Welded Beam Design Research Articles

Dynamic group optimization algorithm with a mean–variance search framework

Dynamic group optimization has recently appeared as a novel algorithm developed to mimic animal and human socialising behaviours. Although the algorithm strongly lends itself to exploration and exploitation, it has two main drawbacks. The first is that the greedy strategy, used in the dynamic group optimization algorithm, guarantees to evolve a generation of solutions without deteriorating than the previous generation but decreases population diversity and limit searching ability. The second is that most information for updating populations is obtained from companions within each group, which leads to premature convergence and deteriorated mutation operators. The dynamic group optimization with a mean–variance search framework is proposed to overcome these two drawbacks, an improved algorithm with a proportioned mean solution generator and a mean–variance Gaussian mutation. The new proportioned mean solution generator solutions do not only consider their group but also are affected by the current solution and global situation. The mean–variance Gaussian mutation takes advantage of information from all group heads, not solely concentrating on information from the best solution or one group. The experimental results on public benchmark test suites show that the proposed algorithm is effective and efficient. In addition, comparative results of engineering problems in welded beam design show the promise of our algorithms for real-world applications.

A new optimization method based on COOT bird natural life model

Recently, many intelligent algorithms have been proposed to find the best solution for complex engineering problems. These algorithms can search volatile and multi-dimensional solution spaces and find optimal answers timely. In this paper, a new meta-heuristic method is proposed that inspires the behavior of the swarm of birds called Coot. The Coot algorithm imitates two different modes of movement of birds on the water surface: in the first phase, the movement of birds is irregular, and in the second phase, the movements are regular. The swarm moves towards a group of leading leaders to reach a food supply; the movement of the end of the swarm is in the form of a chain of coots, each of coot which moves behind its front coots. The algorithm then runs on a number of test functions, and the results are compared with well-known optimization algorithms. In addition, to solve several real problems, such as Tension/Compression spring, Pressure vessel design, Welded Beam Design, Multi-plate disc clutch brake, Step-cone pulley problem, Cantilever beam design, reducer design problem, and Rolling element bearing problem this algorithm is used to confirm the applicability of this algorithm. The results show that this algorithm is capable to outperform most of the other optimization methods. The source code is currently available for public from: https://www.mathworks.com/matlabcentral/fileexchange/89102-coot-optimization-algorithm.

SSC: A hybrid nature-inspired meta-heuristic optimization algorithm for engineering applications

Chimp Optimization Algorithm (ChoA) is a recently developed meta-heuristic approach which is inspired by the individual intelligence and sexual motivation of chimps. It is designed for trapping the local optima to alleviate the slow convergence speed. In this paper, a hybrid algorithm is developed which is based on the sine–cosine functions and attacking strategy of Spotted Hyena Optimizer (SHO). This hybrid algorithm is termed as Sine–cosine and Spotted Hyena-based Chimp Optimization Algorithm (SSC). This algorithm is used to find the best optimal solutions of real-life complex problems. The sine–cosine and attacking strategy of SHO algorithm is responsible for better exploration and exploitation. These strategies are applied to update the equations of chimps during the searching process to overcome the drawbacks of the ChoA algorithm such as slow convergence and local minima. Experimental results based on IEEE CEC’17 and six real-life engineering problems such as welded beam design, tension/compression spring design, pressure vessel design, multiple disk clutch brake design, gear train design, and car side crashworthiness, demonstrate the robustness, effectiveness, efficiency, and convergence analysis of the proposed SSC algorithm in comparison with other competitor approaches. Note that the source codes are available at http://www.dhimangaurav.com.

Flow Direction Algorithm (FDA): A Novel Optimization Approach for Solving Optimization Problems

The present study aimed to propose a new optimization algorithm named Flow Direction Algorithm (FDA), which is a physics-based algorithm. The FDA algorithm mimics the flow direction to the outlet point with the lowest height in a drainage basin. In other words, flow moves to neighbor with lowest high or best objective function. Thirteen classic mathematical benchmark functions, ten new mathematical benchmark functions and five engineering design problems, including three-bar truss, tension/compression spring, speed reducer, gear train, and welded beam design, with different properties are considered to evaluate the proposed algorithm. Comparing the results of the FDA with other optimization algorithms demonstrates the superior performance of the FDA in solving challenging optimization problems.

Stability of salp swarm algorithm with random replacement and double adaptive weighting

The salp swarm algorithm is a newly population-based search algorithm. Because the original salp swarm algorithm has low search efficiency and is easy to fall into local optimum, in this paper, we propose an enhanced salp swarm algorithm, which combines two strategies with the original salp swarm algorithm. One is the random replacement strategy, which can replace the current position with the optimal solution position with a certain probability of speeding up the convergence rate. The other tactic is double adaptive weight, which can expand the search scope throughout the early stages and enhance exploitation capability in the later stages. With the cooperation and guidance of the two mechanisms, the algorithm's convergence speed is accelerated, and the exploitation capacity is meritoriously increased. The proposed method's performance is compared with three mainstream meta-heuristics and four advanced algorithms on four necessary test cases. The extensive analysis and recorded results indicate that the proposed method outperforms these algorithms in terms of the accuracy of the solution and convergence speed. Finally, we apply the developed method to four well-known engineering design problems (welded beam design problem; cantilever beam design; I-beam design; and multiple disk clutch brake) to validate the algorithm's effectiveness for some constrained challenge. The results show that our algorithm has significant advantages in solving practical problems with constraints and unknown search spaces.

A Multi-Swarm Structure for Particle Swarm Optimization: Solving the Welded Beam Design Problem

Several studies exist in the literature that utilized metaheuristics and nature-inspired algorithms to solve engineering problems. Particle Swarm Optimization (PSO) is a well-known nature-inspired algorithm that has been used for different optimization problems due to its simplicity and ability to find near-optimal solutions. However, PSO suffers from a problem of balancing between the global search and local search abilities when applied to engineering problems. Recently, a new variant of PSO based on a novel multi-swarm architecture called Multi-swarm Particle Swarm Optimization (MPSO) was proposed. The proposed MPSO was evaluated on solving normal and large-scale problems. This study evaluated the possibility of using MPSO to simulate Welded Beam Design (WDB) problem which is a mechanical engineering problem. Several simulations were performed using the proposed approach and from the results, MPSO model was observed to simulate WBD problem with better optimal solution compared to the standalone PSO. The outcome of this study further confirmed the robustness of the MPSO over the other known metaheuristics. Generally, MPSO achieved an excellent optimization performance with a fast convergence learning process.

Application of constriction coefficient-based particle swarm optimisation and gravitational search algorithm for solving practical engineering design problems

The constriction coefficient-based particle swarm optimisation and gravitational search algorithm (CPSOGSA) is a heuristic optimisation technique. It uses the diversification capability of the GSA and the convergence power of CPSO. In this paper, the hybrid CPSOGSA is applied to three constrained engineering design problems, namely welded beam design (WBD), compression spring design (CSD), and pressure vessel design (PVD), to find the optimal value of the engineering objective function and design variables. The investigation of experimental outcomes has been performed through various performance metrics like statistical measures, run time analysis, convergence rate, and box plots. Moreover, statistical verification of experimental results is carried out using a signed Wilcoxon rank-sum test. Furthermore, seven heuristic algorithms were employed for comparative analysis. The simulation results clearly indicate that CPSOGSA provides better outcomes for all the three engineering benchmarks than classical PSO, standard GSA, and most of the competing algorithms.

Application of Constriction Coefficient Based Particle Swarm Optimization and Gravitational Search Algorithm for Solving Practical Engineering Design Problems

The constriction coefficient-based particle swarm optimisation and gravitational search algorithm (CPSOGSA) is a heuristic optimisation technique. It uses the diversification capability of the GSA and the convergence power of CPSO. In this paper, the hybrid CPSOGSA is applied to three constrained engineering design problems, namely welded beam design (WBD), compression spring design (CSD), and pressure vessel design (PVD), to find the optimal value of the engineering objective function and design variables. The investigation of experimental outcomes has been performed through various performance metrics like statistical measures, run time analysis, convergence rate, and box plots. Moreover, statistical verification of experimental results is carried out using a signed Wilcoxon rank-sum test. Furthermore, seven heuristic algorithms were employed for comparative analysis. The simulation results clearly indicate that CPSOGSA provides better outcomes for all the three engineering benchmarks than classical PSO, standard GSA, and most of the competing algorithms.

Feasibility-Guided Constraint-Handling Techniques for Engineering Optimization Problems

The particle swarm optimization (PSO) algorithm is an established nature-inspired population-based meta-heuristic that replicates the synchronizing movements of birds and fish. PSO is essentially an unconstrained algorithm and requires constraint handling techniques (CHTs) to solve constrained optimization problems (COPs). For this purpose, we integrate two CHTs, the superiority of feasibility (SF) and the violation constraint-handling (VCH), with a PSO. These CHTs distinguish feasible solutions from infeasible ones. Moreover, in SF, the selection of infeasible solutions is based on their degree of constraint violations, whereas in VCH, the number of constraint violations by an infeasible solution is of more importance. Therefore, a PSO is adapted for constrained optimization, yielding two constrained variants, denoted SF-PSO and VCH-PSO. Both SF-PSO and VCH-PSO are evaluated with respect to five engineering problems: the Himmelblau’s nonlinear optimization, the welded beam design, the spring design, the pressure vessel design, and the three-bar truss design. The simulation results show that both algorithms are consistent in terms of their solutions to these problems, including their different available versions. Comparison of the SF-PSO and the VCH-PSO with other existing algorithms on the tested problems shows that the proposed algorithms have lower computational cost in terms of the number of function evaluations used. We also report our disagreement with some unjust comparisons made by other researchers regarding the tested problems and their different variants.

Application of Particle Swarm Optimization for Classical Engineering Problems

In the design of mechanical elements, designers usually consider certain objectives that are related with cost, time, quality and reliability of product, depending on the requirements. In this paper, parametric optimization of spring design problem, pressure vessel design problem, cantilever beam design problem, cone coupling design problem and welded beam design problem has been carried out using Particle Swarm Optimization (PSO for short). The pseudo code for this algorithm was written using Matlab R2018a software suite. Results of the PSO algorithm will be compared to results obtained by the Differential Evolution (DE), Modified Ant Colony Algorithm, (MACA), Grasshopper Optimization Algorithm (GOA), Water Cycle Algorithm (WCA), Cucko Search (CS) , Genetic Algorithm (GA), Ant Lion Optimization (ALO), Firefly Algorithm (FA) and Method of Moving Asymptotes (MMA), depending of solutions found in literature. The source code of Particle Swarm Optimization (PSO) algorithm is publicly available at https://seyedalimirjalili.com.

Cooperation search algorithm: A novel metaheuristic evolutionary intelligence algorithm for numerical optimization and engineering optimization problems

This paper develops a novel population-based evolutionary method called cooperation search algorithm (CSA) to address the complex global optimization problem. Inspired by the team cooperation behaviors in modern enterprise, the CSA method randomly generates a set of candidate solutions in the problem space, and then three operators are repeatedly executed until the stopping criterion is met: the team communication operator is used to improve the global exploration and determine the promising search area; the reflective learning operator is used to achieve a comprise between exploration and exploitation; the internal competition operator is used to choose solutions with better performances for the next cycle. Firstly, three kinds of mathematical optimization problems (including 24 famous test functions, 25 CEC2005 test problems and 30 CEC2014 test problems) are used to test the convergence speed and search accuracy of the CSA method. Then, several famous engineering optimization problems (like Gear train design, Welded beam design and Speed reducer design) are chosen to testify the engineering practicality of the CSA method. The results in different scenarios demonstrate that as compared with several existing evolutionary algorithms, the CSA method can effectively explore the decision space and produce competitive results in terms of various performance evaluation indicators. Thus, an effective tool is provided for solving the complex global optimization problems.

Reliability-based Design Optimization for Structures Using Particle Swarm Optimization

Studies on structure design optimization have been conducted extensively over the past decades because it can increase structural efficiency and maximize the engineers’ profit. One of the significant current discussions is the reliability aspect of structure design in addition to optimal design. This problem becomes more important especially in sizing and shaping optimization of truss structures. To address the problem, this paper applies Reliability-based Design Optimization (RBDO) by combining Latin Hypercube Sampling (LHS) and metaheuristic algorithms which are Particle Swarm Optimization (PSO) and Barebone PSO (BBPSO). The presence of uncertainty is modeled using LHS and the reliability constraint is added to measure the probability of structural failure. This study aims to investigate the performance of these metaheuristic algorithms in optimizing the structure design while still satisfying the reliability constraints. Two case studies, a welded beam design problem and 15-bar planar truss problem, are used in this study. The performance of these two algorithms will be compared. The obtained results indicate that BBPSO has a better performance than PSO.

An enhanced adaptive butterfly optimization algorithm rigorously verified on engineering problems and implemented to ISAR image motion compensation

PurposeThis study aims to evolve an enhanced butterfly optimization algorithm (BOA) with respect to convergence and accuracy performance for numerous benchmark functions, rigorous constrained engineering design problems and an inverse synthetic aperture radar (ISAR) image motion compensation.Design/methodology/approachAdaptive BOA (ABOA) is thus developed by incorporating spatial dispersal strategy to the global search and inserting the fittest solution to the local search, and hence its exploration and exploitation abilities are improved.FindingsThe accuracy and convergence performance of ABOA are well verified via exhaustive comparisons with BOA and its existing variants such as improved BOA (IBOA), modified BOA (MBOA) and BOA with Levy flight (BOAL) in terms of various precise metrics through 15 classical and 12 conference on evolutionary computation (CEC)-2017 benchmark functions. ABOA has outstanding accuracy and stability performance better than BOA, IBOA, MBOA and BOAL for most of the benchmarks. The design optimization performance of ABOA is also evaluated for three constrained engineering problems such as welded beam design, spring design and gear train design and the results are compared with those of BOA, MBOA and BOA with chaos. ABOA, therefore, optimizes engineering designs with the most optimal variables. Furthermore, a validation is performed through translational motion compensation (TMC) of the ISAR image for an aircraft, which includes blurriness. In TMC, the motion parameters such as velocity and acceleration of target are optimally predicted by the optimization algorithms. The TMC results are elaborately compared with BOA, IBOA, MBOA and BOAL between each other in view of images, motion parameter and numerical image measuring metrics.Originality/valueThe outperforming results reflect the optimization and design successes of ABOA which is enhanced by establishing better global and local search abilities over BOA and its existing variants.

Hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism for global optimization problems

The butterfly optimization algorithm (BOA) is a new metaheuristic algorithm that is inspired from food foraging behavior of the butterflies. Because of its simplicity and effectiveness, the algorithm has been proved to be effective in solving global optimization problems and applied to practical problems. However, BOA is prone to local optimality and may lose its diversity, thus suffering losses of premature convergence. In this work, a hybrid metaheuristic algorithm using butterfly and flower pollination base on mutualism mechanism called MBFPA was proposed. Firstly, the flower pollination algorithm has good exploration ability and the hybrid butterfly optimization algorithm and the flower pollination algorithms greatly improve the exploration ability of the algorithm; secondly, the symbiosis organisms search has a strong exploitation capability in the mutualism phase. By introducing the mutualism phase, the algorithm's exploitation capability is effectively increased and the algorithm's convergence speed is accelerated. Finally, the adaptive switching probability is increased to increase the algorithm's balance in exploration and exploitation capabilities. In order to evaluate the effectiveness of the algorithm, in the 49 standard test functions, the proposed algorithm was compared with six basic metaheuristic algorithms and five hybrid metaheuristic algorithms. MBFPA has also been used to solve five classic engineering problems (three-bar truss design problem; multi-plate disc clutch brake design; welded beam design; pressure vessel design problem; and speed reducer design). The results show that the proposed method is feasible and has good application prospect and competitiveness.

Swarm-based chaotic gravitational search algorithm for solving mechanical engineering design problems

PurposeThe purpose of this paper is to investigate the performance of chaotic gravitational search algorithm (CGSA) in solving mechanical engineering design frameworks including welded beam design (WBD), compression spring design (CSD) and pressure vessel design (PVD).Design/methodology/approachIn this study, ten chaotic maps were combined with gravitational constant to increase the exploitation power of gravitational search algorithm (GSA). Also, CGSA has been used for maintaining the adaptive capability of gravitational constant. Furthermore, chaotic maps were used for overcoming premature convergence and stagnation in local minima problems of standard GSA.FindingsThe chaotic maps have shown efficient performance for WBD and PVD problems. Further, they have depicted competitive results for CSD framework. Moreover, the experimental results indicate that CGSA shows efficient performance in terms of convergence speed, cost function minimization, design variable optimization and successful constraint handling as compared to other participating algorithms.Research limitations/implicationsThe use of chaotic maps in standard GSA is a new beginning for research in GSA particularly convergence and time complexity analysis. Moreover, CGSA can be used for solving the infinite impulsive response (IIR) parameter tuning and economic load dispatch problems in electrical sciences.Originality/valueThe hybridization of chaotic maps and evolutionary algorithms for solving practical engineering problems is an emerging topic in metaheuristics. In the literature, it can be seen that researchers have used some chaotic maps such as a logistic map, Gauss map and a sinusoidal map more rigorously than other maps. However, this work uses ten different chaotic maps for engineering design optimization. In addition, non-parametric statistical test, namely, Wilcoxon rank-sum test, was carried out at 5% significance level to statistically validate the simulation results. Besides, 11 state-of-the-art metaheuristic algorithms were used for comparative analysis of the experimental results to further raise the authenticity of the experimental setup.

A multi-strategy enhanced sine cosine algorithm for global optimization and constrained practical engineering problems

The Sine Cosine Algorithm (SCA) has received much attention from engineering and scientific fields since it was proposed. Nevertheless, when solving multimodal or complex high dimensional optimization tasks, the conventional SCA still has a high probability of falling into the local optimal stagnation or failing to obtain the global optimum solution. Additionally, it performspoorly in convergence. Therefore, in this study, a multi-strategy enhanced SCA, a memetic algorithm termed MSCA, is proposed, which combines multiple control mechanisms including Cauchy mutation operator, chaotic local search mechanism, opposition-based learning strategy and two operators based on differential evolution to achieve a better balance between exploration and exploitation. To verify its performance, MSCA was compared with 11 state-of-the-art original optimizers and variant algorithms on 23 continuous benchmark tasks including 7 unimodal tasks, 6 multimodal tasks, 10 various fixed-dimension multimodal functions, and several typical CEC2014 benchmark problems. Furthermore, MSCA was utilized to solve three constrained practical engineering problems including tension/compression spring design, welded beam design, and pressure vessel design. The experimental results demonstrate that the proposed algorithm MSCA is superior to other competitors in terms of quality of solutions and convergence speed and can serve as an effective andefficient computer-aided tool for practical tasks with complex search space.

Electron radar search algorithm: a novel developed meta-heuristic algorithm

This paper introduces a new optimization algorithm called electron radar search algorithm (ERSA) inspired by the electron discharge mechanism. It is based on the natural phenomenon of electric flow as the form of electron discharge through a gas, liquid, or solid environment. When the voltage between separated electrodes (anode and cathode) increases, electrons tendency to emission from a low potential state to the higher potential condition is grown up. However, electrons are trying to find the best path with the least resistance in the medium. At each point, electrons evaluate the surrounding environment with a radar mechanism and least resistance path is selected for the next move. Hence, in this paper, a novel developed meta-heuristic algorithm based on the electrons’ search approach is presented and the algorithm is benchmarked on 20 mathematical functions with four well-known methods for validation and verification tests. Moreover, the algorithm is implemented in two engineering design problems (tension/expression spring and welded beam design optimization) and the results demonstrate that the ERSA performs more efficiently for solving unknown search spaces and the algorithm found best solution in approximately 95% of the reviewed benchmark functions.

A guided population archive whale optimization algorithm for solving multiobjective optimization problems

This paper proposes a new multiobjective algorithm by extending the recently Whale Optimization Algorithm (WOA) to solve multiobjective optimization problems. Our algorithm which we shall call Guided Population Archive Whale Optimization Algorithm (GPAWOA) is based on Pareto dominance and uses an external archive to store the non-dominated solutions found during the optimization process. The leaders are selected from the archive to guide the population towards promising regions of the search space, also, the mechanism of crowding distance is incorporated into the standard WOA to maintain the diversity. Our proposed algorithm is evaluated on twelve benchmark functions and is applied to four multi-objective engineering design problems: 4-bar truss design, gear train problem, disk brake design and welded beam design and compared against three well-known algorithms: Multiobjective Evolutionary Algorithm Based on Decomposition (MOEA/D), Multi-Objective Grey Wolf Optimizer (MOGWO), and Multi-Objective Particle Swarm Optimization (MOPSO). The experimental results indicate that the proposed GPAWOA is highly competitive and outperforms the selected state-of-the-art multiobjective optimization algorithms, being able to provide an excellent approximation of Pareto front in terms of convergence and diversity.

Chaos-enhanced synchronized bat optimizer

In this paper, a chaos-enhanced bat algorithm is proposed to tackle the global optimization problems. Bat algorithm is a relatively new stochastic optimizer inspired by the echolocation behavior of bats in nature. Due to its effectiveness, it has been applied to many fields such as engineering design, feature selection, and machine learning. However, the classical approach is often prone to falling into local optima. This paper proposes an enhanced bat algorithm to alleviate this problem observed in the original algorithm. The proposed method controls the steps of chaotic mapping by a threshold and synchronizes the velocity of agents using a velocity inertia weight. These mechanisms are designed to boost the stability and convergence speed of the bat algorithm, instantly. Eighteen well-established and the state-of-the-art meta-heuristic approaches are considered to validate the effectiveness of the developed algorithm. Experimental results reveal that the proposed chaos-enhanced bat algorithm is not only superior to the well-established algorithms such as the original method but also the latest improved approaches. Also, the proposed method is successfully applied to I-beam design problems, welded beam design, and pressure vessel design. The results show that chaos-enhanced bat algorithm can deal with unconstrained and constrained feature spaces, effectively.

Optimal Solution of Structural Engineering Design Problems using Crow Search Algorithm

In real world, the structural engineering design problems are large scale non-linear constrained problems. In the present study, crow search algorithm (CSA) is applied to find the optimal solution of structural engineering design problems such as pressure vessel design problem, welded beam design problem and tension/ compression string design problem. The numerical results are compared with the existing results reported in the literature including metaheuristic algorithms and it is found that the results obtained by the crow search algorithm are better than other existing algorithms. Further, the effectiveness of the algorithm is verified to be better than the existing algorithms by statistical analysis using mean, median, best case, and worst case scenarios. The present study confirms that the crow search algorithm may be easily and effectively applied to various structural design problems.