Real-world Engineering Design Problems Research Articles

Automated-tuned hyper-parameter deep neural network by using arithmetic optimization algorithm for Lorenz chaotic system

<p>Deep neural networks (DNNs) are very dependent on their parameterization and require experts to determine which method to implement and modify the hyper-parameters value. This study proposes an automated-tuned hyper-parameter for DNN using a metaheuristic optimization algorithm, arithmetic optimization algorithm (AOA). AOA makes use of the distribution properties of mathematics’ primary arithmetic operators, including multiplication, division, addition, and subtraction. AOA is mathematically modeled and implemented to optimize processes across a broad range of search spaces. The performance of AOA is evaluated against 29 benchmark functions, and several real-world engineering design problems are to demonstrate AOA’s applicability. The hyper-parameter tuning framework consists of a set of Lorenz chaotic system datasets, hybrid DNN architecture, and AOA that works automatically. As a result, AOA produced the highest accuracy in the test dataset with a combination of optimized hyper-parameters for DNN architecture. The boxplot analysis also produced the ten AOA particles that are the most accurately chosen. Hence, AOA with ten particles had the smallest size of boxplot for all hyper-parameters, which concluded the best solution. In particular, the result for the proposed system is outperformed compared to the architecture tested with particle swarm optimization.</p>

Opposition-based learning boosted orca predation algorithm with dimension learning: a case study of multi-degree reduction for NURBS curves

AbstractThe approximate degree reduction of ball non-uniform rational B-splines (NURBS) curves is a pivotal and knotty technique in computer-aided design/computer-aided manufacture. As we all know, the multi-degree reduction of NURBS ones is a mathematical optimization problem that a swarm intelligence algorithm can deal with. This paper uses an improved orca predation algorithm (IOPA) to accomplish the optimal multi-degree reduction of NURBS curves. Firstly, by incorporating a dimension learning strategy and opposition-based learning strategy into the orca predation algorithm (OPA), an IOPA is developed to increase the population diversity and enhance its capability of jumping out of the local minima. Secondly, the superiority of the proposed IOPA is comprehensively verified by comparing it with the original OPA and numerous celebrated and newly developed algorithms on the IEEE Congress on Evolutionary Computation (CEC) 2014 test suite and IEEE CEC2017 benchmark functions, respectively. Meanwhile, the practicability of IOPA is also highlighted by solving three real-world engineering design problems. Furthermore, statistical testing of IOPA has been conducted to validate its significance. Finally, the optimization model of multi-degree reduction for NURBS curves is established by minimizing the distance between the original curve and the approximate curve. The IOPA is utilized to solve the optimization model, and the optimal approximate NURBS curves are obtained. Some representative numerical examples illustrate the ability of the proposed IOPA to effectively solve the multi-degree reduction problem of NURBS curves in terms of precision, robustness, and convergence characteristics.

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.

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>

Posterior Decision Making Based on Decomposition-Driven Knee Point Identification

Knee points, characterized as a small improvement on one objective can lead to a significant degradation on at least one of the other objectives, are attractive to decision makers (DMs) in multicriterion decision making. This article presents a simple and effective knee point identification (KPI) method to help DMs identify solution(s) of interest from a given set of tradeoff solutions thus facilitating posterior decision making. Our basic idea is to sequentially validate whether a solution is a knee point or not by comparing its localized tradeoff utility with others within its neighborhood characterized from a decomposition perspective. In particular, a solution is a knee point if and only if it has the best-localized tradeoff utility among its neighbors. We implement a GPU version that carries out the KPI in a parallel manner. This GPU version reduces the worst-case complexity from quadratic to linear. The performance of our proposed method is compared with five state-of-the-art KPI methods on 134 test problem instances and two real-world engineering design problems. Empirical results demonstrate its outstanding performance especially on problems with many local knee points. We further validate the usefulness of our proposed method for guiding evolutionary multiobjective optimization algorithms to search for knee points on the fly during the evolutionary process.

Improved Bat Algorithm Based on Doppler Effect for Optimal Design of Special Truss Structures

Bat algorithm (BA) is one of the well-established metaheuristic algorithms based on the echolocation characteristics of microbats. Literature studies demonstrate that BA provides good results in a wide range of optimization problems due to its simple structures, easy implementation, and effectiveness. However, the standard BA has two general shortcomings when applied to complex optimization problems. The first is the high probability of falling in local optima, and the second is insufficient population diversity, leading to unwanted premature convergence. This paper proposes an improved bat algorithm based on the Doppler effect (IBA-DE) to improve the performance of the standard BA. In the proposed IBA-DE, a new equation with some idealized rules is driven from the Doppler effect and adopted for updating the bat velocities in the algorithm body. The local search part of the standard BA is also improved via searching around the better bat individuals. This part is also equipped with Lévy flight to maintain the population diversity. The performance of IBA-DE is evaluated on three real-world engineering design problems. The results obtained by these problems show that IBA-DE is superior to the basic BA and other considered algorithms. For further investigation, IBA-DE is applied to the optimal design of four special truss structures. Comparing the optimization results found by the proposed algorithm with those of some other state-of-art metaheuristics indicates that the proposed IBA-DE can be an efficient optimizer for the optimal design of real-size structures.

Directional crossover slime mould algorithm with adaptive Lévy diversity for the optimal design of real-world problems

AbstractThe slime mould algorithm (SMA) has become a classical algorithm applied in many fields since it was presented. Nevertheless, when faced with complex tasks, the algorithm converges slowly and tends to fall into the local optimum. So, there is still room for improvement in the performance of SMA. This work proposes a novel SMA variant (SDSMA), combining the adaptive Lévy diversity mechanism and directional crossover mechanism. Firstly, the adaptive Lévy diversity mechanism can improve population diversity. Then, the directional crossover mechanism can enhance the balance of exploration and exploitation, thus helping SDSMA to increase the convergence speed and accuracy. SDSMA is compared with SMA variants, original algorithms, improved algorithms, improved-SMAs, and others on the benchmark function set to verify its performance. Meanwhile, the Wilcoxon signed-rank test, the Friedman test, and other analytical methods are considered to analyze the experimental results. The analysis results show that SDSMA with two strategies significantly improves the performance of SMA. Meanwhile, the computational cost of SDSMA is smaller than that of SMA on benchmark function. Finally, the proposed algorithm is applied to three real-world engineering design problems. The experiments prove that SDSMA is an effective aid tool for computationally complex practical tasks.

Fitness-distance balance based artificial ecosystem optimisation to solve transient stability constrained optimal power flow problem

ABSTRACT The Transient Stability Constrained Optimal Power Flow (TSCOPF) has become an important tool for power systems today. TSCOPF is a nonlinear optimisation problem, making its solution difficult, especially for small power systems. This paper presents a new optimisation method that incorporates Fitness-Distance Balance (FDB) with the Artificial Ecosystem Optimisation (AEO) algorithm to improve the solution quality in multi-dimensional and nonlinear optimisation problems. The proposed method, named the Fitness-Distance Balance Artificial Ecosystem Optimisation (FDBAEO), also has the capacity to solve the TSCOPF problem efficiently. In order to evaluate the proposed algorithm, it was tested on IEEE CEC benchmarks and on an IEEE 30-bus test system for the TSCOPF problem. Simulation results were compared with the basic AEO algorithm and other current meta-heuristic methods reported in the literature. The results showed that the proposed method was more effective in converging at the global optimum point in solving the TSCOPF problem compared to the other algorithms. This situation indicates that the design changes made in the decomposition phase of the AEO were more suitable for simulating the operation of the algorithm in the real world. The FDBAEO has exhibited a promising performance in solving both single-objective optimisation and constrained real-world engineering design problems.

An effective multi-objective artificial hummingbird algorithm with dynamic elimination-based crowding distance for solving engineering design problems

Artificial hummingbird algorithm (AHA) is a recently developed bio-based metaheuristic and it shows superior performance in handling single-objective optimization problems. Despite the merit, this algorithm can only solve problems with one objective. To solve complex multi-objective optimization problems, including engineering design problems, a multi-objective AHA (MOAHA) is developed in this study. In MOAHA, an external archive is employed to save Pareto optimal solutions, and a dynamic elimination-based crowding distance (DECD) method is developed to maintain this archive to effectively preserve the population diversity. In addition, a non-dominated sorting strategy is merged with MOAHA to construct a solution update mechanism, which effectively refines Pareto optimal solutions for improving the convergence of the algorithm. The superior results over 7 competitors on 28 benchmark functions in terms of convergence, diversity and solution distribution are demonstrated with a suite of comprehensive tests. The MOAHA algorithm is also applied to 5 real-world engineering design problems with multiple objectives, demonstrating its superiority in handling challenging real-world multi-objective problems with unknown true Pareto optimal solutions and fronts. The source code of MOAHA is publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/113535-moaha-multi-objective-artificial-hummingbird-algorithm and https://seyedalimirjalili.com/aha.

Investigation of the Performance of Metaheuristic Optimization Algorithms Used in Solving Real-World Engineering Design Problems

Gerçek dünya mühendislik tasarım problemleri çok sayıda kısıtlamaları olan karmaşık amaç fonksiyonlarına sahip olmasından dolayı çözülmesi nispeten zor problemlerdir. Hem endüstride hem de disiplinler arası çalışmalarda yaygın olarak kullanılmaktadır. Bu tür problemlerle başa çıkmak için birçok optimizasyon algoritması kullanılmıştır. Fakat algoritmanın performansı, ölçeğin artması ve problemin zorluğu ile önemli ölçüde azalmaktadır. Literatürde yer alan mühendislik tasarım problemlerini etkin bir şekilde ele almak için farklı optimizasyon yöntemleri ve onların farklı versiyonları önerilmiştir. Bu çalışmada, mühendislik tasarım problemlerini çözmek için son dönemlerde ortaya çıkmış ve popüler olan metasezgisel optimizasyon algoritmaları incelenmiştir. İncelenen algoritmalar; kısıtları amaç fonksiyonları ve karar değişkenleri farklı beş gerçek dünya mühendislik tasarım problemine uyarlanmıştır ve performans analizleri gerçekleştirilmiştir.

An Improved Pity Beetle Algorithm for Solving Constrained Engineering Design Problems

To cope with increasingly complex models of engineering design problems and to obtain more accurate design solutions, this paper proposed an improved population-based, bio-inspired optimization algorithm, called the pity beetle algorithm based on pheromone dispersion model (PBA-PDM). PBA-PDM enables a local and global search for optimization problems through the pheromone release mechanisms in female beetles and the interaction relationship between male beetles. The experimental results compared with other state-of-the-art metaheuristic optimization algorithms show that PBA-PDM has an ideal performance when dealing with both classical test functions and CEC2017 benchmark test functions. Then, the PBA-PDM is applied in dealing with real-world constrained engineering design problems to verify the effectiveness and applicability. The above experimental results show that the PBA-PDM proposed in this paper is an effective and efficient algorithm for solving real-world optimization problems.

A proportional, integral and derivative differential evolution algorithm for global optimization

The proportional, integral, and derivative differential evolution algorithm (PID-DE) is proposed as a new type of interdisciplinary metaheuristic evolutionary algorithm in this paper. The inspiration of PID-DE is derived from the classical proportional, integral, and derivative control method in engineering, and it is used in the framework of the differential evolution (DE) algorithm. To begin, the mathematical models of proportional search, integral search, and derivative search are established as the fundamental search operations. Five different types of optimizers that use a combination of these three basic operations and an additional mutation operation are presented. The selection and crossover methods in DE are then modified to maintain population diversity while also improving global search capacity, and a feedback strategy is established to adaptively adjust the subgroup member of each optimizer. Following that, an integrated high-accuracy, rapid-convergence, and stable metaheuristic is invented using the comprehensive information utilization principle and flexible parameter determination method. Five groups of experiments are studied to assess the overall performance of the proposed algorithm. The first test comprises 12 standard benchmark functions with minimum optima. In Tests 2 and 3, the 52 functions of Congress on Evolutionary Computation (CEC) 2014 and CEC 11 are evaluated using PID-DE under standard test conditions. Besides, three classic real-world engineering design problems and the CEC 2020 test suit are studied for the constrained optimization test. The experimental tests validate PID-DE’s higher accuracy and faster convergence speed in numerical optimization when compared with the representative approaches and top algorithms in the CEC competitions.

An enhanced hybrid arithmetic optimization algorithm for engineering applications

Arithmetic optimization algorithm (AOA) is a newly well-developed meta-heuristic algorithm that is inspired by the distribution behavior of main arithmetic operators in mathematics. Although the original AOA has shown well competitive performance with popular meta-heuristic algorithms, it still faces the issues of insufficient exploitation ability, ease of falling into local optima and low convergence accuracy in large-scale applications. In order to ameliorate these deficiencies, an enhanced hybrid AOA named CSOAOA, integrated with point set strategy, optimal neighborhood learning strategy and crisscross strategy, is developed in this paper. First, a good point set initialization strategy is added to obtain a higher-quality initial population, which improves the convergence speed of the algorithm. Then, the optimal neighborhood learning strategy is adopted to guide the individual’s search behavior and avoid the algorithm falling into the current local optimum, which boosts the search efficiency and calculation accuracy. Finally, by combining AOA with the crisscross optimization algorithm, the exploration and utilization ability of the crisscross algorithm are integrated into the CSOAOA. These strategies collaborate to enhance AOA in accelerating overall performance. The superiority of the proposed CSOAOA is comprehensively verified by comparing with the original AOA, six improved AOA and numerous celebrated and newly developed algorithms on the well-known 23 classical benchmark functions, IEEE Congress on Evolutionary Computation (CEC) 2019 test suite and IEEE CEC 2020 benchmark functions, respectively. Meanwhile, the practicability of CSOAOA is also highlighted by solving eight real-world engineering design problems. Furthermore, the statistical testing of CSOAOA has been conducted to validate its significance. Experimental results and statistical comparisons manifest the superior performance of CSOAOA over the comparison algorithms in terms of precision, convergence rate and solution quality. Therefore, CSOAOA is potentially a powerful and competitive meta-heuristic algorithm for solving complex engineering optimization problems.

An agent-based blackboard system for multi-objective optimization

Abstract In the field of multi-objective optimization, there are a multitude of algorithms from which to choose. Each algorithm has strengths and weaknesses associated with the mechanics for finding the Pareto front. Recently, researchers have begun to examine how multi-agent environments can be used to help solve multi-objective optimization problems. In this work, we propose a multi-objective optimization algorithm based on a multi-agent blackboard system (MABS). The MABS framework allows for multiple agents to read and write pertinent optimization problem data to a central blackboard agent. Agents can stochastically search the design space, use previously discovered solutions to explore local optima, or update and prune the Pareto front. A centralized blackboard framework allows the optimization problem to be solved in a cohesive manner and permits stopping, restarting, or updating the optimization problem. The MABS framework is tested against three alternative optimization algorithms across a suite of engineering design problems and typically outperforms the other algorithms in discovering the Pareto front. A parallelizability study is performed where we find that the MABS is able to evaluate a set number of designs, which require an evaluation time ranging from 0 to 300 seconds, quicker than a traditional optimization algorithm: this fact becomes more apparent the longer it takes to evaluate a design. To provide context for the benefits provided by MABS, a real-world nuclear engineering design problem is examined. MABS is used to examine the placement of experiments in a nuclear reactor, where we are able to evaluate hundreds of configurations for experimental placement while maintaining a strict set of safety constraints.

A meta-inspired termite queen algorithm for global optimization and engineering design problems

This paper proposes a novel bio-inspired termite queen algorithm (TQA) to solve optimization problems by simulating the division of labor in termite populations under a queen’s rule. TQA is benchmarked on a set of 23 functions to test its performance at solving global optimization problems, and applied to six real-world engineering design problems to verify its reliability and effectiveness. Comparative simulation studies with other algorithms are conducted, from whose results it is observed that TQA satisfactorily solves global optimization problems and engineering design problems.

Solving Many-objective Constraint Real-World Optimization Problems with Multi-objective Optimization Algorithms

In real world engineering optimization problems many constraints must be considered due to the imperfect conditions of the systems or process. Therefore, constraint handling methods are integrated into optimization algorithms. However, since the constraints are succeeded by the algorithm, their value is not considered or watched. Alternatively, it is possible to convert constraints to objectives and these many-objective constraint real-world optimization problems are changed to many-objective optimization problems. In this research for this purpose five real world engineering design problems are converted into many-objective optimization problem which are Gear Train Design, Pressure Vessel Design, Two Bar Truss Design, Disc Brake Design and Vibrating Platform Design problems. The problems are solved by using multi-objective optimization algorithms (NSGA-II, MOEA/D, MOEA/D-DE, MPSO/D and MOPSO) and their performance is compared by using the hypervolume metric.

A Bio-Inspired Multi-Population-Based Adaptive Backtracking Search Algorithm.

Backtracking search algorithm (BSA) is a nature-based optimization technique extensively used to solve various real-world global optimization problems for the past few years. The present work aims to introduce an improved BSA (ImBSA) based on a multi-population approach and modified control parameter settings to apprehend an ensemble of various mutation strategies. In the proposed ImBSA, a new mutation strategy is suggested to enhance the algorithm’s performance. Also, for all mutation strategies, the control parameters are updated adaptively during the algorithm’s execution. Extensive experiments have been performed on CEC2014 and CEC2017 single-objective benchmark functions, and the results are compared with several state-of-the-art algorithms, improved BSA variants, efficient differential evolution (DE) variants, particle swarm optimization (PSO) variants, and some other hybrid variants. The nonparametric Friedman rank test has been conducted to examine the efficiency of the proposed algorithm statistically. Moreover, six real-world engineering design problems have been solved to examine the problem-solving ability of ImBSA. The experimental results, statistical analysis, convergence graphs, complexity analysis, and the results of real-world applications confirm the superior performance of the suggested ImBSA.

Improved gradual change-based Harris Hawks optimization for real-world engineering design problems

Improved gradual change-based Harris Hawks optimization for real-world engineering design problems

Meta-heuristic optimization algorithms for solving real-world mechanical engineering design problems: a comprehensive survey, applications, comparative analysis, and results

Meta-heuristic optimization algorithms for solving real-world mechanical engineering design problems: a comprehensive survey, applications, comparative analysis, and results