Engineering Design Problems Research Articles

Improved bald eagle search algorithm for global optimization and feature selection

The use of metaheuristics is one of the most encouraging methodologies for taking care of real-life problems. Bald eagle search (BES) algorithm is the latest swarm-intelligence metaheuristic algorithm inspired by the intelligent hunting behavior of bald eagles. In recent research works, BES algorithm has performed reasonably well over a wide range of application areas such as chemical engineering, environmental science, physics and astronomy, structural modeling, global optimization, engineering design, energy efficiency, etc. However, it still lacks adequate searching efficiency and has a tendency to stuck in local optima which affects the final outcome. This paper introduces a modified BES (mBES) algorithm that removes the shortcomings of the original BES algorithm by incorporating three improvements; Opposition-based learning (OBL), Chaotic Local Search (CLS), and Transition & Pharsor operators. OBL is embedded in different phases of the standard BES viz. initial population, selecting, searching in space, and swooping phases to update the positions of individual solutions to strengthen exploration, CLS is used to enhance the position of the best agent which will lead to enhancing the positions of all individuals, and Transition & Pharsor operators help to provide sufficient exploration–exploitation trade-off. The efficiency of the mBES algorithm is initially evaluated with 29 CEC2017 and 10 CEC2020 global optimization benchmark functions. In addition, the practicality of the mBES is tested with a real-world feature selection problem and five engineering design problems. Results of the mBES algorithm are compared against a number of classical metaheuristic algorithms using statistical metrics, convergence analysis, box plots, and the Wilcoxon rank sum test. In the case of composite CEC2017 test functions F21-F30, mBES wins against compared algorithms in 70% test cases, whereas for the rest of the test functions, it generates good results in 65% cases. The proposed mBES produces best performance in 55% of the CEC2020 test functions, whereas for the rest of the 45% test cases, it generated competitive results. On the other hand, for five engineering design problems, the mBES is the best among all compared algorithms. In the case of the feature selection problem, the mBES also showed competitiveness with the compared algorithms. Results and observations for all tested optimization problems show the superiority and robustness of the proposed mBES over the baseline metaheuristics. It can be safely concluded that the improvements suggested in the mBES are proved to be effective making it competitive enough to solve a variety of optimization problems.

Marine predator algorithm with elite strategies for engineering design problems

SummaryMarine predator algorithm (MPA) is a powerful metaheuristic optimization algorithm that shows effective convergence ability on complex benchmark functions. The combination of Brownian and Levy flight distributions directly affects the convergence strategy of MPA. Although MPA has good convergence performance, it is open to improvement as it falls to a local optimum and cannot comprehensively scan the search area during the exploration phase. In this study, MPA has been improved by integrating elite natural evolution and elite random mutation strategies. In addition, these two strategies are combined with Gaussian mutation. The proposed method in this study which is named as elite evolution strategy MPA (EEMPA) has achieved comprehensive scanning of the solution space and considerably reduced the risk of falling into the local optimum trap, with elite strategies. The effect of EEMPA has been tested with the CEC2017 and CEC2019 benchmark functions. EEMPA has been compared with some metaheuristic algorithms frequently used in the literature and gives promising results among the considered optimization methods. Furthermore, EEMPA has been examined for seven well‐known real world engineering problems. When the results are compared with both classical MPA and enhanced MPA methods, EEMPA converges to better than the other methods.

A Computational Approach to Identifying Engineering Design Problems

Abstract Identifying new problems and providing solutions are necessary tasks for design engineers at early-stage product design and development. A new problem fosters innovative and inventive solutions. Hence, it is expected that engineering design pedagogy and practice should equally focus on engineering design problem-exploring (EDPE)—a process of identifying or coming up with a new problem or need at the early-stage of design, and engineering design problem-solving (EDPS)—a process of developing engineering design solutions to a given problem. However, studies suggest that EDPE is scarcely practiced or given attention to in academia and industry, unlike EDPS. The aim of this paper is to investigate the EDPE process for any information relating to its scarce practice in academia and industry. This is to explore how emerging technologies could support the process. Natural models and phenomena that explain the EDPE process are investigated, including the “rational” and “garbage can” models, and associated challenges identified. A computational framework that mimics the natural EDPE process is presented. The framework is based on Markovian model and computational technologies, including machine learning. A case study is conducted with a sample size of 43 participants drawn worldwide from the engineering design community in academia and industry. The case study result shows that the first-of-its-kind computational EDPE framework presented in this paper supports both novice and experienced design engineers in EDPE.

OPTIMAL DESIGN OF 16 BAR TRUSS STRUCTURE BY PATTERN SEARCH METHODS

The focus of this research was to formulate optimization model of 16-bar trussesalong with stress, stability and deflection constraints. The derivative free methods were used for theoptimization of engineering design problems. These methods were basically designed forunconstrained optimization problems. In formulated optimization truss problems the constraints werehandled by using exterior penalty functions. The results of the truss optimization model were obtainedby using MATLAB which demonstrated the effectiveness and applicability of these derivative freemethods. It was concluded that the results of Nelder-Mead method were not acceptable due to their faraway convergence even its number of function evaluations were smaller than number of functionevaluations of Multi-Directional Search method and Hooke and Jeeves method. By comparing theoptimal function values obtained by these three methods, the performance of Hooke-Jeeves methodwas better than the other two methods.

MMKE: Multi-trial vector-based monkey king evolution algorithm and its applications for engineering optimization problems.

Monkey king evolution (MKE) is a population-based differential evolutionary algorithm in which the single evolution strategy and the control parameter affect the convergence and the balance between exploration and exploitation. Since evolution strategies have a considerable impact on the performance of algorithms, collaborating multiple strategies can significantly enhance the abilities of algorithms. This is our motivation to propose a multi-trial vector-based monkey king evolution algorithm named MMKE. It introduces novel best-history trial vector producer (BTVP) and random trial vector producer (RTVP) that can effectively collaborate with canonical MKE (MKE-TVP) using a multi-trial vector approach to tackle various real-world optimization problems with diverse challenges. It is expected that the proposed MMKE can improve the global search capability, strike a balance between exploration and exploitation, and prevent the original MKE algorithm from converging prematurely during the optimization process. The performance of the MMKE was assessed using CEC 2018 test functions, and the results were compared with eight metaheuristic algorithms. As a result of the experiments, it is demonstrated that the MMKE algorithm is capable of producing competitive and superior results in terms of accuracy and convergence rate in comparison to comparative algorithms. Additionally, the Friedman test was used to examine the gained experimental results statistically, proving that MMKE is significantly superior to comparative algorithms. Furthermore, four real-world engineering design problems and the optimal power flow (OPF) problem for the IEEE 30-bus system are optimized to demonstrate MMKE's real applicability. The results showed that MMKE can effectively handle the difficulties associated with engineering problems and is able to solve single and multi-objective OPF problems with better solutions than comparative algorithms.

Nutcracker optimizer: A novel nature-inspired metaheuristic algorithm for global optimization and engineering design problems

This work presents a novel nature-inspired metaheuristic called Nutcracker Optimization Algorithm (NOA) inspired by Clark’s nutcrackers. The nutcrackers exhibit two distinct behaviors that occur at separate periods. The first behavior, which occurs during the summer and fall seasons, represents the nutcracker’s search for seeds and subsequent storage in an appropriate cache. During the winter and spring seasons, another behavior based on the spatial memory strategy is regarded to search for the hidden caches marked at different angles using various objects or markers as reference points. If the nutcrackers cannot find the stored seeds, they will randomly explore the search space to find their food. NOA is herein proposed to mimic these various behaviors to present a new, robust metaheuristic algorithm with different local and global search operators, allowing it to solve various optimization problems with better outcomes. NOA is evaluated on twenty-three standard test functions, test suites of CEC-2014, CEC-2017, and CEC-2020 and five real-world engineering design problems. NOA is compared with three classes of existing optimization algorithms: (1) SMA, GBO, EO, RUN, AVOA, RFO, and GTO as recently-published algorithms, (2) SSA, WOA, and GWO as highly-cited algorithms, and (3) AL-SHADE, L-SHADE, LSHADE-cnEpSin, and LSHADE-SPACMA as highly-performing optimizers and winners of CEC competition. NOA was ranked first among all methods and demonstrated superior results when compared to LSHADE-cnEpSin and LSHADE-SPACMA as the best-performing optimizers and the winners of CEC-2017, and AL-SHADE and L-SHADE as the winners of CEC-2014.

ПРИМЕНЕНИЕ КОМПЬЮТЕРНОГО ГЕОМЕТРИЧЕСКОГО МОДЕЛИРОВАНИЯ ДЛЯ РЕШЕНИЯ УЧЕБНЫХ И ПРИКЛАДНЫХ ИНЖЕНЕРНО-СТРОИТЕЛЬНЫХ ЗАДАЧ

This work develops an algorithm for solving computational and graphical work from a cycle of constructive problems of engineering and construction design (construction graphics) using CAD, based on the transition from the traditional method of solving this problem (building a 2D drawing manually) to the method of computer geometric modeling. The application of geometric 3D modeling as a useful CAD tool for solving educational and applied problems is considered. The algorithmization of the solution from the cycle of graphic works on the training course “engineering and computer graphics”, which is the basis for solving problems of engineering and construction design, is shown. A comparison is made between the classical method of solving an engineering problem and using CAD. The use of computer graphic modeling methods using CAD systems facilitates solving the problem, calculating the necessary data, visualizing the results, and contributing to the mastery of universal and professional competencies for students. Their use is expedient in solving applied problems on the training course “engineering and computer graphics” for students of engineering and construction.

A hierarchical chain-based Archimedes optimization algorithm.

The Archimedes optimization algorithm (AOA) has attracted much attention for its few parameters and competitive optimization effects. However, all agents in the canonical AOA are treated in the same way, resulting in slow convergence and local optima. To solve these problems, an improved hierarchical chain-based AOA (HCAOA) is proposed in this paper. The idea of HCAOA is to deal with individuals at different levels in different ways. The optimal individual is processed by an orthogonal learning mechanism based on refraction opposition to fully learn the information on all dimensions, effectively avoiding local optima. Superior individuals are handled by an Archimedes spiral mechanism based on Levy flight, avoiding clueless random mining and improving optimization speed. For general individuals, the conventional AOA is applied to maximize its inherent exploration and exploitation abilities. Moreover, a multi-strategy boundary processing mechanism is introduced to improve population diversity. Experimental outcomes on CEC 2017 test suite show that HCAOA outperforms AOA and other advanced competitors. The competitive optimization results achieved by HCAOA on four engineering design problems also demonstrate its ability to solve practical problems.

A Padé approximation and intelligent population shrinkage chicken swarm optimization algorithm for solving global optimization and engineering problems.

Bio-inspired optimization algorithms are competitive solutions for engineering design problems. Chicken swarm optimization (CSO) combines the advantages of differential evolution and particle swarm optimization, drawing inspiration from the foraging behavior of chickens. However, the CSO algorithm may perform poorly in the face of complex optimization problems because it has a high risk of falling into a local optimum. To address these challenges, a new CSO called chicken swarm optimization combining Pad$ \acute{e} $ approximate, random learning and population reduction techniques (PRPCSO) was proposed in this work. First, a Pad$ \acute{e} $ approximate strategy was combined to help agents converge to the approximate real solution area quickly. Pad$ \acute{e} $ approximate was grounded in a rational function aligning with the power series expansion of the approximated function within a defined number of terms. The fitting function used in this strategy employs the above rational function and the extreme points are calculated mathematically, which can significantly improve the accuracy of the solution. Second, the random learning mechanism encouraged agents to learn from other good agents, resulting in better local exploitation capability compared to traditional CSO. This mechanism has a special idea that when it comes to selecting random individuals, it selects from the same type of high-performing agents, rather than selecting them completely at random. Third, a new intelligent population size shrinking strategy was designed to dynamically adjust the population size to prevent premature convergence. It considers fitness function calls and variations in recent optimal solutions creatively. To validate the algorithm's efficacy, PRPCSO was rigorously tested across 23 standard test functions and six kinds of practical engineering problems. We then compared PRPCSO with several mainstream algorithms, and the results unequivocally established PRPCSO's superior performance in most instances, highlighting its substantial practical utility in real engineering applications.

Solving constrained engineering design problems with multi-objective artificial algae algorithm

Solving constrained engineering design problems with multi-objective artificial algae algorithm

Solving constrained engineering design problems with multi-objective artificial algae algorithm

Solving constrained engineering design problems with multi-objective artificial algae algorithm

Discussion of “Differences between Professionals and Students in Their Visual Attention on Multiple Representation Types While Solving an Open-Ended Engineering Design Problem” by Ananna Ahmed, David Hurwitz, Sean Gestson, and Shane Brown

Discussion of “Differences between Professionals and Students in Their Visual Attention on Multiple Representation Types While Solving an Open-Ended Engineering Design Problem” by Ananna Ahmed, David Hurwitz, Sean Gestson, and Shane Brown

Language Education Optimization: A New Human-Based Metaheuristic Algorithm for Solving Optimization Problems

In this paper, based on the concept of the NFL theorem, that there is no unique algorithm that has the best performance for all optimization problems, a new human-based metaheuristic algorithm called Language Education Optimization (LEO) is introduced, which is used to solve optimization problems. LEO is inspired by the foreign language education process in which a language teacher trains the students of language schools in the desired language skills and rules. LEO is mathematically modeled in three phases: (i) students selecting their teacher, (ii) students learning from each other, and (iii) individual practice, considering exploration in local search and exploitation in local search. The performance of LEO in optimization tasks has been challenged against fifty-two benchmark functions of a variety of unimodal, multimodal types and the CEC 2017 test suite. The optimization results show that LEO, with its acceptable ability in exploration, exploitation, and maintaining a balance between them, has efficient performance in optimization applications and solution presentation. LEO efficiency in optimization tasks is compared with ten well-known metaheuristic algorithms. Analyses of the simulation results show that LEO has effective performance in dealing with optimization tasks and is significantly superior and more competitive in combating the compared algorithms. The implementation results of the proposed approach to four engineering design problems show the effectiveness of LEO in solving real-world optimization applications.

Design Optimization of Noise Filter Using Quantum Annealer

The use of quantum annealers in black-box optimization to obtain the desired properties of a product with a small number of trials has attracted attention. However, the application of this technique to engineering design problems is still limited. Here, we demonstrate the applicability of black-box optimization with a quantum annealer to the design of electric circuit systems, focusing on $\pi$-type noise filters as an example. We develop a framework that uses quantum annealing to find the optimal location of electrical components and conductor paths connecting the components, and confirm that the learning process appropriately works over a number of trials to efficiently search for a design with high performance. The results show the potential applicability of quantum annealing to design problems of electric circuit systems.

Closure to “Differences between Professionals and Students in Their Visual Attention on Multiple Representation Types While Solving an Open-Ended Engineering Design Problem” by Ananna Ahmed, David Hurwitz, Sean Gestson, and Shane Brown

Closure to “Differences between Professionals and Students in Their Visual Attention on Multiple Representation Types While Solving an Open-Ended Engineering Design Problem” by Ananna Ahmed, David Hurwitz, Sean Gestson, and Shane Brown

An adaptive balance optimization algorithm and its engineering application

The policy of balance between exploration capability and exploitation capability directly affects the solution performance of the meta-heuristic algorithm in a limited time. In order to better balance the exploration and exploitation capabilities of the algorithm and meet the solution requirements of complex real-world problems, the adaptive balance optimization algorithm (ABOA) is proposed in this paper. The algorithm consists of a global search phase (GSP) and a local search phase (LSP) and is controlled by a fixed parameter. ABOA not only considers the balance of exploration and exploitation capabilities of the algorithm throughout the whole iterative process but also focuses on the balance of exploration and exploitation in both GSP and LSP. The search in both phases is focused around the respective search centers from outside to inside. ABOA balances the exploration and exploitation capabilities of the algorithm throughout the search process by two adaptive policies: changing the search area and changing the search center. Fifty-two unconstrained benchmark test functions were employed to evaluate the performance of ABOA. The results of ABOA were compared with nine excellent optimization algorithms available in the literature. The statistical results and Friedman test showed that ABOA was significantly competitive. Finally, the results of the examined engineering design problems showed that ABOA can solve the constrained optimization problem better compared to other methods.

Hybrid multi-strategy chaos somersault foraging chimp optimization algorithm research.

To address the problems of slow convergence speed and low accuracy of the chimp optimization algorithm (ChOA), and to prevent falling into the local optimum, a chaos somersault foraging ChOA (CSFChOA) is proposed. First, the cat chaotic sequence is introduced to generate the initial solutions, and then opposition-based learning is used to select better solutions to form the initial population, which can ensure the diversity of the algorithm at the beginning and improve the convergence speed and optimum searching accuracy. Considering that the algorithm is likely to fall into local optimum in the final stage, by taking the optimal solution as the pivot, chimps with better adaptation at the mirror image position replace chimps from the original population using the somersault foraging strategy, which can increase the population diversity and expand the search scope. The optimization search tests were performed on 23 standard test functions and CEC2019 test functions, and the Wilcoxon rank sum test was used for statistical analysis. The CSFChOA was compared with the ChOA and other improved intelligent optimization algorithms. The experimental results show that the CSFChOA outperforms most of the other algorithms in terms of mean and standard deviation, which indicates that the CSFChOA performs well in terms of the convergence accuracy, convergence speed and robustness of global optimization in both low-dimensional and high-dimensional experiments. Finally, through the test and analysis comparison of two complex engineering design problems, the CSFChOA was shown to outperform other algorithms in terms of optimal cost. For the design of the speed reducer, the performance of the CSFChOA is 100% better than other algorithms in terms of optimal cost; and, for the design of a three-bar truss, the performance of the CSFChOA is 6.77% better than other algorithms in terms of optimal cost, which verifies the feasibility, applicability and superiority of the CSFChOA in practical engineering problems.

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>

Red Panda Optimization Algorithm: An Effective Bio-Inspired Metaheuristic Algorithm for Solving Engineering Optimization Problems

This paper presents a new bio-inspired metaheuristic algorithm called Red Panda Optimization (RPO) that imitates the natural behaviors of red pandas in nature. The main design idea of RPO is derived from two characteristic natural behaviors of red pandas: (i) foraging strategy, and (ii) climbing trees to rest. The proposed RPO approach is mathematically modeled in two phases of exploration based on the simulation of red pandas’ foraging strategy and exploitation based on the simulation of red pandas’ movement in climbing trees. The main advantage of the proposed approach is that there is no control parameter in its mathematical modeling, and for this reason, it does not need a parameter adjustment process. The performance of RPO is evaluated on fifty-two standard benchmark functions including unimodal, high-dimensional multimodal, and fixed-dimensional multimodal types as well as CEC 2017 test suite. The optimization results obtained by the proposed RPO approach are compared with the performance of twelve well-known metaheuristic algorithms. The simulation results show that RPO, by maintaining the balance between exploration and exploitation, is effective in solving optimization problems and its performance is superior over competitor algorithms. Based on the analysis of the optimization results, RPO has provided more successful performance compared to the competitor algorithms in 100% of unimodal functions, 100% of high-dimensional multimodal functions, 100% of fixed-dimensional multimodal functions, and 86.2% of CEC 2017 test suite benchmark functions. Also, the statistical analysis of the Wilcoxon rank sum test shows that the superiority of RPO in the competition with the compared algorithms is significant from a statistical point of view. In addition, the results of implementing RPO on four engineering design problems confirms the ability of the proposed approach to handle real-world optimization applications.

HIGH-DIMENSIONAL STOCHASTIC DESIGN OPTIMIZATION UNDER DEPENDENT RANDOM VARIABLES BY A DIMENSIONALLY DECOMPOSED GENERALIZED POLYNOMIAL CHAOS EXPANSION

Newly restructured generalized polynomial chaos expansion (GPCE) methods for high-dimensional design optimization in the presence of input random variables with arbitrary, dependent probability distributions are reported. The methods feature a dimensionally decomposed GPCE (DD-GPCE) for statistical moment and reliability analyses associated with a high-dimensional stochastic response; a novel synthesis between the DD-GPCE approximation and score functions for estimating the first-order design sensitivities of the statistical moments and failure probability; and a standard gradient-based optimization algorithm, constructing the single-step DD-GPCE and multipoint single-step DD-GPCE (MPSS-DD-GPCE) methods. In these new design methods, the multivariate orthonormal basis functions are assembled consistent with the chosen degree of interaction between input variables and the polynomial order, thus facilitating to deflate the curse of dimensionality to the extent possible. In addition, when coupled with score functions, the DD-GPCE approximation leads to analytical formulae for calculating the design sensitivities. More importantly, the statistical moments, failure probability, and their design sensitivities are determined concurrently from a single stochastic analysis or simulation. Numerical results affirm that the proposed methods yield accurate and computationally efficient optimal solutions of mathematical problems and design solutions for simple mechanical systems. Finally, the success in conducting stochastic shape optimization of a bogie side frame with 41 random variables demonstrates the power of the MPSS-DD-GPCE method in solving industrial-scale engineering design problems.