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The Gorilla Troops Optimizer (GTO) is a novel Metaheuristic Algorithm that was proposed in 2021. Its design was inspired by the lifestyle characteristics of gorillas, including migration to a known position, migration to an undiscovered position, moving toward the other gorillas, following silverback gorillas and competing with silverback gorillas for females. However, like other Metaheuristic Algorithms, the GTO still suffers from local optimum, low diversity, imbalanced utilization, etc. In order to improve the performance of the GTO, this paper proposes a modified Gorilla Troops Optimizer (MGTO). The improvement strategies include three parts: Beetle-Antennae Search Based on Quadratic Interpolation (QIBAS), Teaching–Learning-Based Optimization (TLBO) and Quasi-Reflection-Based Learning (QRBL). Firstly, QIBAS is utilized to enhance the diversity of the position of the silverback. Secondly, the teacher phase of TLBO is introduced to the update the behavior of following the silverback with 50% probability. Finally, the quasi-reflection position of the silverback is generated by QRBL. The optimal solution can be updated by comparing these fitness values. The performance of the proposed MGTO is comprehensively evaluated by 23 classical benchmark functions, 30 CEC2014 benchmark functions, 10 CEC2020 benchmark functions and 7 engineering problems. The experimental results show that MGTO has competitive performance and promising prospects in real-world optimization tasks.

Swarm intelligence is inspired by natural group behavior. It is one of the promising metaheuristics for black-box function optimization. Then plenty of swarm intelligence algorithms such as particle swarm optimization (PSO) and firefly algorithm (FA) have been developed. Since these swarm intelligence models have some common properties and inherent characteristics, model hybridization is expected to adjust a swarm intelligence model for the target problem instead of parameter tuning that needs some trial and error approach. This paper proposes a PSO-FA hybrid algorithm with a model selection strategy. An event-driven trigger based on the personal best update makes each individual do the model selection that focuses on the personal study process. By testing the proposed hybrid algorithm on some benchmark problems and comparing it with a simple PSO, the standard PSO 2011, FA, HFPSO to show how the proposed hybrid swarm averagely performs well in black-box optimization problems.

Symbiotic Organisms Search (SOS) algorithm is characterized based on the framework of relationships among the ecosystem species. Nevertheless, it is suffering from wasteful discovery, little productivity, and slack convergence rate. These deficiencies cause stagnation at the local optimum, which is hazardous in deciding the genuine optima of the optimization problem. Backtracking Search Algorithm (BSA) is likewise another streamlining method for comprehending the non-direct complex optimization problem. Consequently, in the current paper, an endeavor has been made toward the expulsion of the downsides from the traditional SOS by proposing a novel ensemble technique called e-SOSBSA to overhaul the degree of intensification and diversification. In e-SOSBSA, firstly, the mutation operator of BSA with the self-adaptive mutation rate is incorporated to produce a mutant of population and leap out from the local optima. Secondly, the crossover operator of BSA with the adaptive component of mixrate is incorporated to leverage the entire active search regions visited previously. The suggested e-SOSBSA has been tested with 20 classical benchmark functions, IEEE CEC2014, CEC2015, CEC2017, and the latest CEC 2020 test functions. Statistical analyses, convergence analysis, and diversity analysis are performed to show the stronger search capabilities of the proposed e-SOSBSA in contrast with the component algorithms and several state-of-the-art algorithms. Moreover, the proposed e-SOSBSA is applied to find the optimum value of the seven problems of engineering optimization. The numerical investigations and examinations show that the proposed e-SOSBSA can be profoundly viable in tackling real-world engineering optimization problems.

The moth-flame optimization algorithm (MFO) is a novel metaheuristic algorithm for simulating the lateral positioning and navigation mechanism of moths in nature, and it has been successfully applied to various optimization problems. This paper segments the flame energy of MFO by introducing the energy factor from the Harris hawks optimization algorithm, and different updating methods are adopted for moths with different flame-detection abilities to enhance the exploration ability of MFO. A new energy-segmented moth-flame optimization algorithm (ESMFO) is proposed and is applied on 21 benchmark functions and an engineering design problem. The experimental results show that the ESMFO yields very promising results due to its enhanced exploration, exploitation, and convergence capabilities, as well as its effective avoidance of local optima, and achieves better performance than other the state-of-the-art metaheuristic algorithms in terms of the performance measures.

While function modeling has been around in engineering design research since the 1960s, there have been no systematic, comparative studies devoted to assessing the adequacy of function modeling frameworks in light of engineering design objectives. This systematic assessment and comparison – called benchmarking – is now recognized as a central research issue in current function modeling research, but insight into how this benchmarking can be done is at present limited. In this paper, we attempt to improve our insight into how benchmarking can be done for a specific but important engineering context: function optimization of reverse-engineered systems. We argue that the capacity to produce technical advantage predictions, viz. predictions concerning the improved functional performance of a redesigned technical system, is an important benchmark criterion in this context. We subsequently illustrate the utility of the criterion by assessing two prominent function modeling frameworks in terms of it. Throughout the paper, we use a case study of the design of an electric wok to clarify and illustrate our ideas.

This paper proposes an improved cuckoo search (CS) algorithm combining nonlinear inertial weight and differential evolution algorithm (WCSDE) to overcome the shortcomings of the CS algorithm, such as low convergence accuracy, lack of information exchange within the population, and inadequate local search capabilities. Compared with other CS variants, two strategies are proposed in this paper to improve the properties of the WCSDE. On the one hand, a non-linearly decreasing inertia weight with the number of evolutionary iterations is employed in the WCSDE to improve the update method of the bird’s nest position, enhance the balance between the exploration and development capabilities, and strengthen the local optimization capability. On the other hand, the mutation and cross-selection mechanisms of the differential evolution (DE) algorithm are introduced to make up for the lack of the mutual relationship between the populations, avoid the loss of practical information, and increase the convergence accuracy. In the experiment part, 13 classic benchmark functions are selected to execute the function optimization tasks among the standard CS, the WCSDE, and other four CS variants to verify the effectiveness of the proposed algorithm from two aspects. The results and corresponding statistical analysis reveal that the proposed algorithm has better global search ability and strengthener robustness.

This paper presents an improved extension of the previous algorithm of the authors called KAdam that was proposed as a combination of a first-order gradient-based optimizer of stochastic functions, known as the Adam algorithm and the Kalman filter. In the extension presented here, it is proposed to filter each parameter of the objective function using a 1-D Kalman filter; this allows us to switch from matrix and vector calculations to scalar operations. Moreover, it is reduced the impact of the measurement noise factor from the Kalman filter by using an exponential decay in function of the number of epochs for the training. Therefore in this paper, is introduced our proposed method sKAdam, a straightforward improvement over the original algorithm. This extension of KAdam presents a reduced execution time, a reduced computational complexity, and better accuracy as well as keep the properties from Adam of being well suited for problems with large datasets and/or parameters, non-stationary objectives, noisy and/or sparse gradients.

This paper explains the construction of a novel augmented hunger games search algorithm using a logarithmic spiral opposition-based learning technique. The proposed algorithm (LsOBL-HGS) is used as an efficient tool for both function optimization and controller design. To assess the performance of the algorithm for function optimization, benchmark functions from the CEC2017 test suite were employed and comparisons were made with available and good performing algorithms. In terms of controller design, the proposed LsOBL-HGS algorithm was utilized to design a FOPID controlled magnetic ball suspension system. Comparative assessments were also performed for FOPID controller design, as well using other state-of-the-art methods reported for the magnetic ball suspension system. The results showed that the proposed LsOBL-HGS algorithm has good capability for FOPID controller design employed in a magnetic ball suspension system as it provided an improvement of more than 13% in terms of the transient response-related parameters and more than 34% in terms of bandwidth compared to the best-reported approach used for comparisons. © 2022 Karabuk University

The number of publications related to complex-valued encoding metaheuristic optimization research is increasing the area of metaheuristic optimization is gaining in popularity. In this paper, we aim to provide researchers with a comprehensive and extensive overview of complex-valued encoding metaheuristic algorithms and applications for function optimization, engineering optimization design, and combination optimization. Compared with the basic metaheuristic algorithm, which are based on real-valued encoding or binary encoding, the complex-valued encoding metaheuristic algorithm expands the dimension of the search region and efficiently avoids the problem of falling into the local minimum. Finally, eight complex-valued encoding metaheuristic algorithms were used for 29 benchmark test functions and five engineering optimization design problems. Through the analysis and comparison of the results with statistical significance, the superiority of complex-value encoding was proved, and the complex-value encoding metaheuristic algorithm with the best performance was obtained. The purpose of this review is to present a relatively comprehensive list of all the complex-value encoding metaheuristic algorithms in the literature to inspire further research.

Iterative algorithms for solving the inverse problem, presented as a quadratic programming problem, developed by modifying algorithms based on the inverse calculation mechanism are proposed. Iterative algorithms consist in a sequential change of the argument values using iterative formulas until the function reaches the value that most corresponds to the constraint. Two solutions are considered: by determining the shortest distance to the line of the given level determined by the constraint, and by moving along the gradient. This approach was also adapted to solve more general nonlinear programming optimization problems. The solution of four problems is considered: formation of production output and storage costs, optimization of the securities portfolio and storage costs for the given volume of purchases. It is shown that the solutions obtained using iterative algorithms are consistent with the result of using classical methods (Lagrange multiplier, penalty), standard function of the MathCad package. In this case, the greatest degree of compliance was obtained using the method based on constructing the level line; the method based on moving along the gradient is more universal.The advantage of the algorithms is a simpler computer implementation of iterative formulas, the ability to get a solution in less time than known methods (for example, the penalty method, which requires multiple optimizations of a modified function with a change in the penalty parameter). The algorithms can also be used to solve other nonlinear programming problems of the presented kind.The paper can be useful for specialists when solving problems in the field of economics, as well as developing decision support systems., Предложены итерационные алгоритмы решения обратной задачи, представленной в виде задачи квадратичного программирования, разработанные путем модификации алгоритмов, основанных на механизме обратных вычислений. Итерационные алгоритмы заключаются в последовательном изменении значений аргументов с помощью итерационных формул до достижения функцией величины, наиболее соответствующей ограничению. При этом рассмотрено два варианта решения задачи: путем определения кратчайшего расстояния до линии заданного уровня, определяемого ограничением, и путем движения вдоль градиента. Данный подход также был адаптирован для решения оптимизационных задач нелинейного программирования более общего вида. Рассмотрено решение четырех задач: формирование выпуска продукции и складских затрат, оптимизация портфеля ценных бумаг и складских затрат при заданном объеме закупок. Показано, что получаемые при использовании итерационный алгоритмов решения согласуются с результатом использования классических методов (множителей Лагранжа, штрафов), стандартной функции математического пакета MathCad. При этом наибольшая степень соответствия была получена с помощью метода на основе построения линии уровня, метод на основе движения вдоль градиента является более универсальным.Достоинством алгоритмов является более простая компьютерная реализация итерационных формул, возможность получить решение за меньшее время по сравнению с известными методами (например, методом штрафов, требующим многократной оптимизации модифицированной функции с изменением штрафного параметра). Алгоритмы могут быть также использованы для решения других задач нелинейного программирования представленного вида.Статья может быть полезна для специалистов, осуществляющих решение задач в области экономики, а также разработку программных систем поддержки принятия решений, Запропоновано ітераційні алгоритми розв'язання зворотної задачі, представленої у вигляді задачі квадратичного програмування, розроблені шляхом модифікації алгоритмів, заснованих на механізмі зворотних обчислень. Ітераційні алгоритми полягають у послідовній зміні значень аргументів за допомогою ітераційних формул до досягнення функцією величини, найбільш відповідної обмеженню. При цьому розглянуто два варіанти вирішення задачі: шляхом визначення найкоротшої відстані до лінії заданого рівня, що визначається обмеженням, і шляхом руху вздовж градієнта. Даний підхід також був адаптований для вирішення оптимізаційних завдань нелінійного програмування більш загального вигляду. Розглянуто вирішення чотирьох завдань: формування випуску продукції та складських витрат, оптимізація портфеля цінних паперів та складських витрат при заданому обсязі закупівель. Показано, що одержувані при використанні ітераційний алгоритмів рішення узгоджуються з результатом використання класичних методів (множників Лагранжа, штрафів), стандартної функції математичного пакету MathCad. При цьому найбільша ступінь відповідності була отримана за допомогою методу на основі побудови лінії рівня, метод на основі руху вздовж градієнта є більш універсальним.Перевагою алгоритмів є більш проста комп'ютерна реалізація ітераційних формул, можливість отримати рішення за менший час в порівнянні з відомими методами (наприклад, методом штрафів, що вимагає багаторазової оптимізації модифікованої функції зі зміною штрафного параметра). Алгоритми можуть бути також використані для вирішення інших завдань нелінійного програмування представленого виду.Стаття може бути корисна для фахівців, які здійснюють вирішення завдань в області економіки, а також розробку програмних систем підтримки прийняття рішень

Bacterial foraging optimization (BFO), a novel bio-inspired heuristic optimization algorithm, has been attracted widespread attention and widely applied to various practical optimization problems. However, the standard BFO algorithm exists some potential deficiencies, such as the weakness of convergence accuracy and a lack of swarm communication. Owing to the improvement of these issues, an improved BFO algorithm with comprehensive swarm learning strategies (LPCBFO) is proposed. As for the LPCBFO algorithm, each bacterium keeps on moving with stochastic run lengths based on linear-decreasing Lévy flight strategy. Moreover, illuminated by the social learning mechanism of PSO and CSO algorithm, the paper incorporates cooperative communication with the current global best individual and competitive learning into the original BFO algorithm. To examine the optimization capability of the proposed algorithm, six benchmark functions with 30 dimensions are chosen. Finally, experimental results demonstrate that the performance of the LPCBFO algorithm is superior to the other five algorithms.

Ant Lion Optimizer (ALO) is a new meta-heuristic algorithm that simulates the ant lion predator mechanism in nature. Five main steps of hunting include: random walks of ants, building traps, trapping in antlion’s pits, sliding ants towards antlion, catching prey and re-building pits. As the predator radius of antlion decreases with the number of iterations, there is an unbalanced between the ant lion optimizer between exploration and exploitation, and it is easy to fall into the local optimal solution. An improved ant lion optimizer based on spiral complex path searching pattern is proposed, where eight spiral paths (Hypotrochoid, Rose spiral curve, Logarithmic spiral curve, Archimedes spiral curve, Epitrochoid, Inverse spiral curve, Cycloid, Overshoot parameter setting of the spiral) searching strategies were adopted to improve the diversity of the population and the ability of the algorithm to balance exploration and exploitation. The proposed algorithm can accelerate the convergence speed of ALO and improve its performance. The algorithm is verified by simulation experiments in three parts. Firstly, 28 function optimization problems were adopted to test the optimization performance of the improved ALO. Secondly, it is applied to the lightest design engineering problem of pressure vessels. Finally, the spiral complex path searching patterns are introduced into the muti-objective ALO and 4 typical muti-objective functions are optimized. Simulation results show that the superior performance of the proposed algorithm for exploiting the optimum and it has advantages in terms of exploration. The improved algorithm can better solve function optimization, classical engineering problems with constraints and multi-objective function optimization problems. The improved ALO based on the spiral complex path searching mode has the characteristics of balanced exploration and exploitation, fast convergence speed and high precision.

To improve the convergence speed and accuracy of the Pity Beetle Algorithm(PBA), we propose an improved algorithm called one-way pioneer guide PBA (OPGPBA). First of all, given the specificity of the random sampling technology(RST), resulting in search holes, we propose a new rRST search mechanism, which integrates the random generation mode of the full-space traversal search capability. According to the algorithm’s different requirements for neighborhood search, medium-scale search, large-scale search, and global search, the fixed-size mode factor is adaptively processed to make its size change adaptively with iteration. Finally, we propose a mechanism for the pioneer to guide population reproduction. The evolutionary direction of the population in each dimension is determined according to the change in the pioneer position, which effectively improves the convergence ability of the algorithm. Experiments on the CEC2013 test set show that the OPGPBA algorithm has apparent advantages in convergence speed and solution accuracy compared with the three excellent algorithms so far.

Fast detection and high-precision tracking of multiple UAVs are the keys to achieving efficient low-altitude defense. However, as there are many hyper-parameters which need to be optimized in target detection network, commonly used methods such as random search method are computationally intensive and cannot quickly obtain multiple optimal hyper-parameters combinations. In addition, angular random walk due to low-frequency noise of speed sensor in servo loop can cause target tracking accuracy to decrease. Fortunately, those two problems can be regarded as a single-mode function optimization problem and a multi-mode function optimization problem, respectively. In the paper, in order to overcome the aforementioned problems, GSOM (glowworm swarm optimization mutation) algorithm and GSOMLDW (glowworm swarm optimization mutation linearly decreasing weight) algorithm are firstly proposed. Furthermore, the global convergence of GSOMLDW has been proven in the paper, which has not been analyzed in currently available literature. Then, experimental results on four multi-modal benchmark functions have strongly illustrated that the novel GSOM algorithm can enhance glowworms’ memory ability and improve peak detection rate effectively. When it is used for optimizing hyper-parameters of multi-target detection network, it can be expected to obtain much more hyper-parameter combination selections. Meanwhile, experimental results on ten uni-modal benchmark functions have obviously demonstrated that GSOMLDW algorithm can balance glowworms’ exploration and exploitation abilities powerfully and obtain superior global solution accuracy at last. When the GSOMLDW algorithm is used for servo system identification and drift error model identification, the final position error fluctuation after compensation is almost zero while it reaches $1500~urad$ before compensation. Consequently, the proposed method can effectively improve target tracking precision.

The salp swarm algorithm (SSA) is a swarm intelligence optimization algorithm that simulates the chain movement behavior of salp populations in the sea. Aiming at the shortcomings of the SSA, such as low precision, low optimization dimension and slow convergence speed, an improved salp swarm algorithm based on Levy flight and sine cosine operator (LSC-SSA) was proposed. The Levy flight mechanism uses the route of short walks combined with long jumps to search the solution space, which can effectively improve the global exploration capability of the algorithm. Improved sine cosine operator use sine search for global exploration and cosine search for local exploitation. At the same time, an adaptively switching between the two function search methods can achieve a smooth transition between global exploration and local exploitation. In the simulation experiment, salp swarm algorithm (SSA), whale optimization algorithm (WOA), particle swarm algorithm (PSO), sine cosine algorithm (SCA), firefly algorithm (FA) and LSC-SSA were adopted for solving function optimization problems. Then, the feasibility of the improved algorithm for solving high-dimensional large-scale optimization problems and the effectiveness of the improvement strategy are evaluated. Finally, LSC-SSA was applied to train muti-layer perceptron neural network. Simulation results show that the introduction of Levy flight and improved sine cosine operator in LSC-SSA significantly improves optimization accuracy and convergence speed compared with other swarm optimization algorithms. In addition, the improved algorithm can effectively solve high-dimensional large-scale optimization problems. In the application of training muti-layer perceptron NN, the improved algorithm can avoid falling into the local optimal value and obtain the ideal classification accuracy.

Harris's hawks optimization (HHO) algorithm proposed in 2019 is a novel population-based, nature-inspired optimization paradigm that imitates the cooperative behavior and chasing style of Harris's hawks in nature called surprise pounce. Inspired by particle swarm optimization algorithm, velocity is added into the HHO algorithm in the exploration phase. The soft besiege with progressive rapid dives and the hard besiege with progressive rapid dives in the attacking stages of the HHO algorithm are improved by use of the crossover operator of the artificial tree algorithm. Thus the improved HHO algorithm is obtained, written as IHHO. The effectiveness of the IHHO algorithm is tested on 23 benchmark problems by comparison with the other 11 state-of-art meta-heuristic algorithms. The IHHO algorithm is used to optimize the parameters of support vector machine for synthetic aperture radar (SAR) target recognition and of the extreme learning machine for stock market index prediction by considering Google Trends. The comparable results show that the IHHO algorithm is very promising and has some competitive potential.

The grasshopper optimization algorithm (GOA) is a new meta-heuristic algorithm inspired by the behavior of grasshopper groups. Aiming at the shortcomings of poor development ability and low convergence accuracy of GOA, this paper introduces the gravity search operator into the optimization process of GOA to improve the grasshopper’s global exploration and avoid falling into local optimum in advance. At the same time, a pigeon search operator-landmark operator is introduced to improve and balance the algorithm’s exploration and development capabilities. In order to verify the validity of the improved algorithm, this paper will adopts the gravity search operator and a deterrent landmark operator hybrid grasshoppers algorithm (HGOA) with basic grasshopper algorithm (GOA), particle swarm optimization (PSO) algorithm, sine and cosine algorithm (SCA), moth-flame optimization (MFO) algorithm, salp swarm algorithm (SSA), and bat algorithm (BA) to optimize 28 test functions. And the analysis and comparison of the obtained statistical data results finally show that the proposed improved grasshopper algorithm has better optimization ability.

Grey wolf optimizer (GWO) is a new meta-heuristic algorithm. The GWO algorithm mimics the leadership hierarchy and hunting mechanism of grey wolves in nature. Three main stages of hunting include: encircling, tracking and attacking. It is easy to fall into local optimum when used to optimize high-dimensional data, and there is imbalance between exploration and exploitation. An improved grey wolf optimizer based on tracking mode and seeking mode is proposed to improve the diversity of the population and the ability of the algorithm to balance exploration and exploitation. The algorithm is verified by simulation experiments in three parts. Firstly, the proposed grey wolf optimizer based on tracking mode (TGWO), the improved grey wolf optimizer based on seeking mode (SGWO), the improved grey wolf optimizer based on tracking and seeking mode (TSGWO), Grey Wolf Optimizer (GWO), Particle Swarm Optimization (PSO), Salp Swarm Algorithm (SSA), Sine Cosine Algorithm (SCA), Ant Lion Optimizer (ALO), Whale Optimization Algorithm (WOA) and Moth-flame Optimization (MFO) are adopted to optimize 21 typical benchmark functions respectively, and the obtained statistical simulation results are compared; Secondly, the improved algorithm proposed in this paper is compared with Binary Grey Wolf Optimizer (BGWO), Hybrid PSOGWO Optimization (PSOGWO) and GWO Algorithm Integrated with Cuckoo Search (GWOCS); Finally, it is applied to the lightest design engineering problem of pressure vessels. Simulation results show that the superior performance of the proposed algorithm for exploiting the optimum and it has advantages in terms of exploration. The improved grey wolf optimizer based on tracking mode and seeking mode can better solve function optimization and classical engineering problems with constraints. It was found the improved grey wolf optimizer based on tracking mode has the high precision and the characteristics of balanced exploration and exploitation.

We proposed a method to automatically eliminate the obscuration in the design of off-axis mirror systems without plane of symmetry. Off-axis settings and local surface expression are designed to simplify the system representation. Obscuration error function is established based on the positional relation between the proposed mirror boxes and ray boxes, and through function optimization, the obscuration is eliminated. The method is demonstrated by two examples, indicating its ability to eliminate obscuration for totally off-axis mirror system and the searching for such systems from co-axial starting points.

Metaheuristic algorithms are effectively used in searching some optical solution space. for optical solution. It is basically the type of local search generalization that can provide useful solutions for issues related to optimization. Several benefits are associated with this type of algorithms due to that such algorithms can be better to solve many issues in an effective way. To provide fast and accurate solutions to huge range of complex issues is one main benefit metaheuristic algorithms. Some metaheuristic algorithms are effectively used to classify the problems and BAT Algorithm (BA) is one of them is more popular in use to sort out issues related to optimization of theoretical and realistic. Sometimes BA fails to find global optima and gets stuck in local optima because of the absence of investigation and manipulation. We have improved the BA to boost its local searching ability and diminish the premature problem. An improved equation of search with more necessary information through the search is set for the generation of the solution. Test set of benchmark functions are utilized to verify the proposed method’s performance. The results of simulation showed that proposed methods are best optimal solution as compare to others.

he last 10 years have been the decade of autonomous vehicles. Advances in intelligent sensors and control schemes have shown the possibility of real applications. Deep learning, and in particular convolutional networks have become a fundamental tool in the solution of problems related to environment identification, path planning, vehicle behavior, and motion control. In this paper, we perform a comparative study of the most used optimization strategies on the convolutional architecture residual neural network (ResNet) for an autonomous driving problem as a previous step to the development of an intelligent sensor. This sensor, part of our research in reactive systems for autonomous vehicles, aims to become a system for direct mapping of sensory information to control actions from real-time images of the environment. The optimization techniques analyzed include stochastic gradient descent (SGD), adaptive gradient (Adagrad), adaptive learning rate (Adadelta), root mean square propagation (RMSProp), Adamax, adaptive moment estimation (Adam), nesterov-accelerated adaptive moment estimation (Nadam), and follow the regularized leader (Ftrl). The training of the deep model is evaluated in terms of convergence, accuracy, recall, and F1-score metrics. Preliminary results show a better performance of the deep network when using the SGD function as an optimizer, while the Ftrl function presents the poorest performances.

A new model for evolving Evolutionary Algorithms (EAs) is proposed in this paper. The model is based on the Multi Expression Programming (MEP) technique. Each MEP chromosome encodes an evolutionary pattern that is repeatedly used for generating the individuals of a new generation. The evolved pattern is embedded into a standard evolutionary scheme that is used for solving a particular problem. Several evolutionary algorithms for function optimization are evolved by using the considered model. The evolved evolutionary algorithms are compared with a human-designed Genetic Algorithm. Numerical experiments show that the evolved evolutionary algorithms can compete with standard approaches for several well-known benchmarking problems., arXiv admin note: substantial text overlap with arXiv:2109.13110

When using Inductively Coupled Plasma (ICP) as a machining tool, its processing method based on the principle of chemical etching leads to no contact stress between the tool and the material, thereby generating no mechanical damage. In recent years, this issue has been widely concerned in the field of optical fabrication. However, there are many differences between low power ICP jet and conventional ICP jet, one of which is that the former does not easily form a rotation-symmetric removal function due to its obvious pinch effect. In this research, the electromagnetism principle of the plasma pinch effect was analyzed firstly, and the jet shape under the pinch effect was classified. Then, experimental study was carried out on the plasma jet shape under the pure Ar and mixed gas of CF4-Ar, and the influence law of the reaction gas on the jet propagation shape was analyzed. Finally, the rotational symmetry of the removal function of plasma jet processing was optimized, and the nozzle design criteria based on pinch effect were proposed.

Finding the optimal parameter setting (i.e. the optimal population size, the optimal mutation probability, the optimal evolutionary model etc) for an Evolutionary Algorithm (EA) is a difficult task. Instead of evolving only the parameters of the algorithm we will evolve an entire EA capable of solving a particular problem. For this purpose the Multi Expression Programming (MEP) technique is used. Each MEP chromosome will encode multiple EAs. An nongenerational EA for function optimization is evolved in this paper. Numerical experiments show the effectiveness of this approach., 8 pages, 2 figures. arXiv admin note: text overlap with arXiv:2109.13110

A new model for evolving Evolutionary Algorithms is proposed in this paper. The model is based on the Linear Genetic Programming (LGP) technique. Every LGP chromosome encodes an EA which is used for solving a particular problem. Several Evolutionary Algorithms for function optimization, the Traveling Salesman Problem, and the Quadratic Assignment Problem are evolved by using the considered model. Numerical experiments show that the evolved Evolutionary Algorithms perform similarly and sometimes even better than standard approaches for several well-known benchmarking problems., 23 pages, 3 figures

The clonal selection algorithm (CSA), which describes the basic features of an immune response to an antigenic stimulus, has drawn a lot of attention in the biologically inspired computing community, due to its highly adaptive and easy-to-implement nature. Despite many successful applications, CSA still suffers from limited ability to explore the solution space. In this paper, we incorporate the differential evolution (DE) algorithm and the estimation of distribution algorithm (EDA) into CSA, and thus propose a novel bio-inspired algorithm referred to as CSA-DE/EDA. In the proposed algorithm, the hypermutation and receptor editing processes are implemented based on DE and EDA, which provide improved local and global search ability, respectively. We have applied the proposed algorithm to five commonly used benchmark functions for optimization and brain magnetic resonance (MR) image segmentation. Our comparative experimental results show that the proposed CSA-DE/EDA algorithm outperforms several bio-inspired computing techniques. CSA-DE/EDA is a compelling bio-inspired algorithm for optimization tasks.

Motivation Protein structure refinement is an important step of protein structure prediction. Existing approaches have generally used a single scoring function combined with Monte Carlo method or Molecular Dynamics algorithm. The one-dimension optimization of a single energy function may take the structure too far away without a constraint. The basic motivation of our study is to reduce the bias problem caused by minimizing only a single energy function due to the very diversity of different protein structures. Results We report a new Artificial Intelligence-based protein structure Refinement method called AIR. Its fundamental idea is to use multiple energy functions as multi-objectives in an effort to correct the potential inaccuracy from a single function. A multi-objective particle swarm optimization algorithm-based structure refinement is designed, where each structure is considered as a particle in the protocol. With the refinement iterations, the particles move around. The quality of particles in each iteration is evaluated by three energy functions, and the non-dominated particles are put into a set called Pareto set. After enough iteration times, particles from the Pareto set are screened and part of the top solutions are outputted as the final refined structures. The multi-objective energy function optimization strategy designed in the AIR protocol provides a different constraint view of the structure, by extending the one-dimension optimization to a new three-dimension space optimization driven by the multi-objective particle swarm optimization engine. Experimental results on CASP11, CASP12 refinement targets and blind tests in CASP 13 turn to be promising. Availability and implementation The AIR is available online at: www.csbio.sjtu.edu.cn/bioinf/AIR/. Supplementary information Supplementary data are available at Bioinformatics online.

This article introduces Fuzzy Inspired Bat Algorithm (FIBA), which is an improved variant of the original Bat algorithm. The novelty of FIBA lies in the integration of a fuzzy controller with the basic Bat algorithm that tries to bring balance between the degree of explorations and exploitations during the mutation operation. Another novelty of FIBA is the introduction of a step size parameter, maintained separately for every candidate solution, to customize and control the mix of explorative and exploitative operations around each candidate solution. FIBA is tested on a standard benchmark set that includes 10 complex, scalable, high dimensional functions. The results on benchmark functions reveal that FIBA can perform sufficiently well, and often better than the original Bat algorithm and another recently proposed improved Bat variant. Such improvements on the experimental results imply that the fuzzy technique adopted by FIBA might be effective on other existing problems as well, and hence demand further research and investigation.

Grey wolf optimizer (GWO) is a very efficient metaheuristic inspired by the hierarchy of the Canis lupus wolves. It has been extensively employed to a variety of practical applications. Crow search algorithm (CSA) is a recently proposed metaheuristic algorithm, which mimics the intellectual conduct of crows. In this paper, a hybrid GWO with CSA, namely GWOCSA is proposed, which combines the strengths of both the algorithms effectively with the aim to generate promising candidate solutions in order to achieve global optima efficiently. In order to validate the competence of the proposed hybrid GWOCSA, a widely utilized set of 23 benchmark test functions having a wide range of dimensions and varied complexities is used in this paper. The results obtained by the proposed algorithm are compared to 10 other algorithms in this paper for verification. The statistical results demonstrate that the GWOCSA outperforms other algorithms, including the recent variants of GWO called, enhanced grey wolf optimizer (EGWO) and augmented grey wolf optimizer (AGWO) in terms of high local optima avoidance ability and fast convergence speed. Furthermore, in order to demonstrate the applicability of the proposed algorithm at solving complex real-world problems, the GWOCSA is also employed to solve the feature selection problem as well. The GWOCSA as a feature selection approach is tested on 21 widely employed data sets acquired from the University of California at Irvine repository. The experimental results are compared to the state-of-the-art feature selection techniques, including the native GWO, the EGWO, and the AGWO. The results reveal that the GWOCSA has comprehensive superiority in solving the feature selection problem, which proves the capability of the proposed algorithm in solving real-world complex problems.

The fireworks algorithm, which is inspired by the explosion of fireworks, is a new swarm-based meta-heuristic algorithm for global optimization. This work proposes an improved fireworks optimization algorithm (IFWA) based on the enhanced fireworks algorithm (EFWA). Three aspects of improvement are presented after an analysis of the drawbacks of EFWA. These improvements are a new explosion scheme, GS-Gaussian explosion operator, and deep information exchange strategy. The proposed IFWA is tested on 23 benchmark function optimization problems and a real engineering problem, namely, optimal controller design for automotive active suspension. Optimization results prove that IFWA has competitive advantage compared with EFWA and other popular meta-heuristic algorithms and demonstrates the potential to solve real problems effectively.

The black hole (BH) algorithm is a new type of natural heuristic algorithm inspired by the movement law of the “black hole” celestial body in the universe. BH algorithm has received extensive attention due to its advantages such as fewer parameters, simple algorithm structure and strong exploitation. For the shortcomings of poor exploaration and premature convergence of BH algorithm, the improved golden sine (G-S) operator is introduced into BH algorithm to greatly improve the exploaration. Then the Levy flight operator with controlled step size has become a better local search operator from the global search operator, so the improved Levy flight operator is introduced to further improve the exploitation of BH algorithm. Ultimately, the golden sine operator and Levy flight operator based black hole (GSLBH) algorithm is able to balance the exploaration with exploitation. GSLBH, BH, Particle Swarm Optimization (PSO), Whale Optimization Algorithm (WAO), Firefly Algorithm (FA), Golden Sine Algorithm (Gold-SA) were adopted to carry out the simulation experiments with 17 benchmark functions, respectively, and the statistical data results are analyzed and compared. Finally, it can be concluded that the proposed improved black hole algorithm has better exploaration, and the convergence speed and accuracy of the algorithm have been further improved.

Gravitational search algorithm (GSA) is a population-based heuristic algorithm, which is inspired by Newton’s laws of gravity and motion. Although GSA provides a good performance in solving optimization problems, it has a disadvantage of premature convergence. In this paper, the concept of repulsive force is introduced and the definition of exponential $Kbest$ is used in a new version of GSA, which is called repulsive GSA with exponential $Kbest$ (EKRGSA). In this algorithm, heavy particles repulse or attract all particles according to distance, and all particles search the solution space under the combined action of repulsive force and gravitational force. In this way, the exploration ability of the algorithm is improved and a proper balance between exploration and exploitation is established. Moreover, the exponential $Kbest$ significantly decreases the computational time. The proposed algorithm is tested on a set of benchmark functions and compared with other algorithms. The experimental results confirm the high efficiency of EKRGSA.

Nature-inspired computing (NIC) has been widely studied for many optimization scenarios. However, miscellaneous solution space of real-world problem causes it is challenging to guarantee the global optimum. Besides, cumbersome structure and complex parameters setting-up make the existed algorithms hard for most users who are not specializing in NIC, to understand and use. To alleviate these limitations, this paper devises a succinct and efficient optimization algorithm called Nomad Algorithm (NA). It is inspired by the migratory behaviour of nomadic tribes on the prairie. Extensive experiments are implemented with respects to accuracy, rate, stability, and cost of optimization. Mathematical proof is given to guarantee the global convergence, and the nonparametric tests are conducted to confirm the significance of experiment results. The statistical results of optimization accuracy denote NA outperforms its rivals for most cases (23/28) by orders of magnitude significantly. It is considered as a promising optimizer with excellent efficiency and adaptability.

Bacterial foraging optimization (BFO), a biological-inspired optimization algorithm, has been applied in various fields, such as complex function optimization, robot path planning. However, there still exist several insufficiencies in BFO algorithm due to the fixed chemotaxis step-size, the less-efficient search direction for tumbling and the swarming strategy with lower convergence rate. In order to deal with these issues, based on the Levy flight step-size and particle swarm optimization (PSO) operator, this paper proposes the improved BFO algorithm (LPBFO). To reduce the mutual interference among different dimensions, each bacterium selects one dimension for tumbling randomly during the chemotactic process in LPBFO. The step-size of each bacterium is determined by the stochastic flight lengths of the improved Levy flight which can generate small step-size with high frequency and big step-size occasionally; moreover, the stochastic step-size is also reduced adaptively based on the evolutionary generations, which makes the bacteria transform from global search to local search. Furthermore, inspired by the social information term in PSO, this paper employed the global best solution to improve the swarming performance. Several experiments on benchmark functions are carried out with the purpose of evaluating the performance of the proposed method. Experimental results show that the proposed algorithm achieves noticeable improvement compared with other competitive algorithms.

A pure material proportion estimation method based on a spectral database is proposed. The method transforms the non-negative and linear constraints into a pure material proportional cost function minimization problem with a linear mixed model. The Newton algorithm is used to optimize the cost function, and the optimized extreme value is the optimal estimate of the proportion of pure material. Spectral simulation experiments are carried out for space target materials using the US Geological Survey database, and the experimental results show that the method proposed in this paper can help to estimate the proportion of pure substances in such targets quickly and accurately, especially when the number of mixed pure materials is large. Compared with some existing common algorithms, the proposed method is robust and can estimate the proportion of pure material in a space target when the signal-tonoise ratio is less than 40 dB. The accuracy of the method is 30% higher than that of the existing method.

The marine environment is the most biologically and chemically diverse habitat on Earth, and provides numerous marine-derived products, including enzymes and molecules, for industrial and pharmaceutical applications. Marine biotechnology provides important biological resources from marine habitat conservation to applied science. In recent years, advances in techniques in interdisciplinary research fields, including metabolic engineering and synthetic biology have significantly improved the production of marine-derived commodities. In this review, we outline the recent progress in the use or marine enzymes and molecules in biotechnology, including newly discovered products, function optimization of enzymes, and production improvement of small molecules.

This paper anticipates to frame a hybrid Seagull Optimization Algorithm - Cuckoo Search (SOA-CS) algorithm for objective function minimization. The migration and attacking strategies of Seagulls are complimented by the social breeding behaviour of cuckoo birds. In addition, the thought of Levy flight walking methodology is also inherited. Twenty-three standard benchmark test functions are used for validation. To figure out the outcomes - the proposed algorithm converges faster and provides better results over both the SOA and CS algorithms.

Until now, there is no clear definition of microtissue; it usually refers to the microtissue formed by the aggregation of seed cells under the action of cell-cell or cell-extracellular matrix (ECM). Compared with traditional cell monolayer culture, cells are cultivated into a three-dimensional microstructure in a specific way. The microstructure characteristics of microtissue are similar to natural tissues and can promote cell proliferation and differentiation. Therefore, it has a broader range of biomedical applications in tissue engineering. The traditional tissue engineering strategy is to add high-density seed cells and biomolecules on a preformed scaffold to construct a tissue engineering graft. However, due to the destruction of the ECM of the cells cultured in a monolayer during the digestion process with trypsin, the uneven distribution of the cells in the scaffold, and the damage of various adverse factors after the cells are implanted in the scaffold, this strategy is often ineffective, and the subsequent applications still face challenges. This article reviews the latest researches of a new strategy-tissue engineering microtissue strategy; discuss several traditional construction methods, structure, and function optimization; and practical application of microtissue. The review aims to provide a reference for future research on tissue engineering microtissue. Impact statement The traditional tissue engineering strategies have several disadvantages, researchers have conducted extensive research on tissue engineering microtissues in recent years, and they make significant progress. Microtissue is a kind of microtissue with three-dimensional structure, its microstructure is similar to that of natural tissue. In addition, microtissue implantation can protect cells from mechanical interference, inflammation, and other adverse factors. Furthermore, it improves the survival rate of cells and the therapeutic effect of tissue-engineered grafts. However, the practical conditions, advantages, and disadvantages of tissue engineering microtissue have not been fully elucidated. The purpose of this review is to discuss the latest research progress of microtissue and provide a reference for future research.

This paper aims to improve one of the recently proposed metaheuristic approaches known as Lévy flight distribution (LFD) algorithm by adopting a well-known simplex search algorithm named Nelder-Mead (NM) method. Three new strategies were utilized to demonstrate the improved capability of the original LFD algorithm. In the first strategy, NM was run twice as much the number of iterations of LFD after the latter completes its task. In the second strategy, NM was applied after each iterations of LFD instead of waiting for the completion of the latter. Lastly, in the third strategy, NM was applied after each iterations of LFD and run for the total number of current iterations of the latter algorithm. Well-known unimodal and multimodal benchmark functions were adopted, and statistical analysis was performed for performance evaluation. Further assessment was carried out through a nonparametric statistical test. The obtained results have shown the proposed versions of LFD algorithm provide significant performance improvement in general. In addition, the efficiency of the third strategy was found to be better for NM modified LFD algorithm which has greater balance between global and local search stages and can be used as an effective tool for function optimization.

Teaching-Learning optimization (TLBO) is simple, easy to implement, requires few parameters to be tuned, and has a higher computational efficiency than traditional methods, which has been widely used in function optimization, neural network optimization, engineering optimization and other fields. However, there is also the phenomenon of precocious convergence. The paper briefly introduces the current state of research, the TLBO algorithm, analyzes the improvements and applications of the algorithm, and makes a prospect for the research.

For premature convergence and instability of particle Swarm Optimization (PSO) and Cuckoo Search algorithm (CS) in solving function optimization problem, a new hybrid algorithm which based on the combination of PSO and CS is presented. In this algorithm, all individuals are randomly divided into two populations, and the evolutions of two sub-groups are simultaneously performed with different optimization strategies. The information interaction mechanism with last out strategy is introduced to achieve complementary advantages between the algorithm. Finally, the algorithm is put through six benchmark functions and an application example, the results demonstrate that its a powerful global optimization algorithm with rapid convergence rate and high computational precision.

The flower pollination algorithm (FPA) was firstly proposed in 2012 as one of the population-based metaheuristic optimization search techniques. It is conceptualized by the pollination behavior of flowering plants. In this paper, the new enhanced version of the original FPA named the modified flower pollination algorithm (MoFPA) is proposed to improve its search performance for function optimization. The switching probability of the original FPA used for selection between local and global pollinations is changed from the fixed manner to the random manner according to the pollination behavior of flowering plants in nature. To perform its effectiveness, the proposed MoFPA is tested against ten standard benchmark functions compared with the original FPA. As simulation results, it was found that the proposed MoFPA performs superior search performance for function optimization to the original FPA with higher success rates and faster search time consumed.

Behind every discovery, observation plays a vital role. The neural networks (NNs) are the result of a very minute neuron observation. This led to a revolution in the field of artificial intelligence. On the contrary of the biological inspirations, we present some of the physical sciences models that could be further related to neural network training phase. These relations are the momentum, solar orbits and the shape of a water droplet. Momentum is related to the weight optimization during NNs training phase and Solar orbits helps to understand the epoch’s concept. At the end, shape of a water droplet concept gives us the motivation behind the loss function optimization. These three are just some of the many inspirations that we can obtain from physical sciences. This paper can be the beginning of a whole new theory to the neural networks.