuristic algorithms, including the original MPA. In terms of the mean rank of success, the proposed MultiPopMPA has been ranked first in precision, sensitivity, and F1-score metrics and ranked second in the specificity metric. In addition, it has been observed that the proposed algorithm outperforms its competitors in most cases in terms of convergence and stability. Finally, Wilcoxon’s signed-rank test results calculated through the MSE metric showed that the proposed algorithm produced statistically significant results in most cases. [ABSTRACT FROM AUTHOR]

The metaheuristic optimization algorithms are relatively new optimization algorithms introduced to solve optimization problems in recent years. For example, the firefly algorithm (FA) is one of the metaheuristic algorithms inspired by the fireflies' flashing behavior. However, its weakness in terms of exploration and early convergence has been pointed out. In this paper, two approaches were proposed to improve the FA. In the first proposed approach, a new improved opposition-based learning FA (IOFA) method was presented to accelerate the convergence and improve the FA's exploration capability. In the second proposed approach, a symbiotic organisms search (SOS) algorithm improved the exploration and exploitation of the first approach; two new parameters set these two goals, and the second approach was named IOFASOS. The purpose of the second method is that in the process of the SOS algorithm, the whole population is effective in the IOFA method to find solutions in the early stages of implementation, and with each iteration, fewer solutions are affected in the population. The experiments on 24 standard benchmark functions were conducted, and the first proposed approach showed a better performance in the small and medium dimensions and exhibited a relatively moderate performance in the higher dimensions. In contrast, the second proposed approach was better in increasing dimensions. In general, the empirical results showed that the two new approaches outperform other algorithms in most mathematical benchmarking functions. Thus, The IOFASOS model has more efficient solutions. [ABSTRACT FROM AUTHOR]

Parameter-free algorithms are of an increasing interest in applications that require out-of-the-box solving techniques. For instance, scheduling in volatile environments or control parameters optimisation often requires flexible solving approaches without the need to tune or retune the parameters. In addition, parameter-free algorithms are usually beneficial in solving previously unexplored real-world problem instances. In this paper, we propose a parameter-free local search strategy to solve graph colouring, which is the underlying problem for a number of scheduling applications. Two variants of parameter-free local search are computationally investigated: PFLS-A and PFLS-B. Both of these algorithms are based on accepting strictly improving moves and operating as a random walk if no strictly improving move is found. PFLS-A and PFLS-B differ in randomised versus systematic exploration of the neighbourhood of the current solution. Their cooperative variant CPFLS is also proposed. We compare the results of these three algorithms to the results obtained by 13 other local search methods from the literature. CPFLS provides better or equal results as the other local search algorithms in 67.25 % of per-instance comparisons. This is without employing any explicit or implicit parameters that are usually used in metaheuristics. This hints the promising nature of parameter-free metaheuristics not only for this problem but also metaheuristics in general. [ABSTRACT FROM AUTHOR]

One of the most common tasks of groundwater engineers is to estimate aquifer parameters from transient time-drawdown data which are measured during the execution of pumping tests. The classical method consists in the manual superimposition of the observed time-drawdown data over a type-curve, and the appreciation of the goodness-of-fit is left to the visual inspection of the engineer. The present paper proposes a computerized method based on a new hybrid algorithm named CSARao-1. It combines two recent metaheuristic algorithms: the crow search algorithm (CSA) and Rao-1 algorithm for the optimal aquifer parameters estimation, which inherits the advantages of both algorithms. The CSARao-1 hybrid algorithm along with CSA and Rao-1 algorithm was applied in conjunction with both the Theis solution to analyze time-drawdown datasets coming from confined aquifers systems and the Hantush and Jacob solution to analyze datasets coming from leaky aquifers systems. The proposed approach was coded in FORTRAN programming language and evaluated on fourteen time-drawdown datasets coming from different confined and leaky aquifers systems. The results obtained using CSARao-1 hybrid algorithm were compared to those obtained by applying CSA and Rao-1 algorithm separately, and to those recently published. Globally, the proposed CSARao-1 hybrid algorithm was found to exhibit more accuracy, better robustness and higher rate of convergence over the analyzed transient time-drawdown datasets. [ABSTRACT FROM AUTHOR]

The traffic light cycle optimization problem (TLCOP) is certainly one of the most critical problems in a modern traffic management system because a "good solution" will be able to reduce the total waiting time of vehicles on roads of an entire city. In addition to heuristic algorithms, metaheuristic algorithms provide an alternative way for solving this optimization problem in the sense that they provide a better solution to adjust the traffic lights to mitigate the traffic congestion problem. However, there is still plenty of room for improvement. One of the open issues is that most metaheuristic algorithms will converge to a few regions at the later stage of the convergence process and thus are likely to fall into local optima. The proposed algorithm—a hybrid heuristic algorithm called grey wolf with grasshopper optimization (GWGO)—is developed to leverage the strength of grey wolf and grasshopper optimization algorithms. The underlying idea is to use the grey wolf optimization to avoid falling into local optimum too quickly while using the grasshopper optimization to dynamically adjust the convergence speed of the search algorithm. The experimental results show that the proposed algorithm is able to find out better results than all the other state-of-the-art search algorithms for the TLCOP evaluated in this study in terms of the quality of the end results. [ABSTRACT FROM AUTHOR]

Cuckoo search algorithm is one of the most prominent meta-heuristic optimization algorithms which is applied to various applications. The discovery probability is the one and the only tuning parameter of the cuckoo search algorithm. The physical meaning of this parameter contradicts its implementation in the standard algorithm. Therefore, this study concerns the correction to the definition and implementation of the cuckoo search algorithm to resolve this conflict. Moreover, a novel algorithm called double exponential cuckoo search is proposed, in which the discovery probability became adaptive based on the concept of the double Mersenne numbers. The proposed algorithm is compared to nine other variants to find the best variant that makes the discovery probability adaptive. All the variants are compared and tested on 30 and 50 dimensions of CEC2017 benchmark functions. The results have been statistically proved using the sign test, Wilcoxon signed-rank test, and Friedman test. Moreover, multiple graphical methods are also used to visualize the median performance such as Violin plots and mean convergence graphs. Simulation results prove the superior performance of the proposed algorithm over all other variants. [ABSTRACT FROM AUTHOR]

The present study proposes a novel optimization framework of the reservoir operation in terms of optimizing storage benefits while alleviating downstream environmental impacts. We utilized adaptive neuro fuzzy inference system as the habitat model to assess physical habitat loss at downstream of the reservoir. Furthermore, we applied metaheuristic algorithms including genetic algorithm, particle swarm optimization, invasive weed optimization, differential evolution algorithm, shuffled frog leaping algorithm, gravity search algorithm, atom search algorithm and bat algorithm to optimize reservoir operation. The developed objective function minimizes difference between physical habitat suitability in the natural flow and the optimal release in the simulated period. Based on the results in the case study, The Nash–Sutcliffe model efficiency coefficient demonstrated that the proposed ANFIS model is reliable to assess physical habitats. Hence, it could be used in a coupled simulation-optimization framework to optimize environmental flow regime downstream of a reservoir. Moreover, decision-making system indicated that gravity search algorithm is the best solution for optimization in terms of reliability, vulnerability and mean absolute error. The proposed method can be a robust framework to minimize physical habitat loss at downstream of the reservoirs. [ABSTRACT FROM AUTHOR]

Since real-world problems are quite complex, developing more effective methods to optimize them is taken into consideration at the present age. One of the most popular strategies to solve such problems is nature-inspired metaheuristic algorithms which have presented promising solutions in different fields. The JAYA algorithm is an innovative and promising technique for solving a wide range of optimization problems. Hence, this investigation provides a new hybrid algorithm based on JAYA and crow search algorithm (CSA), known as HJCSA, to enhance its performance. In other words, the mechanism of updating position in CSA is integrated with JAYA algorithm to reinforce the convergence and search capabilities of JAYA algorithm. The proposed hybrid algorithm is evaluated through solving 20 well-known benchmark functions, and obtained results are compared with various up-to-date algorithms, including CSA, JAYA, particle swarm optimization (PSO), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), moth-flame optimization (MFO), and sine–cosine algorithm (SCA). In addition, a real-world engineering problem is optimized by the proposed optimization approach and compared with other published works. The results showed that the suggested optimization algorithm is much more vigorous in escaping from local minima, possessing better convergence, and discovering more accurate solutions. [ABSTRACT FROM AUTHOR]

In the present article, an advanced charged system search (ACSS) algorithm is designed for optimizing the large-scale frame structures using box-shaped sections for columns. The proposed ACSS is an extended version of the charged system search (CSS) which is a metaheuristic algorithm that uses the electrostatics and Newtonian laws of mechanics under the conditions of the Coulomb law. Two large-scale 3D frames with 1026 and 1935 components are optimized using AISC-LRFD to show the efficiency of using the box-shaped sections. Overall performance of the ACSS algorithm with box-shaped sections is compared to those of the upper bound strategy for integrated versions of the standard Big Bang Big Church algorithm and two of its newly developed variants. The results show the successful performance of using steel box-shaped columns in comparison to the frames with I-shaped sections. The numerical results show that the ACSS is efficient and robust compared to its standard version. [ABSTRACT FROM AUTHOR]

In recent decades, researches on optimizing the parameter of the artificial neural network (ANN) model has attracted significant attention from researchers. Hybridization of superior algorithms helps improving optimization performance and capable of solving complex applications. As a traditional gradient-based learning algorithm, ANN suffers from a slow learning rate and is easily trapped in local minima when training techniques such as gradient descent (GD) and back-propagation (BP) algorithm are used. The characteristics of randomization and selection of the best or near-optimal solution of metaheuristic algorithm provide an effective and robust solution; therefore, it has always been used in training of ANN to improve and overcome the above problems. New metaheuristic algorithms are proposed every year. Therefore, the review of its latest developments is essential. This article attempts to summarize the metaheuristic algorithms which have been proposed from the year 1975 to 2020 from various journals, conferences, technical papers, and books. The comparison of the popularity of the metaheuristic algorithm is presented in two time frames, such as algorithms proposed in the recent 20 years and those proposed earlier. Then, some of the popular metaheuristic algorithms and their working principle are reviewed. This article further categorizes the latest metaheuristic search algorithm in the literature to indicate their efficiency in training ANN for various industry applications. More and more researchers tend to develop new hybrid optimization tools by combining two or more metaheuristic algorithms to optimize the training parameters of ANN. Generally, the algorithm's optimal performance must be able to achieve a fine balance of their exploration and exploitation characteristics. Hence, this article tries to compare and summarize the properties of various metaheuristic algorithms in terms of their convergence rate and the ability to avoid the local minima. This information is useful for researchers working on algorithm hybridization by providing a good understanding of the convergence rate and the ability to find a global optimum. [ABSTRACT FROM AUTHOR]

Wireless powered communication network (WPCN) is a promising technique to resolve the power constraint issue faced by wireless nodes at the same time it also provides green and a safer solution. This paper studies, mutual sharing between WPCN and simultaneous wireless information and power transfer model where optimal resource allocation occurs between licensed/bandwidth group and an unlicensed/power group to enhance the system performance. The main aim of this paper is to maximize system weighted sum rate and minimize power consumption during transmission by optimal time allocation and energy beamforming vector allocation. These multiobjective combinatorial problems are solved using joint metaheuristic particle swarm optimization-cuckoo search algorithm to provide an optimal solution. The results are compared using a conventional mathematical optimization algorithm to set as a baseline for performance parameters. The obtained results demonstrate that the efficient joint metaheuristic approach provides a significant gain in the system performance and also offers a computationally less complex approach for solving a complicated non-convex multiobjective problem of wireless powered network. [ABSTRACT FROM AUTHOR]

The buffer allocation problem (BAP) aims to determine the optimal buffer configuration for a production line under the predefined constraints. The BAP is an NP-hard combinatorial optimization problem and the solution space exponentially grows as the problem size increases. Therefore, problem specific heuristic or meta-heuristic search algorithms are widely used to solve the BAP. In this study two population-based search algorithms; i.e. Combat Genetic Algorithm (CGA) and Big Bang-Big Crunch (BB-BC) algorithm, are proposed in solving the BAP to maximize the throughput of the line under the total buffer size constraint for unreliable production lines. Performances of the proposed algorithms are tested on existing benchmark problems taken from the literature. The experimental results showed that the proposed BB–BC algorithm yielded better results than the proposed CGA as well as other algorithms reported in the literature. [ABSTRACT FROM AUTHOR]

This paper demonstrates an application of the improved crow search algorithm (I-CSA), which is a modified version of the crow search algorithm (CSA). CSA is a recent, nature-inspired meta-heuristic optimization algorithm. I-CSA differs from CSA by allowing application on a discrete problem, which is P-median and fortifying faster convergence to an optimal or near-optimal solution. Improvements are provided by local searches which support escaping from local optima or convergence to the optimal solution, elitism enhances the intensification through the utilization of nodes by selecting the most frequent centers that appeared in hiding better locations for local search, on the P-median problem. The application of the I-CSA is structured in three phases. In the first phase, parameters of I-CSA are analyzed and optimized using well-known data tests. The test datasets for the application of I-CSA on the P-median problem were retrieved from the OR-library to present the effectiveness and applicability of I-CSA. In the second phase, 40-pmed test problems from the library are solved using I-CSA and the results are compared with known optimal results and recorded results of other meta-heuristic approaches. In addition, Wilcoxon signed-rank test is applied in order to demonstrate the performance of I-CSA compared to well-known algorithms. The results of the proposed method demonstrated a faster convergence rate and better solution in most cases when compared with the standard CSA and other well-known meta-heuristic approaches. Finally, the proposed I-CSA approach is tested on a real-life case problem including 2121 nodes in Tunceli, Turkey. Obtaining the optimal results in a reasonable time indicates that the potential of the I-CSA is high and promising. In nutshell, this paper presents an improvement to CSA and evaluates its performance in a three-phase test procedure. [ABSTRACT FROM AUTHOR]

Meta-heuristic algorithms have shown promising results in solving various optimization problems. The crow search algorithm (CSA) is a new and effective meta-heuristic algorithm that emulates crows' intelligent group behavior in nature. However, it suffers from several problems, such as trapping into local optimum and premature convergence. This paper proposes an improved crow search algorithm (ICSA), which has been tested and evaluated by a set of well-known benchmark functions. A new update mechanism that uses the merits of the global best position to move toward the best position is proposed. This mechanism increases the convergence of the algorithm and improves its local search-ability. Twenty benchmark functions are used to evaluate the performance of the proposed ICSA. Moreover, the ICSA algorithm is compared with the conventional CSA and other meta-heuristic algorithms such as particle swarm optimization (PSO), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), gray wolf optimizer (GWO), moth-flame optimization (MFO), and sine-cosine algorithm (SCA). The experimental result shows that the proposed ICSA algorithm has produced promising results and outperformed conventional CSA and other meta-heuristic algorithms. Also, the proposed ICSA has a more robust convergence for optimizing objective functions in terms of solution accuracy and efficiency. [ABSTRACT FROM AUTHOR]

This paper discusses a new variant of Henry Gas Solubility Optimization (HGSO) Algorithm, called Hybrid HGSO (HHGSO). Unlike its predecessor, HHGSO allows multiple clusters serving different individual meta-heuristic algorithms (i.e., with its own defined parameters and local best) to coexist within the same population. Exploiting the dynamic cluster-to-algorithm mapping via penalized and reward model with adaptive switching factor, HHGSO offers a novel approach for meta-heuristic hybridization consisting of Jaya Algorithm, Sooty Tern Optimization Algorithm, Butterfly Optimization Algorithm, and Owl Search Algorithm, respectively. The acquired results from the selected two case studies (i.e., involving team formation problem and combinatorial test suite generation) indicate that the hybridization has notably improved the performance of HGSO and gives superior performance against other competing meta-heuristic and hyper-heuristic algorithms. [ABSTRACT FROM AUTHOR]

Multilevel thresholding image segmentation is an important technique, which has attracted much attention in recent years. The conventional exhaustive search method for image segmentation is efficient for bilevel thresholding. However, they are time expensive when dealing with multilevel thresholding image segmentation. To better tackle this problem, an improved cuckoo search algorithm (ICS) is proposed to search for the optimal multilevel thresholding in this paper, and Otsu is considered as its objective function. In the ICS, two modifications are used to improve the standard cuckoo search algorithm. First, a parameter adaptation strategy is utilized to improve exploration performance. Second, a dynamic weighted random-walk method is adopted to enhance the local search efficiency. A total of six benchmark test images are used to perform the experiments, and seven state-of-the-art metaheuristic algorithms are introduced to compare with the ICS. A series of measure indexes such as objective function value and standard deviation, PSNR, FSIM, and SSIM as well as the Wilcoxon rank sum and convergence performance are performed in the experiments; the experimental results show that the proposed algorithm is superior to other seven well-known heuristic algorithms. [ABSTRACT FROM AUTHOR]

Pathfinder algorithm (PFA) for finding the best food area or prey based on the leadership of collective action in animal groups is a new metaheuristic algorithm for solving optimization problems with different structures. PFA is divided into two stages to search: pathfinder stage and follower stage. They represent the exploration phase and mining phase of PFA respectively. However, the original algorithm also has the problem of falling into a local optimum. In order to solve this problem, the teaching phase in the teaching and learning algorithm is added to the pathfinder stage in the text. In order to balance the exploration and mining capabilities of the algorithm, the learning phase of the teaching and learning algorithm is added to the follower phase in the article. In order to further enhance the depth search ability of the algorithm and increase the convergence speed, the exponential step is given to the followers. Therefore, a teaching-learning-based pathfinder algorithm (TLPFA) is proposed. 19 benchmark functions of four different types and six engineering design problems are used to test of the TLPFA exploration and exploiting capabilities. The experimental results show that the proposed TLPFA algorithm is superior to the state-of-the-art metaheuristic algorithms in terms of the performance measures. [ABSTRACT FROM AUTHOR]

In the field of computer science, the metaheuristics is a top level approach that is configured to discover, to yield or to pick a biased searching algorithm that may deliver an adequate and proper explication to an optimization problem, particularly with deficient information or with restricted reckoning potential. Metaheuristic algorithms experiments to figure out finest explication compared to all feasible explications of an optimizing problems. Because of scanty link authenticity, dynamic changing topology and overloading this type networks have least network traffic capacity in mobile adhoc networks. In this present study paper, a new nature stimulated metaheuristics algorithm called Emperor Penguin Optimizing Algorithm is proposed to find out an energy efficient routing with QoS requirements in Mobile Adhoc Networks. This proposed Emperor penguin colony optimizing algorithm is governed by the penguin heat emission and their spiral shaped movement in the huddle to determine an optimal routing that satisfies various QoS requirements. Simulation results outperforms that the proposed work enhances packet delivery ratio, throughput of a network and the reliability of the routing process. [ABSTRACT FROM AUTHOR]

The backpropagation (BP) algorithm is a gradient-based algorithm used for training a feedforward neural network (FNN). Despite the fact that BP is still used today when FNNs are trained, it has some disadvantages, including the following: (i) it fails when non-differentiable functions are addressed, (ii) it can become trapped in local minima, and (iii) it has slow convergence. In order to solve some of these problems, metaheuristic algorithms have been used to train FNN. Although they have good exploration skills, they are not as good as gradient-based algorithms at exploitation tasks. The main contribution of this article lies in its application of novel memetic approaches based on the Gravitational Search Algorithm (GSA) and Chaotic Gravitational Search Algorithm (CGSA) algorithms, called respectively Memetic Gravitational Search Algorithm (MGSA) and Memetic Chaotic Gravitational Search Algorithm (MCGSA), to train FNNs in three classical benchmark problems: the XOR problem, the approximation of a continuous function, and classification tasks. The results show that both approaches constitute suitable alternatives for training FNNs, even improving on the performance of other state-of-the-art metaheuristic algorithms such as ParticleSwarm Optimization (PSO), the Genetic Algorithm (GA), the Adaptive Differential Evolution algorithm with Repaired crossover rate (Rcr-JADE), and the Covariance matrix learning and Bimodal distribution parameter setting Differential Evolution (COBIDE) algorithm. Swarm optimization, the genetic algorithm, the adaptive differential evolution algorithm with repaired crossover rate, and the covariance matrix learning and bimodal distribution parameter setting differential evolution algorithm. [ABSTRACT FROM AUTHOR]

In this paper, an improved electro-search algorithm is proposed to solve topology optimization problem of nonlinear single-layer domes. The electro-search algorithm is one of the newly developed metaheuristics inspirited by the movement of electrons around the nucleus of atoms in a molecule. This algorithm exhibits a good performance in solving optimization problems of benchmark functions. However, this algorithm cannot present appropriate performance in tackling discrete structural optimization problems. In the proposed improved algorithm, to reduce the probability of getting stuck in local minima, one electron is assigned to each nucleus and a new equation is defined to determine its orbital's radius. Moreover, a new scheme is developed to update the position of nuclei in design space. In addition, in order to increase the convergence speed, a memory containing some historically best solutions is added to the algorithm. Parametric and nonparametric statistical tests are applied to analyze the performance of the algorithms. The numerical results are presented in two parts including size optimization of benchmark steel structures and topology optimization problems of single-layer domes. The results demonstrate that the proposed improved algorithm is superior over other well-known metaheuristic algorithms in terms of optimum solution, convergence rate, and overall performance. [ABSTRACT FROM AUTHOR]

Cloud manufacturing as an emerging service-oriented manufacturing paradigm integrates and manages geographically distributed manufacturing resources such that complex and highly customized manufacturing tasks can be performed cooperatively. The service composition and optimal selection (SCOS) problem, in which manufacturing cloud services are optimally selected for performing subtasks, is one of the key issues for implementing a cloud manufacturing system. In this paper, we propose a new mixed-integer programming model for solving the SCOS problem with sequential composition structure. Unlike the majority of previous research on the problem, in the proposed model, the transportation between distributed resources and its effects on quality of services are considered. Although a wide variety of metaheuristics have been tailored for solving the SCOS problem, no consistent and comprehensive conclusion has been reached so far on the superiority of a specific algorithm. Therefore, for the first time, solution space landscape of the problem was analyzed through several statistical criteria which demonstrated that the landscape is rugged and local optima are clustered in a small region of the search space. Therefore, to find good solutions, a metaheuristic algorithm needs to perform both proper exploitation and exploration of the search space. According to the landscape analysis, the basic imperialist competitive algorithm (ICA) was hybridized with a local search (LS) algorithm resulting in the hybrid ICA (HICA). To examine the performance of the proposed HICA, an example of online motorcycle production in the USA as well as four randomly generated large-scale instances, were solved through the LS, ICA, and HICA. Computational results showed that transportation consideration is indispensable for obtaining more realistic solutions in cloud manufacturing. The results also revealed that the HICA outperformed the LS and basic ICA in terms of the value of cost objective function, the stability of solutions and convergence speed. Hence, not only statistically but also analytically, it was proved that algorithms incorporating both exploitation and exploration are able to solve the SCOS problem more efficiently. [ABSTRACT FROM AUTHOR]

For the purpose of usability feature extraction and prediction, an innovative metaheuristic algorithm is introduced. Generally, the term "usability" is defined by the several researchers with respect to the hierarchical-based software usability model and it has become one of the important methods in terms of software quality. In hierarchically based software, its usability factors, attributes, and its characteristics are combined. The paper presented an algorithm, i.e., modified crow search algorithm (MCSA) mainly for extraction of usability features from hierarchical model with the optimal solution under the search for useful features. MCSA is an extension of original crow search algorithm (CSA), which is a naturally inspired algorithm. The mechanism of this algorithm is based on the process of hiding food and prevents theft and hence introduced this CSA in the field of software engineering practices as an inspiration. The algorithm generates a particular number of selected features/attributes and is applied on software development life cycles models, finding out the best among them. The results of the presented algorithm are compared with the standard binary bat algorithm (BBA), original CSA, and modified whale optimization algorithm (MWOA). The outcomes conclude that the proposed MCSA performs well than the standard BBA and original CSA as the proposed algorithms generate fewer number of feature selection equal to 17 than 18 in BBA, 23 in CSA, and 19 in MWOA. [ABSTRACT FROM AUTHOR]

Automation of test data generation is of prime importance in software testing because of the high cost and time incurred in manual testing. This paper proposes an Improved Crow Search Algorithm (ICSA) to automate the generation of test suites using the concept of mutation testing by simulating the intelligent behaviour of crows and Cauchy distribution. The Crow Search Algorithm suffers from the problem of search solutions getting trapped into the local search. The ICSA attempts to enhance the exploration capabilities of the metaheuristic algorithm by utilizing the concept of Cauchy random number. The concept of Mutation Sensitivity Testing has been used for defining the fitness function for the search based approach. The fitness function used, aids in finding optimal test suite which can achieve high detection score for the Program Under Test. The empirical evaluation of the proposed approach with other popular meta-heuristics, prove the effectiveness of ICSA for test suite generation using the concepts of mutation testing. [ABSTRACT FROM AUTHOR]

We discuss at length the dynamical behavior of Grover's search algorithm for which all the Walsh-Hadamard transformations contained in this algorithm are exposed to their respective random perturbations inducing the augmentation of the dimension of the search space. We give the concise and general mathematical formulations for approximately characterizing the maximum success probabilities of finding a unique desired state in a large unsorted database and their corresponding numbers of Grover iterations, which are applicable to the search spaces of arbitrary dimension and are used to answer a salient open problem posed by Grover (Phys Rev Lett 80:4329-4332, ). [ABSTRACT FROM AUTHOR]