Real-world Engineering Design Problems Research Articles

Performance Comparison of Recent Population-Based Metaheuristic Optimisation Algorithms in Mechanical Design Problems of Machinery Components

The optimisation of complex engineering design problems is highly challenging due to the consideration of various design variables. To obtain acceptable near-optimal solutions within reasonable computation time, metaheuristics can be employed for such problems. However, a plethora of novel metaheuristic algorithms are developed and constantly improved and hence it is important to evaluate the applicability of the novel optimisation strategies and compare their performance using real-world engineering design problems. Therefore, in this paper, eight recent population-based metaheuristic optimisation algorithms—African Vultures Optimisation Algorithm (AVOA), Crystal Structure Algorithm (CryStAl), Human-Behaviour Based Optimisation (HBBO), Gradient-Based Optimiser (GBO), Gorilla Troops Optimiser (GTO), Runge–Kutta optimiser (RUN), Social Network Search (SNS) and Sparrow Search Algorithm (SSA)—are applied to five different mechanical component design problems and their performance on such problems are compared. The results show that the SNS algorithm is consistent, robust and provides better quality solutions at a relatively fast computation time for the considered design problems. GTO and GBO also show comparable performance across the considered problems and AVOA is the most efficient in terms of computation time.

An improved African vultures optimization algorithm based on tent chaotic mapping and time-varying mechanism.

Metaheuristic optimization algorithms are one of the most effective methods for solving complex engineering problems. However, the performance of a metaheuristic algorithm is related to its exploration ability and exploitation ability. Therefore, to further improve the African vultures optimization algorithm (AVOA), a new metaheuristic algorithm, an improved African vultures optimization algorithm based on tent chaotic mapping and time-varying mechanism (TAVOA), is proposed. First, a tent chaotic map is introduced for population initialization. Second, the individual’s historical optimal position is recorded and applied to individual location updating. Third, a time-varying mechanism is designed to balance the exploration ability and exploitation ability. To verify the effectiveness and efficiency of TAVOA, TAVOA is tested on 23 basic benchmark functions, 28 CEC 2013 benchmark functions and 3 common real-world engineering design problems, and compared with AVOA and 5 other state-of-the-art metaheuristic optimization algorithms. According to the results of the Wilcoxon rank-sum test with 5%, among the 23 basic benchmark functions, the performance of TAVOA has significantly better than that of AVOA on 13 functions. Among the 28 CEC 2013 benchmark functions, the performance of TAVOA on 9 functions is significantly better than AVOA, and on 17 functions is similar to AVOA. Besides, compared with the six metaheuristic optimization algorithms, TAVOA also shows good performance in real-world engineering design problems.

Chaotic neural network algorithm with competitive learning for global optimization

Neural network algorithm (NNA) is one of the newest proposed metaheuristic algorithms. NNA has strong global search ability due to the unique structure of artificial neural networks. Further, NNA is an algorithm without any effort for fine tuning initial parameters. Thus, it is very easy for NNA to solve different types of optimization problems. However, when used for solving complex optimization problems, slow convergence and premature convergence are its drawbacks. To overcome the two drawbacks, this work presents an improved NNA, namely chaotic neural network algorithm with competitive learning (CCLNNA), for global optimization. In CCLNNA, population is first divided into excellent subpopulation and common subpopulation according to the built competitive mechanism. Then, to balance exploration and exploitation of CCLNNA, excellent subpopulation is optimized by the designed transfer operator while common subpopulation is updated by the combination of the designed bias operator and transfer operator. Besides, chaos theory is introduced to increase the chance of CCLNNA to escape from the local optimum. To investigate the effectiveness of the improved strategies, CCLNNA is first used to solve the well-known CEC 2014 test suite with 30 benchmark functions. Then it is employed for solving three constrained real-world engineering design problems. Experimental results reveal that the improved strategies introduced to NNA can significantly improve the optimization performance of NNA and CCLNNA is a very powerful algorithm in solving complex optimization problems with multimodal properties by comparing with the other competitive algorithms.

A novel evolutionary algorithm based on even difference grey model

Evolutionary algorithm is an important subdomain of the meta-heuristics as a kind of the most popular optimization technology. Inspired by the grey prediction theory, this paper proposes a novel evolution algorithm based on the even difference grey model. Unlike population-based meta-heuristics with employing mutation and crossover operators to generate trial populations, the proposed algorithm develops a reproduction operator by using the even difference grey model. The novel reproduction operator regards population series as a time series. It firstly transforms an unorder data selected from the population series to a series data with approximate exponential law by using a grey operator. Based on the series data generated, an exponential model is constructed by using the even difference grey model. Finally, the reproduction operator obtains a trail population according to the prediction results of the exponential model. The effectiveness and superiority of the proposed algorithm are demonstrated on CEC2005 benchmark functions and six real-world engineering design problems. Philosophically speaking, the proposed algorithm towards a brand-new point of view to achieve the optimization process by forecasting the evolutionary direction at the macroscopic level, while the conventional evolutionary algorithms manipulate the chromosomes to realize their optimization at the microscopic level. It could be hoped from the algorithm to open a door for other prediction theories to construct new meta-heuristics.

Optimization of weight and cost of cantilever retaining wall by a hybrid metaheuristic algorithm

A retaining wall is a structure used to resist the lateral pressure of soil or any backfill material. Cantilever retaining walls provide resistance to overturning and sliding by using backfill weight. In this paper, the weight and cost of the cantilever retaining wall have been minimized using a hybrid metaheuristic optimization technique, namely, h-BOASOS. The algorithm has been developed by the ensemble of two popular metaheuristics, butterfly optimization algorithm (BOA) and symbiosis organism search (SOS) algorithm. BOA’s exploratory intensity is coupled with SOS’s greater exploitative capacity to find the superior algorithm h-BOASOS. The newly developed algorithm has been tested with a suite of 35 classical benchmark functions, and the results are compared with several state-of-the-art metaheuristic algorithms. The results are evaluated statistically by the Friedman rank test, and convergence curves measure the convergence speed of the algorithm. It is observed in both cases that h-BOASOS is superior to other algorithms. The suggested approach is then used to solve four real-world engineering design problems to examine the problem-solving capacity of the proposed algorithm, and the results are contrasted with a wide range of algorithms. The proposed h-BOASOS is considered to be the winner on each occasion. Finally, the newly suggested algorithm is applied to find the cost and weight of the cantilever retaining wall problems of two different heights, 3.2 m and 6.3 m. The obtained results are compared with the component algorithms and found that the new algorithm works better than the compared algorithms.

The Arithmetic Optimization Algorithm

This work proposes a new meta-heuristic method called Arithmetic Optimization Algorithm (AOA) that utilizes the distribution behavior of the main arithmetic operators in mathematics including (Multiplication (M), Division (D), Subtraction (S), and Addition (A)). AOA is mathematically modeled and implemented to perform the optimization processes in a wide range of search spaces. The performance of AOA is checked on twenty-nine benchmark functions and several real-world engineering design problems to showcase its applicability. The analysis of performance, convergence behaviors, and the computational complexity of the proposed AOA have been evaluated by different scenarios. Experimental results show that the AOA provides very promising results in solving challenging optimization problems compared with eleven other well-known optimization algorithms. Source codes of AOA are publicly available at and .

A modified equilibrium optimizer using opposition-based learning and novel update rules

Equilibrium Optimizer (EO) is a newly developed physics-based metaheuristic algorithm that is based on control volume mass balance models, and has shown competitive performance with other state-of-the-art algorithms. However, the original EO has the disadvantages of a low exploitation ability, ease of falling into local optima, and an immature balance between exploration and exploitation. To address these shortcomings, this paper proposes a modified EO (m-EO) using opposition-based learning (OBL) and novel update rules that incorporates four main modifications: the definition of the concentrations of some particles based on OBL, a new nonlinear time control strategy, novel population update rules and a chaos-based strategy. Based on these modifications, the optimization precision and convergence speed of the original EO are greatly improved. The validity of m-EO is tested on 35 classical benchmark functions, 25 of which have variants belonging to multiple difficulty categories (Dim = 30, 100, 300, 500 and 1000). In addition, m-EO is used to solve three real-world engineering design problems. The experimental results and two different statistical tests demonstrate that the proposed m-EO shows higher performance than original EO and other state-of-the-art algorithms.

Multi-Objective Crystal Structure Algorithm (MOCryStAl): Introduction and Performance Evaluation

In many optimization problems, the main goal is to improve a single performance index in which a minimum or maximum value of this index fully reflects the quality of the response obtained from a system. However, in some cases, it is impossible to rely solely on a single index, so a multi-objective optimization problem with multiple performance indicators is considered where the values of all of them should be optimized simultaneously. The mentioned process requires a multi-objective optimization algorithm that can deal with the complexity of problems with simultaneous indexes. This paper presents the multi-objective version of a recently proposed metaheuristic algorithm called Crystal Structure Algorithm (CryStAl) which was inspired by the principles underlying the formation crystal structures. For the performance evaluation of this algorithm which is called MOCryStAl, the benchmark problems of the Completions on Evolutionary Computation (CEC) on multi-objective optimization, called CEC-09, are utilized. Some real-world engineering design problems are used to evaluate the efficiency of the proposed approach. The results demonstrate that the proposed methods can provide excellent results in dealing with the considered multi-objective problems.

MOSMA: Multi-Objective Slime Mould Algorithm Based on Elitist Non-Dominated Sorting

This paper proposes a multi-objective Slime Mould Algorithm (MOSMA), a multi-objective variant of the recently-developed Slime Mould Algorithm (SMA) for handling the multi-objective optimization problems in industries. Recently, for handling optimization problems, several meta-heuristic and evolutionary optimization techniques have been suggested for the optimization community. These methods tend to suffer from low-quality solutions when evaluating multi-objective optimization (MOO) problems than addressing the objective functions of identifying Pareto optimal solutions’ accurate estimation and increasing the distribution throughout all objectives. The SMA method follows the logic gained from the oscillation behaviors of slime mould in the laboratory experiments. The SMA algorithm shows a powerful performance compared to other well-established methods, and it is designed by incorporating the optimal food path using the positive-negative feedback system. The proposed MOSMA algorithm employs the same underlying SMA mechanisms for convergence combined with an elitist non-dominated sorting approach to estimate Pareto optimal solutions. As a posteriori method, the multi-objective formulation is maintained in the MOSMA, and a crowding distance operator is utilized to ensure increasing the coverage of optimal solutions across all objectives. To verify and validate the performance of MOSMA, 41 different case studies, including unconstrained, constrained, and real-world engineering design problems are considered. The performance of the MOSMA is compared with Multiobjective Symbiotic-Organism Search (MOSOS), Multi-objective Evolutionary Algorithm Based on Decomposition (MOEA/D), and Multiobjective Water-Cycle Algorithm (MOWCA) in terms of different performance metrics, such as Generational Distance (GD), Inverted Generational Distance (IGD), Maximum Spread (MS), Spacing, and Run-time. The simulation results demonstrated the superiority of the proposed algorithm in realizing high-quality solutions to all multi-objective problems, including linear, nonlinear, continuous, and discrete Pareto optimal front. The results indicate the effectiveness of the proposed algorithm in solving complicated multi-objective problems. This research will be backed up with extra online service and guidance for the paper’s source code at https://premkumarmanoharan.wixsite.com/mysite and https://aliasgharheidari.com/SMA.html . Also, the source code of SMA is shared with the public at https://aliasgharheidari.com/SMA.html .

EMoSOA: a new evolutionary multi-objective seagull optimization algorithm for global optimization

This study introduces the evolutionary multi-objective version of seagull optimization algorithm (SOA), entitled Evolutionary Multi-objective Seagull Optimization Algorithm (EMoSOA). In this algorithm, a dynamic archive concept, grid mechanism, leader selection, and genetic operators are employed with the capability to cache the solutions from the non-dominated Pareto. The roulette-wheel method is employed to find the appropriate archived solutions. The proposed algorithm is tested and compared with state-of-the-art metaheuristic algorithms over twenty-four standard benchmark test functions. Four real-world engineering design problems are validated using proposed EMoSOA algorithm to determine its adequacy. The findings of empirical research indicate that the proposed algorithm is better than other algorithms. It also takes into account those optimal solutions from the Pareto which shows high convergence.

An intensify atom search optimization for engineering design problems

Atom search optimization is a newly developed metaheuristic algorithm inspired by molecular basis dynamics. The main changes of premature convergence and poor balance between exploration and exploitation still persist, which cannot yet do well in solving some complex optimization problems. To solve the above problems and get better performance, an improved atom search optimization with nonlinear inertia weight factor, neighbor learning component and updating mechanisms is proposed in this paper. First, to balance exploration and exploitation better, a nonlinear inertia weight factor is proposed to determine how much the previous velocity and acceleration is preserved. Second, to effectively increase the exchange of information among atoms, a neighbor learning component is integrated into the velocity updating equation, which is beneficial to enhance the exploitation ability. Thirdly, to help atoms jump out from the local optima, an updating mechanism of the best and worst atoms of the current population is proposed, and a greedy selection strategy is employed to boost the probability of finding the optimal solution. Finally, the well-known CEC2017 benchmark functions and four real-world engineering design problems were employed to demonstrate the performance of our algorithm. The experimental results and statistical analysis show that the performance of our algorithm is better than the comparison algorithms.

Stability analysis of the human behavior-based particle swarm optimization without stagnation assumption

Human behaviour-based particle swarm optimization (HPSO) is an improved particle swarm optimization (PSO) algorithm, which can effectively increase the diversity of population, convergence speed and precision by changing particles’ flight schema. In this paper, the first- and second-order stabilities of HPSO on the assumption that the personal optimum, the global optimum and the global worst particle are mutual independence during the whole evolutionary process, while the expectations and variances of particles’ positions vary with time so that our calculations do not require the stagnation assumption. The first- and second-order stabilities of HPSO are expressed by stochastic recurrence relation. The convergence boundaries of HPSO are obtained, and which show that the stabilities of HPSO are independent of the expectations and variances of the personal best and the global best. In addition, the reason for choosing the coefficient of the impelled/penalized term in HPSO is analysed, and the results of simulation experiments further confirm the theoretical analysis. Finally, HPSO is used to solve four real-world engineering design problems. Experimental results further confirm the theoretic results and illustrate that the performance of HPSO is promising and competitive.

Marine Predators Algorithm: A nature-inspired metaheuristic

This paper presents a nature-inspired metaheuristic called Marine Predators Algorithm (MPA) and its application in engineering. The main inspiration of MPA is the widespread foraging strategy namely Lévy and Brownian movements in ocean predators along with optimal encounter rate policy in biological interaction between predator and prey. MPA follows the rules that naturally govern in optimal foraging strategy and encounters rate policy between predator and prey in marine ecosystems. This paper evaluates the MPA's performance on twenty-nine test functions, test suite of CEC-BC-2017, randomly generated landscape, three engineering benchmarks, and two real-world engineering design problems in the areas of ventilation and building energy performance. MPA is compared with three classes of existing optimization methods, including (1) GA and PSO as the most well-studied metaheuristics, (2) GSA, CS and SSA as almost recently developed algorithms and (3) CMA-ES, SHADE and LSHADE-cnEpSin as high performance optimizers and winners of IEEE CEC competition. Among all methods, MPA gained the second rank and demonstrated very competitive results compared to LSHADE-cnEpSin as the best performing method and one of the winners of CEC 2017 competition. The statistical post hoc analysis revealed that MPA can be nominated as a high-performance optimizer and is a significantly superior algorithm than GA, PSO, GSA, CS, SSA and CMA-ES while its performance is statistically similar to SHADE and LSHADE-cnEpSin. The source code is publicly available at: https://github.com/afshinfaramarzi/Marine-Predators-Algorithm, http://built-envi.com/portfolio/marine-predators-algorithm/, https://www.mathworks.com/matlabcentral/fileexchange/74578-marine-predators-algorithm-mpa, and http://www.alimirjalili.com/MPA.html.

Artificial ecosystem-based optimization: a novel nature-inspired meta-heuristic algorithm

A novel nature-inspired meta-heuristic optimization algorithm, named artificial ecosystem-based optimization (AEO), is presented in this paper. AEO is a population-based optimizer motivated from the flow of energy in an ecosystem on the earth, and this algorithm mimics three unique behaviors of living organisms, including production, consumption, and decomposition. AEO is tested on thirty-one mathematical benchmark functions and eight real-world engineering design problems. The overall comparisons suggest that the optimization performance of AEO outperforms that of other state-of-the-art counterparts. Especially for real-world engineering problems, AEO is more competitive than other reported methods in terms of both convergence rate and computational efforts. The applications of AEO to the field of identification of hydrogeological parameters are also considered in this study to further evaluate its effectiveness in practice, demonstrating its potential in tackling challenging problems with difficulty and unknown search space. The codes are available at https://www.mathworks.com/matlabcentral/fileexchange/72685-artificial-ecosystem-based-optimization-aeo .

A constrained multi-swarm particle swarm optimization without velocity for constrained optimization problems

The original particle swarm optimization (PSO) is not able to tackle constrained optimization problems (COPs) due to the absence of constraint handling techniques. Furthermore, most existing PSO variants can only perform well in certain types of optimization problem and tend to suffer with premature convergence due to the limited search operator and directional information used to guide the search process. An improved PSO variant known as the constrained multi-swarm particle swarm optimization without velocity (CMPSOWV) is proposed in this paper to overcome the aforementioned drawbacks. Particularly, a constraint handling technique is first incorporated into CMPSOWV to guide population searching towards the feasible regions of search space before optimizing the objective function within the feasible regions. Two evolution phases known as the current swarm evolution and memory swarm evolution are also introduced to offer the multiple search operators for each CMPSOWV particle, aiming to improve the robustness of algorithm in solving different types of COPs. Finally, two diversity maintenance schemes of multi-swarm technique and probabilistic mutation operator are incorporated to prevent the premature convergence of CMPSOWV. The overall optimization performances of CMPSOWV in solving the CEC 2006 and CEC 2017 benchmark functions and real-world engineering design problems are compared with selected constrained optimization algorithms. Extensive simulation results report that the proposed CMPSOWV has demonstrated the best search accuracy among all compared methods in solving majority of problems.

Multi-Objective Stochastic Fractal Search: a powerful algorithm for solving complex multi-objective optimization problems

Stochastic Fractal Search (SFS) is a novel and powerful metaheuristic algorithm. This paper presents a Multi-Objective Stochastic Fractal Search (MOSFS) for the first time, to solve complex multi-objective optimization problems. The presented algorithm uses an external archive to collect efficient Pareto optimal solutions during the optimization process. Using dominance rules, leader selection and grid mechanisms, MOSFS precisely approximates the true Pareto optimal front. The MOSFS is implemented on nine multi-objective benchmark functions (CEC 2009) with multimodal, convex, discrete and non-convex optimal Pareto fronts. Performance of the proposed algorithm is compared to well-known algorithms. In addition, different performance measures are considered to evaluate the convergence and coverage abilities of the algorithms including Inverted Generational Distance, Maximum Spread and Spacing. Furthermore, statistical analyses are utilized to determine the superior algorithm. The results revealed that the MOSFS performs significantly better than other algorithms in both convergence and coverage and it is able to approximate true Pareto front precisely. In the end, MOSFS is implemented to solve a real-world engineering design problem called welded beam design problem and efficiency of the algorithm is compared to recently developed algorithms. The results of simulations and the Wilcoxon rank-sum test showed that the MOSFS is able to provide the most promising Pareto front for the problem considering various performance metrics at a 95% confidence level.

Discontinuous isogeometric boundary element (IGABEM) formulations in 3D automotive acoustics

The isogeometric boundary element method (IGABEM) is a technique that employs non-uniform rational B-splines (NURBS) as basis functions to discretise the solution variables as well as the problem geometry in a boundary element formulation. IGABEM has shown improved convergence properties over the conventional boundary element method (BEM) algorithms. However, in acoustics, IGABEM has only been applied to problems with simple smooth boundary conditions. In most real-world engineering design and analysis acoustic problems, geometric corners and discontinuities in boundary conditions can give rise to more complexity in the solution field that may be more efficiently modelled using a discontinuous approach.In the current work, we develop a discontinuous IGABEM formulation based on discontinuous elements and a suitable collocation scheme. Continuous and discontinuous formulations are compared. In this paper, a three dimensional model with different sets of boundary conditions is presented to explore the conditions under which a discontinuous formulation outperforms the continuous IGABEM. A simple car passenger compartment model characterised by panels with piecewise continuous impedance boundaries is presented to illustrate the potential of the proposed method for integrated engineering design and analysis.

Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine

There are a large number of real-world engineering design problems that are multi-objective and multiconstrained, having uncertainty in their inputs. Robust optimization is developed to obtain solutions that are optimal and less sensitive to uncertainty. Since most of complex engineering design problems rely on time-consuming simulations, the robust optimization approaches may become computationally intractable. To address this issue, an advanced multi-objective robust optimization approach based on Kriging model and support vector machine (MORO-KS) is proposed in this work. First, the main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Second, each objective function is approximated by a Kriging model to predict the response value. Third, a support vector machine (SVM) classifier is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. The proposed MORO-KS approach is tested on two numerical examples and the design optimization of a micro-aerial vehicle (MAV) fuselage. Compared with the results obtained from other MORO approaches, the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

Differential evolution with the adaptive penalty method for structural multi-objective optimization

Real-world engineering design problems, like structural optimization, can be characterized as a multi-objective optimization when two or more conflicting objectives are in the problem formulation. The differential evolution (DE) algorithm is nowadays one of the most popular meta-heuristics to solve optimization problems in continuous search spaces and has attracted much attention in multi-objective optimization due to its simple implementation and efficiency when solving real-world problems. A recent paper has shown that GDE3, a well-known DE-based algorithm, performs efficiently when solving structural multi-objective optimization problems. Also an adaptive penalty technique called APM was adopted to handle constraints. However, the authors did not investigate the contribution of this technique and that of the GDE3 algorithm separately. So, in this work, the results obtained by GDE3 equipped with the APM scheme (denoted here by GDE3 + APM) are compared with those found by the original GDE3 in order to investigate the advantages and limitations of this constraint handling technique in those problems. The results of the GDE3 + APM are also compared with the most commonly used multi-objective meta-heuristic, namely NSGA-II, in order to comparatively evaluate the quality of the solutions obtained with respect to other algorithms from the literature. The analysis indicates that GDE3 + APM is more efficient than both GDE3 and NSGA-II in most performance metrics used when solving the structural multi-objective optimization problems considered here, suggesting that the GDE3 + APM algorithm is promising in this area, and that the APM technique makes a considerable contribution to its performance.

A modified particle swarm optimization for large-scale numerical optimizations and engineering design problems

Particle swarm optimization (PSO) has attracted the attention of many researchers because of its simple concept and easy implementation. However, it suffers from premature convergence due to quick loss of population diversity. Meanwhile, real-world engineering design problems are generally nonlinear or large-scale or constrained optimization problems. To enhance the performance of PSO for solving large-scale numerical optimizations and engineering design problems, an adaptive disruption strategy which originates from the disruption phenomenon of astrophysics, is proposed to shift the abilities between global exploration and local exploitation. Meanwhile, a Cauchy mutation is utilized to a certain dimension of the best particle to help particle jump out the local optima. Nine well-known large-scale unconstrained problems, ten complicated shifted and/or rotated functions and four famous constrained engineering problems are utilized to validate the performance of the proposed algorithm compared against those of state-of-the-art algorithms. Experimental results and statistic analysis confirm effectiveness and promising performance of the proposed algorithm.