Swarm-based Metaheuristic Algorithm Research Articles

Design cost minimization of a reinforced concrete column section using overnew swarm-based optimization algorithms

AbstractIt is very tiresome for a practiser to detect the best feasible sizing design of structural members including reinforced concrete columns that is a highly nonlinear and complicated structural engineering optimization problem. This is due to such a design is practically conducted via conventional trial-and-error computing methods in which resistance to external loads, cost efficiency, and aesthetic factors, etc. have to be considered. This study focuses on minimizing the design cost of primarily proposed reinforced concrete column design problem via three overnew swarm-based optimizers such as Coati Optimization Algorithm, Fox Optimizer and Pelican Optimization Algorithm (POA) that are firstly utilized for this purpose. In this regard, the type of steel rebar distribution, the characteristic strength of the concrete, the height and width of the column section, and the number and diameter of the rebars are treated as discrete design variables of the newly proposed complex reinforced concrete column design cost optimization problem. In solution, the design requirements specified in practice code provisions should also be met. Here, Turkish Building Earthquake Code 2018 specifications are considered as practice structural design constraints. Consequently, the algorithmic performances of three overnew swarm-based metaheuristic optimization algorithms are compared and evaluated in detail. Amongst them, the POA shows most fruitful algorithmic design solution performance.

Probabilistic sizing and scheduling co-optimisation of hybrid battery/super-capacitor energy storage systems in micro-grids

While established deterministic capacity planning models for single-component energy storage systems exist, little attention has been given to probabilistic sizing of hybrid energy storage systems (ESSs) using swarm-based meta-heuristic algorithms. This highlights two key research opportunities, namely: (1) studying the impact of preserving model-inherent characteristics and optimising daily system dispatch on narrowing reality gaps in hybrid ESS designs, and (2) the optimal integration of hybrid ESSs into grid-connected micro-grids based on their applications, with potentially significant financial implications for model designs. In response, this paper introduces a novel probabilistic hybrid ESS capacity planning optimisation model based on a state-of-the-art meta-heuristic algorithm. To demonstrate the effectiveness of the model within a community micro-grid scheme, a case study of an eco-village in Aotearoa New Zealand is presented. The simulation results indicate a ∼4 % and ∼36 % premium above the deterministic results respectively in the most likely case and worst-case probabilistic scenarios. On the other hand, the best-case stochastic estimate of the life-cycle cost of the hybrid ESS is found to be ∼39 % lower than that of the deterministic modelling. Additionally, the economics of temporal energy arbitrage using the battery bank is investigated, indicating that at the current capital cost of stationary LiFePO4 batteries and the present fixed feed-in-tariff (NZ$0.08/kWh), it is not economically viable to cycle the storage for arbitrage reasons alone. In conclusion, this paper highlights the critical need to incorporate probabilistic optimisation techniques and emphasises the importance of sizing and scheduling co-optimisation when designing hybrid ESSs for integration into grid-connected micro-grids.

Swarm-based search algorithms: A comparative study on sizing optimization of truss structures

Metaheuristic algorithms belong to the category of non-deterministic optimization methods. Extensive research conducted in this domain has elucidated that each of these methods possesses distinctive merits and demerits. To illustrate, one algorithm may exhibit a notable penchant for exploration, whereas another algorithm may demonstrate exceptional prowess in exploitation. The judicious selection of a suitable and efficient algorithm for a given problem can profoundly influence both the rate of convergence and the level of accuracy. Over the past few decades, various swarm-based metaheuristic algorithms have been introduced in technical literature. Consequently, undertaking a comprehensive comparative evaluation of a subset of these methodologies can furnish researchers with an essential framework to discern the most appropriate algorithm for their objectives. The current investigation focuses on evaluating and comparing four swarm-based metaheuristic algorithms especially on solving size optimization of truss structures for this purpose. To cover the research conducted in the past two decades as comprehensively as possible, a hierarchical selection process was employed for choosing the methods. As a result, the following algorithms were chosen Firefly Algorithm (FA), Drosophila Food-search Algorithm (DFO), Harris Hawk Optimization (HHO), and Butterfly Optimization Algorithm (BOA). Various characteristics of the selected algorithms, such as convergence rate, diversity variation, complexity, and accuracy of the final solutions, were compared. The findings indicate Harris Hawk Optimization (HHO) could nearly outperform the other selected methods on solving structural size optimization problems.

Enhanced variants of crow search algorithm boosted with cooperative based island model for global optimization

The Crow Search Algorithm (CSA) is a swarm-based metaheuristic algorithm that simulates the intelligent foraging behaviors of crows. While CSA effectively handles global optimization problems, it suffers from certain limitations, such as low search accuracy and a tendency to converge to local optima. To address these shortcomings, researchers have proposed modifications and enhancements to CSA’s search mechanism. One widely explored approach is the structured population mechanism, which maintains diversity during the search process to mitigate premature convergence. The island model, a common structured population method, divides the population into smaller independent sub-populations called islands, each running in parallel. Migration, the primary technique for promoting population diversity, facilitates the exchange of relevant and useful information between islands during iterations. This paper introduces an enhanced variant of CSA, called Enhanced CSA (ECSA), which incorporates the cooperative island model (iECSA) to improve its search capabilities and avoid premature convergence. The proposed iECSA incorporates two enhancements to CSA. Firstly, an adaptive tournament-based selection mechanism is employed to choose the guided solution. Secondly, the basic random movement in CSA is replaced with a modified operator to enhance exploration. The performance of iECSA is evaluated on 53 real-valued mathematical problems, including 23 classical benchmark functions and 30 IEEE-CEC2014 benchmark functions. A sensitivity analysis of key iECSA parameters is conducted to understand their impact on convergence and diversity. The efficacy of iECSA is validated by conducting an extensive evaluation against a comprehensive set of well-established and recently introduced meta-heuristic algorithms, encompassing a total of seventeen different algorithms. Significant differences among these comparative algorithms are established utilizing statistical tests like Wilcoxon’s rank-sum and Friedman’s tests. Experimental results demonstrate that iECSA outperforms the fundamental ECSA algorithm on 82.6% of standard test functions, providing more accurate and reliable outcomes compared to other CSA variants. Furthermore, Extensive experimentation consistently showcases that the iECSA outperforms its comparable algorithms across a diverse set of benchmark functions.

Comparison of Swarm-based Metaheuristic and Gradient Descent-based Algorithms in Artificial Neural Network Training

This paper aims to compare the gradient descent-based algorithms under classical training model and swarm-based metaheuristic algorithms in feed forward backpropagation artificial neural network training. Batch weight and bias rule, Bayesian regularization, cyclical weight and bias rule and Levenberg-Marquardt algorithms are used as the classical gradient descent-based algorithms. In terms of the swarm-based metaheuristic algorithms, hunger games search, gray wolf optimizer, Archimedes optimization, and the Aquila optimizer are adopted. The Iris data set is used in this paper for the training. Mean square error, mean absolute error and determination coefficient are used as statistical measurement techniques to determine the effect of the network architecture and the adopted training algorithm. The metaheuristic algorithms are shown to have superior capability over the gradient descent-based algorithms in terms of artificial neural network training. In addition to their success in error rates, the classification capabilities of the metaheuristic algorithms are also observed to be in the range of 94%-97%. The hunger games search algorithm is also observed for its specific advantages amongst the metaheuristic algorithms as it maintains good performance in terms of classification ability and other statistical measurements.

Numerical investigation and optimisation of flat plate solar collectors using two swarm-based metaheuristic algorithms

In the present work, four flat-plate solar collectors of similar dimensions have been simulated using the CFD approach. Model 1 has been considered as circular with a U-shaped zigzag channel, while model 2 is a square-shaped plate. In the 3rd model, the number of turns in the channel has been increased by keeping the geometry of the pipe constant, while in the 4th model, multiple straight channels have been incorporated instead of a single U-shaped zigzag channel. Three-dimensional simulations have been primarily done to understand the effect of channel geometry area and turnings on the collector's performance. A steady-state incompressible forced convective heat transfer analysis has been performed here. Water is used as a fluid in the channel to carry heat. The results of the numerical analysis led to the conclusion that model 3 is the best flat plate solar collector where turnings are maximum. With a maximum collector performance of 41.57, model 3 performs 36.7% better than model 1. Additionally, when water flows at a rate of 8 m/s inside the collector's channel, the rate of heat transfer in model 3 is 2.5% faster than in model 1. Moreover, a global optimization study has been performed using two swarm-based metaheuristic algorithms, Gravitational Search Algorithm (GSA) and Firefly Algorithm (FA), with the aim of determining good optimum values of the design variables that will maximize collector efficiency for model 3 at different flow velocities. For model 3, the percentage variation in collector efficiency between CFD and optimised findings using metaheuristic algorithms is found to be (a) 41.08% for v = 2 m/s; (b) 28.41% for v = 4 m/s; (c) 21.71% for v = 6 m/s; and (d) 13.09% for v = 8 m/s. Therefore, it is possible to anticipate that as flow velocity increases, there will be a steady decrease in the variation between computed and optimized results.

Rhizostoma optimization algorithm and its application in different real-world optimization problems

<p>In last decade, numerous meta-heuristic algorithms have been proposed for dealing the complexity and difficulty of numerical optimization problems in the realworld which is growing continuously recently, but only a few algorithms have caught researchers’ attention. In this study, a new swarm-based meta-heuristic algorithm called Rhizostoma optimization algorithm (ROA) is proposed for solving the optimization problems based on simulating the social movement of Rhizostoma octopus (barrel jellyfish) in the ocean. ROA is intended to mitigate the two optimization problems of trapping in local optima and slow convergence. ROA is proposed with three different movement strategies (simulated annealing (SA), fast simulated annealing (FSA), and Levy walk (LW)) and tested with 23 standard mathematical benchmark functions, two classical engineering problems, and various real-world datasets including three widely used datasets to predict the students’ performance. Comparing the ROA algorithm with the latest meta-heuristic optimization algorithms and a recent published research proves that ROA is a very competitive algorithm with a high ability in optimization performance with respect to local optima avoidance, the speed of convergence and the exploration/exploitation balance rate, as it is effectively applicable for performing optimization tasks.</p>

Enhanced opposition-based grey wolf optimizer for global optimization and engineering design problems

A recently developed swarm-based meta-heuristic algorithm namely Grey Wolf Optimization algorithm (GWO), which is based on the hunting and leadership behaviours of the grey wolves in nature, has shown superior performance when compared with existing meta-heuristic algorithms. However, like other approaches, the GWO has the limitation of poor exploitation ability and being stuck in local optima when solving challenging optimization problems. To overcome these limitations, a novel technique, namely “Enhanced Opposition-Based Learning” (EOBL), has been proposed and is implemented with the GWO algorithm. The EOBL technique is largely inspired by Opposition-Based Learning (OBL) and Random Opposition-Based Learning (ROBL) techniques to efficiently balance exploration and exploitation. As a result, the Enhanced Opposition-Based Grey Wolf Optimizer (EOBGWO), an innovative approach, is proposed to increase the effectiveness of the conventional GWO algorithm. To test the efficiency of the proposed EOBGWO method, it has been tested on the standard IEEECEC2005, IEEECEC2017, and IEEECEC2019 test functions, along with several real-life engineering design problems. Furthermore, to evaluate the effectiveness and stability of the proposed technique, it has been evaluated on the challenging IEEECEC2008 special session on large scale global optimization problems. The experimental outcomes and statistical measures such as the t-test and Wilcoxon rank-sum test demonstrate that the proposed EOBGWO method outperforms the other state-of-the-art algorithms in both global optimization and engineering design problems.

An Advanced Crow Search Algorithm for Solving Global Optimization Problem

The conventional crow search (CS) algorithm is a swarm-based metaheuristic algorithm that has fewer parameters, is easy to apply to problems, and is utilized in various fields. However, it has a disadvantage, as it is easy for it to fall into local minima by relying mainly on exploitation to find approximations. Therefore, in this paper, we propose the advanced crow search (ACS) algorithm, which improves the conventional CS algorithm and solves the global optimization problem. The ACS algorithm has three differences from the conventional CS algorithm. First, we propose using dynamic AP (awareness probability) to perform exploration of the global region for the selection of the initial population. Second, we improved the exploitation performance by introducing a formula that probabilistically selects the best crows instead of randomly selecting them. Third, we improved the exploration phase by adding an equation for local search. The ACS algorithm proposed in this paper has improved exploitation and exploration performance over other metaheuristic algorithms in both unimodal and multimodal benchmark functions, and it found the most optimal solutions in five engineering problems.

Marine Predators Algorithm for Sizing Optimization of Truss Structures with Continuous Variables

In this study, the newly developed Marine Predators Algorithm (MPA) is formulated to minimize the weight of truss structures. MPA is a swarm-based metaheuristic algorithm inspired by the efficient foraging strategies of marine predators in oceanic environments. In order to assess the robustness of the proposed method, three normal-sized structural benchmarks (10-bar, 60-bar, and 120-bar spatial dome) and three large-scale structures (272-bar, 942-bar, and 4666-bar truss tower) were selected from the literature. Results point to the inherent strength of MPA against all state-of-the-art metaheuristic optimizers implemented so far. Moreover, for the first time in the field, a quantitative evaluation and an answer to the age-old question of the proper convergence behavior (exploration vs. exploitation balance) in the context of structural optimization is conducted. Therefore, a novel dimension-wise diversity index is adopted as a methodology to investigate each of the two schemes. It was concluded that the balance that produced the best results was about 90% exploitation and 10% exploration (on average for the entire computational process).

Discrete Mayfly Algorithm for spherical asymmetric traveling salesman problem

The Asymmetric Traveling Salesman Problem (ATSP), as a branch of the traveling salesman problem, aims to find a group of circuits when a salesman travels all cities at the minimum cost and returns to the starting city under the condition of different round-trip costs between the two cities. Mayfly Algorithm (MA) is a swarm-based metaheuristic algorithm, which has been applied to many fields successfully. In this paper, we arrange all cities on the sphere. A Discrete Mayfly Algorithm (DMA) for solving spherical asymmetric traveling salesman problem is proposed. The algorithm applies inver-over operator, crossover operator and 3-opt operator to simplify the parameters of the algorithm, enrich the diversity of the population and enhance the local search ability. By experimenting, analyzing and comparing the effects of DMA and other metaheuristic algorithms in twelve scales, this study proves that the proposed algorithm is superior to others for the spherical ATSP, especially in high-dimensional cases.

A modified crow search algorithm based on group strategy and adaptive mechanism

ABSTRACT As a swarm-based metaheuristic algorithm, the crow search algorithm (CSA) has attracted a lot of attention owing to its simplicity and flexibility. However, CSA tends to have low efficiency. To improve the optimization efficiency, this article proposes a modified version of CSA based on group strategy with an adaptive mechanism (GCSA). On this basis, crows are divided into multiple competing groups, and are assigned different roles and statuses. Then, the group strategy including different search modes is implemented to increase the solution diversity and search efficiency. Moreover, benefiting from the adaptive mechanism, the search range of crows changes in different stages to balance exploration and exploitation capabilities. To evaluate the performance of the proposed algorithm, 35 benchmark test functions (including 10 CEC2020 functions) and three engineering design problems are solved by GCSA and 11 other algorithms. The results prove that GCSA generally provides more competitive results than other metaheuristic algorithms.

Multi-objective SHADE with manta ray foraging optimizer for structural design problems

This paper presents a hybrid multi-objective success history-based parameter adaptive differential evolution (SHADE) with manta ray foraging optimizer (MRFO) for structural design problems, called MO-SHADE-MRFO. In the proposed algorithm, the updating rules of SHADE, a variant of differential evolution with great performance, are combined with the operators from MRFO, a recent swarm-based metaheuristic algorithm inspired from the manta ray with cyclone, chain and somersault foraging behaviors, which can balance the exploration and exploitation of the algorithm for structural design problems. Furthermore, MO-SHADE-MRFO utilizes the external archive to save and update the obtained Pareto fronts during the optimization process. The proposed algorithm is verified by multi-objective truss optimization problems with two objectives of minimizing the structural weight and the compliance, including 10-bar, 25-bar, 37-bar, 120-bar, 200-bar and 942-bar truss problems. Moreover, 9 different multi-objective metaheuristic algorithms are implemented to compare with the proposed algorithm, where three metrics are used to measure the performance of the algorithms, including hypervolume (HV), inverted generational distance (IGD), and spacing-to-extent (STE). According to the experimental results, MO-SHADE-MRFO can provide the best statistical values of HV, IGD and STE in most cases, ranking the first among the compared algorithms. Besides, the proposed algorithm also gives well-distributed Pareto solutions for the tested problems, illustrating the effectiveness of the hybrid updating rules of SHADE and MRFO.

Eagle perching optimizer for the online solution of constrained optimization

The paper proposes a novel nature-inspired optimization technique called Eagle Perching Optimizer (EPO). It is an addition to the family of swarm-based meta-heuristic algorithms. It mimics eagles’ perching nature to find prey (food). The EPO is based on the exploration and exploitation of an eagle when it descends from the height such that it formulates its trajectory in a way to get to the optimal solution (prey). The algorithm takes bigger chunks of search space and looks for the optimal solution. The optimal solution in that chunk becomes the search space for the next iteration, and this process is continuous until EPO converges to the optimal global solution. We performed the theoretical analysis of EPO, which shows that it converges to the optimal solution. The simulation includes three sets of problems, i.e., uni-model, multi-model, and constrained real-world problems. We employed EPO on the benchmark problems and compared the results with state-of-the-art meta-heuristic algorithms. For the real-world problems, we used a cantilever beam, three-bar truss, and gear train problems to test the robustness of EPO and later made the comparison. The comparison shows that EPO is comparable with other known meta-heuristic algorithms.

A Modified Reptile Search Algorithm for Numerical Optimization Problems.

The reptile search algorithm (RSA) is a swarm-based metaheuristic algorithm inspired by the encirclement and hunt mechanisms of crocodiles. Compared with other algorithms, RSA is competitive but still suffers from low population diversity, unbalanced exploitation and exploration, and the tendency to fall into local optima. To overcome these shortcomings, a modified variant of RSA, named MRSA, is proposed in this paper. First, an adaptive chaotic reverse learning strategy is employed to enhance the population diversity. Second, an elite alternative pooling strategy is proposed to balance exploitation and exploration. Finally, a shifted distribution estimation strategy is used to correct the evolutionary direction and improve the algorithm performance. Subsequently, the superiority of MRSA is verified using 23 benchmark functions, IEEE CEC2017 benchmark functions, and robot path planning problems. The Friedman test, the Wilcoxon signed-rank test, and simulation results show that the proposed MRSA outperforms other comparative algorithms in terms of convergence accuracy, convergence speed, and stability.

Improved Slime Mold Algorithm with Dynamic Quantum Rotation Gate and Opposition-Based Learning for Global Optimization and Engineering Design Problems

The slime mold algorithm (SMA) is a swarm-based metaheuristic algorithm inspired by the natural oscillatory patterns of slime molds. Compared with other algorithms, the SMA is competitive but still suffers from unbalanced development and exploration and the tendency to fall into local optima. To overcome these drawbacks, an improved SMA with a dynamic quantum rotation gate and opposition-based learning (DQOBLSMA) is proposed in this paper. Specifically, for the first time, two mechanisms are used simultaneously to improve the robustness of the original SMA: the dynamic quantum rotation gate and opposition-based learning. The dynamic quantum rotation gate proposes an adaptive parameter control strategy based on the fitness to achieve a balance between exploitation and exploration compared to the original quantum rotation gate. The opposition-based learning strategy enhances population diversity and avoids falling into the local optima. Twenty-three benchmark test functions verify the superiority of the DQOBLSMA. Three typical engineering design problems demonstrate the ability of the DQOBLSMA to solve practical problems. Experimental results show that the proposed algorithm outperforms other comparative algorithms in convergence speed, convergence accuracy, and reliability.

SIDELOBE REDUCTION OF LINEAR ANTENNA ARRAY BY POSITION-ONLY CONTROL USING NOVEL METAHEURISTIC OPTIMIZATION METHODS

In this study, the positions only of linear antenna array (LAA) elements are optimized for the first time in the literature by using Honey Badger Algorithm (HBA) and Chameleon Swarm Algorithm (CSA) methods, one of the new metaheuristic algorithms, for antenna design with the desired radiation pattern. LAAs with 10, 12, 24 and 32 elements are considered in the simulations. While designing the antenna, the half-beam power width (HPBW) of the antenna array is kept at a minimum level and the maximum sidelobe level (MSL) is suppressed as much as possible. In addition, to test the performance and accuracy of the HBA and CSA methods, the results obtained with the swarm-based metaheuristic algorithms Artificial Bee Colony (ABC) and Particular Swarm Algorithm (PSO) methods, which are quite well known in the literature are compared. As a result of these comparisons, the antenna design with high directivity, gain and desired pattern has been successfully obtained with the HBA and CSA optimization methods.

Multi-strategy boosted marine predators algorithm for optimizing approximate developable surface

Marine predators algorithm (MPA) is a newly developed swarm-based meta-heuristic algorithm that is inspired by the foraging strategies of marine predators: Lévy, Brownian motions and optimal encounter rate strategies, and has shown competitive performance with other state-of-the-art algorithms. Despite the effectiveness of original MPA and existing improved MPA in many real applications, the diversity of the population and the solution accuracy of MPA still deserve to be improved. To this end, an enhanced marine predators algorithm with the neighborhood-based learning strategy and the adaptive population size strategy is proposed in this paper, which is termed NMPA. Also, the superiority of the proposed NMPA is verified by being compared with the original MPA, other improved MPA and popular nature-inspired optimization algorithms on the well-known CEC 2017 and CEC 2020 test suites as well as three engineering design problems, respectively. Furthermore, the practicability of NMPA is illustrated by solving a real-world application of approximate developable surface modeling. By taking the maximization of developability degree of the developable surface as the evaluation criterion, the model for interpolating two given spatial curves to design an approximate developable surface is established. Then, the proposed NMPA is used to solve the optimization model, and the approximate developable surfaces with the maximum developability degree can be obtained. The experimental results show the superior performance of NMPA over other algorithms in terms of precision, convergence rate and solution quality. To sum up, NMPA is potentially a competitive and excellent meta-heuristic algorithm for constructing approximate developable surface and solving engineering optimization problems.

Inverse Kinematics Analysis of Novel 6-Dof Robotic Arm Manipulator for Oil and Gas Welding Using Grey Wolf Algorithm

his paper presents a grey-wolf algorithm for solving the inverse kinematics of a newly designed 6-degree-of-freedom robotic arm for oil and gas pipeline welding which has not been used in the literature. Consequently, due to the robot’s multiple joints with compounding combinatory possibilities of joint angles, analysis of the inverse kinematics is relatively complex. In this research, grey-wolf algorithm, a swarm-based meta-heuristic algorithm, has been used to solve for the inverse kinematics of the robotic arm with respect to tracking a rectangular trajectory with six sets of waypoints in the 3D [X, Y, Z] space. The results were further analyzed in terms of the accuracy of the position of end effector from the accurate position of the rectangular target trajectory via a mean squared error cost function. Furthermore, results of comparison between the grey-wolf algorithm and the particle swarm optimisation, an alternate swarm algorithm with respect to position error from the inverse kinematics task is also presented. The results obtained via simulation clearly demonstrates the superior performance of the grey-wolf algorithm compared to particle swarm optimisation with respect to the solving an inverse kinematics task

Beluga whale optimization: A novel nature-inspired metaheuristic algorithm

In this paper, a novel swarm-based metaheuristic algorithm inspired from the behaviors of beluga whales, called beluga whale optimization (BWO), is presented to solve optimization problem. Three phases of exploration, exploitation and whale fall are established in BWO, corresponding to the behaviors of pair swim, prey, and whale fall, respectively. The balance factor and probability of whale fall in BWO are self-adaptive which play significant roles to control the ability of exploration and exploitation. Besides, the Levy flight is introduced to enhance the global convergence in the exploitation phase. The effectiveness of the proposed BWO is tested using 30 benchmark functions, with qualitative, quantitative and scalability analysis, and the statistical results are compared with 15 other metaheuristic algorithms. According to the results and discussion, BWO is a competitive algorithm in solving unimodal and multimodal optimization problems, and the overall rank of BWO is the first in the scalability analysis of benchmark functions among compared metaheuristic algorithms through the Friedman ranking test. Finally, four engineering problems demonstrate the merits and potential of BWO in solving complex real-world optimization problems. The source code of BWO is currently available to public: https://ww2.mathworks.cn/matlabcentral/fileexchange/112830-beluga-whale-optimization-bwo/.