Engineering Design Optimization Problems Research Articles

Al-Biruni Earth Radius (BER) Metaheuristic Search Optimization Algorithm

Metaheuristic optimization algorithms present an effective method for solving several optimization problems from various types of applications and fields. Several metaheuristics and evolutionary optimization algorithms have been emerged recently in the literature and gained widespread attention, such as particle swarm optimization (PSO), whale optimization algorithm (WOA), grey wolf optimization algorithm (GWO), genetic algorithm (GA), and gravitational search algorithm (GSA). According to the literature, no one metaheuristic optimization algorithm can handle all present optimization problems. Hence novel optimization methodologies are still needed. The Al-Biruni earth radius (BER) search optimization algorithm is proposed in this paper. The proposed algorithm was motivated by the behavior of swarm members in achieving their global goals. The search space around local solutions to be explored is determined by Al-Biruni earth radius calculation method. A comparative analysis with existing state-of-the-art optimization algorithms corroborated the findings of BER’s validation and testing against seven mathematical optimization problems. The results show that BER can both explore and avoid local optima. BER has also been tested on an engineering design optimization problem. The results reveal that, in terms of performance and capability, BER outperforms the performance of state-of-the-art metaheuristic optimization algorithms.

A Novel Meta-Heuristic Algorithm for Numerical and Engineering Optimization Problems: Piranha Foraging Optimization Algorithm (PFOA)

This paper provides a novel meta-heuristic optimization algorithm for solving continuous optimization problems efficiently in the field of numerical and engineering optimization: Piranha Foraging Optimization Algorithm (PFOA). The algorithm is inspired by the flexible and mobile foraging behaviour of piranha swarm and divides their foraging behavior into three patterns: localized group attack, bloodthirsty cluster attack and scavenging foraging, simulates the above behaviors to construct two dynamic search processes for exploration and exploitation. PFOA uses three strategies of non-linear parameter control, population survival and reverse evasion search to enable populations to have better population diversity at different stages of the search and to help find better solutions. To gain insight into the performance of PFOA, visualization methods were used to assess the efficiency of PFOA optimization and to analyse the impact of the characteristics of the three foraging modes, the sensitivity of the parameters and the size of the piranha population on the algorithm. The algorithm performance was further tested with 27 CEC benchmark functions and four real engineering design optimization problems, and the results were compared with 13 well-known meta-heuristics. Test results based on statistical methods such as box-line plots, Wilcoxon rank sum test and Friedman test in multiple dimensions (30, 50, 100 and fixed dimensions) show significant differences compared to other algorithms and that the performance of the algorithm is stable and in significant improvement. The unique advantages of PFOA in terms of the equilibrium of convergence speed and exploration can avoid getting trapped in local optimum regions and effectively solve optimization problems in complex search spaces.

Updated Particle Swarm Optimization for Mechanical Engineering Design Optimization

In the optimization area, particle swarm optimization is an excellent optimization algorithm. It influenced thru position and velocity update of the particles. Particles velocity update significantly depend on its factor inertia weight (with previous velocity) and acceleration coefficients (with cognitive and social components). Also, PSO has various advantages like simplicity and fast convergence. However, PSO easily trapped into local optima due to simple search procedure. To improve the presentation of PSO, this article advises an updated-PSO (U-PSO) for solving mechanical engineering design optimization problems. In U-PSO, novel parameters (inertia weight, acceleration coefficients and lively coefficient) for velocity update and position update equation are employed to retain exploitation and exploration. To verify the efficiency and robustness, proposed U-PSO applied to solve two complex mechanical engineering designs optimization problems. The experimental outcomes validate that the suggested U-PSO has significant advantages over the compared algorithms.

LX-BBSCA: Laplacian biogeography-based sine cosine algorithm for structural engineering design optimization

<abstract> <p>In this paper, an ensemble metaheuristic algorithm (denoted as LX-BBSCA) is introduced. It combines the strengths of Laplacian biogeography-based optimization (LX-BBO) and the sine cosine algorithm (SCA) to address structural engineering design optimization problems. Our primary objective is to mitigate the risk of getting stuck in local minima and accelerate the algorithm's convergence rate. We evaluate the proposed LX-BBSCA algorithm on a set of 23 benchmark functions, including both unimodal and multimodal problems of varying complexity and dimensions. Additionally, we apply LX-BBSCA to tackle five real-world structural engineering design problems, comparing the results with those obtained using other metaheuristics in terms of objective function values and convergence behavior. To ensure the statistical validity of our findings, we employ rigorous tests such as the t-test and the Wilcoxon rank test. The experimental outcomes consistently demonstrate that the ensemble LX-BBSCA algorithm outperforms not only the basic versions of BBO, SCA and LX-BBO but also other state-of-the-art metaheuristic algorithms.</p> </abstract>

Dynamic Interconnection Approach With BLX-Based Search Applied to Multi-Swarm Optimizer: An Empirical Analysis to Real Constrained Optimization

The Multi-Swarm approach allows the use of multiple configurations between two or more populations of particles, where each one can present different approaches (e.g. lbest, gbest, Unified, Guaranteed-Convergence) directed towards improving the optimization process. This article presents a proposal for local/global stochastic interconnection applied to the context of the Multi-Swarm algorithm, as well as for incrementing a local search method for refining previously obtained solutions. Two proposals are introduced for this new Multi-Swarm PSO (MSO). The first one is the inclusion of “counterpart particles”, which establishes a sub-topology between inter-swarm particles, accessed by migration and evaluability rules. The other involves using customized crossover operators and is based on the BLX scheme (Blend Crossover) with direction information used as a reference for establish a subspace search around the particles. Performance and robustness of the new approaches were assessed by ten constrained engineering design optimization problems (COPs), as is compared to other solutions already published in the scientific literature. Results indicate significant performance improvements for all 10 COPs when compared to concurrent-based MSOs. By making available new references from other swarms, the counterpart particles approach tends to improve the optimization process in the search space, while an intermediate layer of local search based on a modified directed BLX crossover should provide an extra search around the particle, and thus, refining previously obtained solutions.

Tournament constriction coefficient based particle swarm optimization (TPSO-Co) for engineering design optimization problems

Tournament constriction coefficient based particle swarm optimization (TPSO-Co) for engineering design optimization problems

Hybrid Sine Cosine Algorithm for Solving Engineering Optimization Problems

Engineering design optimization problems are difficult to solve because the objective function is often complex, with a mix of continuous and discrete design variables and various design constraints. Our research presents a novel hybrid algorithm that integrates the benefits of the sine cosine algorithm (SCA) and artificial bee colony (ABC) to address engineering design optimization problems. The SCA is a recently developed metaheuristic algorithm with many advantages, such as good search ability and reasonable execution time, but it may suffer from premature convergence. The enhanced SCA search equation is proposed to avoid this drawback and reach a preferable balance between exploitation and exploration abilities. In the proposed hybrid method, named HSCA, the SCA with improved search strategy and the ABC algorithm with two distinct search equations are run alternately during working on the same population. The ABC with multiple search equations can provide proper diversity in the population so that both algorithms complement each other to create beneficial cooperation from their merger. Certain feasibility rules are incorporated in the HSCA to steer the search towards feasible areas of the search space. The HSCA is applied to fifteen demanding engineering design problems to investigate its performance. The presented experimental results indicate that the developed method performs better than the basic SCA and ABC. The HSCA accomplishes pretty competitive results compared to other recent state-of-the-art methods.

A new flower pollination algorithm with improved convergence and its application to engineering optimization

The flower pollination algorithm (FPA) is a nature-inspired optimization algorithm that mimics the pollination behaviour of flowering plants. Despite the promising performance of FPA in solving single objective optimization problems, its convergence still poses challenges in practice. This study proposes a modified FPA with additional features from chaos theory and frog leaping algorithm augmented by inertia weights. The modified FPA proposed in this study is tested against benchmark mathematical functions, mechanical engineering design optimization problems, and machining process optimization problems. Performance comparison with other state-of-the-art optimization algorithms has demonstrated its ability in terms of convergence. The modified FPA significantly reduced the number of function evaluations by 84.14%, as compared to FPA in optimizing the benchmark mathematical functions. Besides, the proposed modified FPA outperformed others in 12 out of 15 mechanical engineering optimization problems.

HWMWOA: A Hybrid WMA–WOA Algorithm with Adaptive Cauchy Mutation for Global Optimization and Data Classification

Combinatorial metaheuristic optimization algorithms have newly become a remarkable domain for handling real-world and engineering design optimization problems. In this paper, the Whale Optimization Algorithm (WOA) and the Woodpecker Mating Algorithm (WMA) are combined as HWMWOA. WOA is an effective algorithm with the advantage of global searching ability, where the control parameters are very less. But WOA is more probable to get trapped in the local optimum points and miss diversity of population, therefore suffering from premature convergence. The fundamental goal of the HWMWOA algorithm is to overcome the drawbacks of WOA. This betterment includes three basic mechanisms. First, a modified position update equation of WMA by efficient exploration ability is embedded into HWMWOA. Second, a new self-regulation Cauchy mutation operator is allocated to the proposed hybrid method. Finally, an arithmetic spiral movement with a novel search guide pattern is used in the suggested HWMWOA algorithm. The efficiency of the suggested algorithm is appraised over 48 test functions, and the optimal outcomes are compared with 15 most popular and newest metaheuristic optimization algorithms. Moreover, the HWMWOA algorithm is applied for simultaneously optimizing the parameters of SVM (Support Vector Machine) and feature weighting to handle the data classification problem on several real-world datasets from the UCI database. The outcomes prove the superiority of the suggested hybrid algorithm compared to both WOA and WMA. In addition, the results represent that the HWMWOA algorithm outperforms other efficient techniques impressively.

Reptile search algorithm and kriging surrogate model for structural design optimization with natural frequency constraints

Abstract This study explores the use of a recent metaheuristic algorithm called a reptile search algorithm (RSA) to handle engineering design optimization problems. It is the first application of the RSA to engineering design problems in literature. The RSA optimizer is first applied to the design of a bolted rim, which is constrained optimization. The developed algorithm is then used to solve the optimization problem of a vehicle suspension arm, which aims to solve the weight reduction under natural frequency constraints. As function evaluations are achieved by finite element analysis, the Kriging surrogate model is integrated into the RSA algorithm. It is revealed that the optimum result gives a 13% weight reduction compared to the original structure. This study shows that RSA is an efficient metaheuristic as other metaheuristics such as the mayfly optimization algorithm, battle royale optimization algorithm, multi-level cross-entropy optimizer, and red fox optimization algorithm.

Methods for constrained optimization of expensive mixed-integer multi-objective problems, with application to an internal combustion engine design problem

Engineering design optimization problems increasingly require computationally expensive high-fidelity simulation models to evaluate candidate designs. The evaluation budget may be small, limiting the effectiveness of conventional multi-objective evolutionary algorithms. Bayesian optimization algorithms (BOAs) are an alternative approach for expensive problems but are underdeveloped in terms of support for constraints and non-continuous design variables—both of which are prevalent features of real-world design problems. This study investigates two constraint handling strategies for BOAs and introduces the first BOA for mixed-integer problems, intended for use on a real-world engine design problem. The new BOAs are empirically compared to their closest competitor for this problem—the multi-objective evolutionary algorithm NSGA-II, itself equipped with constraint handling and mixed-integer components. Performance is also analysed on two benchmark problems which have similar features to the engine design problem, but are computationally cheaper to evaluate. The BOAs offer statistically significant convergence improvements of between 5.9% and 31.9% over NSGA-II across the problems on a budget of 500 design evaluations. Of the two constraint handling methods, constrained expected improvement offers better convergence than the penalty function approach. For the engine problem, the BOAs identify improved feasible designs offering 36.4% reductions in nitrogen oxide emissions and 2.0% reductions in fuel consumption when compared to a notional baseline design. The use of constrained mixed-integer BOAs is recommended for expensive engineering design optimization problems.

An Improved Blind Kriging Surrogate Model for Design Optimization Problems

Surrogate modeling techniques are widely employed in solving constrained expensive black-box optimization problems. Therein, Kriging is among the most popular surrogates in which the trend function is considered as a constant mean. However, it also encounters several challenges related to capturing the overall trend with a relatively limited number of function evaluations as well as searching feasible points with complex or discontinuous feasible regions. To address this above issue, this paper presents an improved surrogate blind Kriging (IBK) and a combined infill strategy to find the optimal solution. According to enhancing the prediction accuracy of metamodels of objective and constraints, the high-order effects of regression function in the blind Kriging are identified by promising a variable selection technique. In addition, an infill strategy is developed based on the probability of feasibility, penalization, and constrained expected improvement for updating blind Kriging metamodels of the objective and constraints. At each iteration, two infill sample points are allocated at the positions to achieve improvement in optimality and feasibility. The IBK metamodels are updated by the newly-added infill sample points, which leads the proposed framework search to rapidly converge to the optimal solution. The performance and applicability of the proposed model are tested on several numerical benchmark problems via comparing with other metamodel-based constrained optimization methods. The obtained results indicate that IBK generally has a greater efficiency performance and outperforms the competitors in terms of a limited number of function evaluations. Finally, IBK is successfully applied to structural design optimization. The optimization results show that IBK is able to find the best feasible design with fewer evaluation functions compared with other studies, and this demonstrates the effectiveness and practicality of the proposed model for solving the constrained expensive black-box engineering design optimization problems.

Golden-Sine dynamic marine predator algorithm for addressing engineering design optimization

In engineering design optimization problems, the optimal solution can improve the design quality of complex engineering system and reduce a lot of cost consumption, so it is of great practical significance to study the optimization algorithm of engineering design problems. Evolutionary computation is widely used to solve engineering design optimization problems, which are mostly mixed-integer nonlinear programming (MINLP) problems. As a newly developed evolutionary computing method, Marine Predator Algorithm (MPA) currently suffers from weak convergence and easily falls into local optimum. In order to overcome the disadvantage, this study proposed a Golden-Sine Dynamic Marine Predator Algorithm (GDMPA). Firstly, Logistic-Logistic (L-L) cascade chaos was used to adjust the initial position of the population to generate a high-quality initial prey population while ensuring ergodicity and randomness. Secondly, the dynamic adjustment transition probability strategy was added to improve the discriminant conditions when predators entered different stages, which effectively maintained the balance between global exploration and local exploitation. The adaptive inertial weight based on Sigmoid function was used in updating the step information of predators to avoid the problem of falling into local extrema. Finally, the Golden-Sine factor is employed to achieve a better balance between exploration and exploitation, further improve the premature convergence problem, enhance the population diversity, and improve the convergence rate. A series of validation studies were conducted over twelve standard test functions and the CEC2017 test set to verify the effectiveness and robustness of the improved GDMPA strategy. Mechanical optimization and size optimization study for truss structures was carried out using the proposed GDMPA, which yielded excellent results. The results of the 27-bar truss structure show that the proposed GDMPA reduces 3.24%, 27.18%, 39.38%, 27.65% and 9.67% compared to the total mass of MPA, BOA, SSA, SOA and HHO, respectively. In the other cases, the optimization results of GDMPA have been improved substantially compared with other algorithms. Therefore, GDMPA has a broad application prospect in structural design and optimization.

LSMA-TLBO: A hybrid SMA-TLBO algorithm with lévy flight based mutation for numerical optimization and engineering design problems

The objective of this paper is to present a novel hybrid algorithm LSMA-TLBO for solving the numerical and engineering design optimization problems. The proposed algorithm utilizes the features of Slime Mould Algorithm (SMA) and the Teaching–Learning Based Optimization (TLBO) to balance the exploitation and exploration ability. In addition, a lévy flight based mutation is introduced in this study to maximize the exploration ability of the algorithm. SMA is one of the meta-heuristic algorithms (MHAs) which mimics the oscillation mechanism of slime mould in nature. It is an efficient technique that has been successfully applied to the complex optimization problems (OPs) due to its global exploration ability. However, despite its popularity, the SMA also suffers from some shortcomings, such as local optima stagnation, slow convergence rate and improper balance between exploitation and exploration. In view of this weaknesses, the hybrid algorithm LSMA-TLBO is proposed considering the good global search ability of SMA, fast convergence of TLBO and the features of the lévy flight based mutation to maximize the exploration ability. The performance of the proposed LSMA-TLBO is evaluated on 23 different benchmark functions including uni-modal and multi-modal problems. In addition, IEEE CEC-C06 2019 test suite and six engineering design problems are also considered to examine the practicable abilities of the proposed method. The results are compared with several recently proposed state-of-the-art algorithms and the simulation results show that the proposed method outperforms other algorithms. Further, the LSMA-TLBO is executed through statistical testing of hypothesis namely Wilcoxon’s rank-sum test. It is concluded that the proposed LSMA-TLBO is more competitive and effective algorithm to solve real-world complex OPs.

A Novel Chimp Optimization Algorithm with Refraction Learning and Its Engineering Applications

The Chimp Optimization Algorithm (ChOA) is a heuristic algorithm proposed in recent years. It models the cooperative hunting behaviour of chimpanzee populations in nature and can be used to solve numerical as well as practical engineering optimization problems. ChOA has the problems of slow convergence speed and easily falling into local optimum. In order to solve these problems, this paper proposes a novel chimp optimization algorithm with refraction learning (RL-ChOA). In RL-ChOA, the Tent chaotic map is used to initialize the population, which improves the population’s diversity and accelerates the algorithm’s convergence speed. Further, a refraction learning strategy based on the physical principle of light refraction is introduced in ChOA, which is essentially an Opposition-Based Learning, helping the population to jump out of the local optimum. Using 23 widely used benchmark test functions and two engineering design optimization problems proved that RL-ChOA has good optimization performance, fast convergence speed, and satisfactory engineering application optimization performance.

Ensembles strategies for backtracking search algorithm with application to engineering design optimization problems

This paper proposes two ensemble strategies for the backtracking search algorithm (BSA). The first one is an ensemble of two sets of evolutionary operators that balances exploration and exploitation abilities. The second one is an ensemble of values for each parameter associated with the evolutionary operators. The second strategy provides diverse search moves with various search step lengths that are essential for searching different search landscapes. In addition to the ensemble strategies, another strategy is used to reinitialize specific individuals of the population to escape from local optima. Sixteen variants of the BSA are built based on different combinations of these strategies or their modified versions. The best variant for solving 29 problems of CEC2017 test suite is statistically compared with nineteen state-of-the-art algorithms. The results confirm its superiority to all the considered algorithms. Remarkably, according to the Wilcoxon rank-sum test with a significance level of 0.05, it is better than others for solving at least 20 and 18 functions with 30 and 50 dimensions, respectively. Furthermore, it is applied to five engineering design optimization problems. Its solutions are at least as well as or better than those obtained by the best existing algorithms in the literature for three problems.

LWMEO: An efficient equilibrium optimizer for complex functions and engineering design problems

Optimization algorithm is an important method to solve complex extremum function and engineering design constraint problems, and the improvement of algorithm optimization performance is inseparable from efficient strategies and mechanisms. Equilibrium optimizer (EO) is a novel intelligent optimization algorithm with simple mechanism and easy implementation. It has a good solution effect on some optimization problems. However, when solving complex multimodal problems and engineering design problems, EO has some disadvantages, such as easy to fall into local optimal, low searching accuracy and slow convergence speed. In order to solve complex function extremum and engineering design optimization problems more effectively, improve the optimization performance and application ability of the equilibrium optimizer, and further expand the application field and space of the algorithm, an adaptive equilibrium optimizer (LWMEO) with three efficient optimization strategies is proposed. Based on the basic update strategy of the equilibrium optimizer, the random walk strategy of preferred area based on Lévy flight is introduced to expand the algorithm’s search range and enhances its exploration capability; by adding the whale optimization algorithm’s spiral encirclement mechanism enables the individuals in the population to perform a spiral search near the best solution and improves the algorithm’s exploitation capability; the introduction of the adaptive proportional mutation strategy strengthens the algorithm’s ability to jump out of the local optimal solutions, while accelerating its convergence speed. Time complexity analysis proves that the LWMEO algorithm has the same time complexity as the equilibrium optimizer. Using the Markov chain process, it is theoretically proven that the LWMEO has convergence and can converge to the global optimum. LWMEO and 6 representative comparison algorithms with superior performance are used to solve CEC2014 test function suite and several classical multimodal test functions with different optimization characteristics. Each algorithm is run independently for 50 times in the same environment, and the best value, average value and standard deviation obtained by LWMEO were generally superior to the other six comparison algorithms. The convergence curve drops faster and the line body is smoother. These experimental data and convergence curves show that the LWMEO’s optimization ability, convergence speed and solution stability are obviously superior to the comparison algorithm. Meanwhile, the p-value of Wilcoxon’s rank-sum test are less than 0.05, indicating that LWMEO has significant differences over comparison algorithm. Finally, the LWMEO is applied to 8 different engineering design optimization problems, and the best value, average value and standard deviation obtained from 50 optimization designs are also significantly better than other comparison algorithms, which verifies the applicability, stability and efficiency of LWMEO in solving engineering design constrained optimization problems.

Engineering Design Optimization Using an Advanced Hybrid Algorithm

An advanced hybrid algorithm (haDEPSO) proposed in this paper for engineering design optimization problems. It integrated with suggested advanced differential evolution (aDE) and particle swarm optimization (aPSO). In aDE introduced a novel mutation, crossover and selection strategy, to avoiding premature convergence. And aPSO consists of novel gradually varying parameters, to escape stagnation. So, convergence characteristic of aDE and aPSO provides different approximation to the solution space. Thus, haDEPSO achieve better solutions due to integrating merits of aDE and aPSO. Also, in haDEPSO individual population is merged with other in a pre-defined manner, to balance between global and local search capability. Proposed hybrid haDEPSO as well as its integrating component aDE and aPSO has been applied to five engineering design optimization problems. Numerical, statistical and graphical experiments (best, worst, mean and standard deviation plus convergence analysis) confirm the superiority of the proposed algorithms over many state-of-the-art algorithms.

Engineering Design Optimization Using an Advanced Hybrid Algorithm

An advanced hybrid algorithm (haDEPSO) proposed in this paper for engineering design optimization problems. It integrated with suggested advanced differential evolution (aDE) and particle swarm optimization (aPSO). In aDE introduced a novel mutation, crossover and selection strategy, to avoiding premature convergence. And aPSO consists of novel gradually varying parameters, to escape stagnation. So, convergence characteristic of aDE and aPSO provides different approximation to the solution space. Thus, haDEPSO achieve better solutions due to integrating merits of aDE and aPSO. Also, in haDEPSO individual population is merged with other in a pre-defined manner, to balance between global and local search capability. Proposed hybrid haDEPSO as well as its integrating component aDE and aPSO has been applied to five engineering design optimization problems. Numerical, statistical and graphical experiments (best, worst, mean and standard deviation plus convergence analysis) confirm the superiority of the proposed algorithms over many state-of-the-art algorithms.

An improved remora optimization algorithm with autonomous foraging mechanism for global optimization problems.

The remora optimization algorithm (ROA) is a newly proposed metaheuristic algorithm for solving global optimization problems. In ROA, each search agent searches new space according to the position of host, which makes the algorithm suffer from the drawbacks of slow convergence rate, poor solution accuracy, and local optima for some optimization problems. To tackle these problems, this study proposes an improved ROA (IROA) by introducing a new mechanism named autonomous foraging mechanism (AFM), which is inspired from the fact that remora can also find food on its own. In AFM, each remora has a small chance to search food randomly or according to the current food position. Thus the AFM can effectively expand the search space and improve the accuracy of the solution. To substantiate the efficacy of the proposed IROA, twenty-three classical benchmark functions and ten latest CEC 2021 test functions with various types and dimensions were employed to test the performance of IROA. Compared with seven metaheuristic and six modified algorithms, the results of test functions show that the IROA has superior performance in solving these optimization problems. Moreover, the results of five representative engineering design optimization problems also reveal that the IROA has the capability to obtain the optimal results for real-world optimization problems. To sum up, these test results confirm the effectiveness of the proposed mechanism.