Real-world Engineering Design Problems Research Articles

A novel metaheuristic based on object-oriented programming concepts for engineering optimization

This paper presents a novel, robust, efficient, and simple optimization algorithm called the Object-Oriented Programming Optimization Algorithm (OOPOA) for tackling constrained and unconstrained optimization problems. The algorithm is inspired by the inheritance concept of Object-Oriented programming languages, where the features of a class are classified into three types according to inheritance probability: public, private, and protected. The object-oriented programming inheritance concept is implemented in the algorithm to update the population for the next generations. The proposed algorithm ensures exploitation by selecting the solution with the highest fitness to be inherited in each iteration. It ensures exploration by applying a mutation process that helps explore wide regions in the search space. The performance of this technique is demonstrated by solving 34 different optimization tasks, including 20 standard benchmark problems, ten IEEE Congress of Evolutionary Computation benchmark test functions, and four constrained real-world engineering design problems.

A novel multi-strategy ameliorated quasi-oppositional chaotic tunicate swarm algorithm for global optimization and constrained engineering applications

Over the last few decades, a number of prominent meta-heuristic algorithms have been put forth to address complex optimization problems. However, there is a critical need to enhance these existing meta-heuristics by employing a variety of evolutionary techniques to tackle the emerging challenges in engineering applications. As a result, this study attempts to boost the efficiency of the recently introduced bio-inspired algorithm, the Tunicate Swarm Algorithm (TSA), which is motivated by the foraging and swarming behaviour of bioluminescent tunicates residing in the deep sea. Like other algorithms, the TSA has certain limitations, including getting trapped in the local optimal values and a lack of exploration ability, resulting in premature convergence when dealing with highly challenging optimization problems. To overcome these shortcomings, a novel multi-strategy ameliorated TSA, termed the Quasi-Oppositional Chaotic TSA (QOCTSA), has been proposed as an enhanced variant of TSA. This enhanced method contributes the simultaneous incorporation of the Quasi-Oppositional Based Learning (QOBL) and Chaotic Local Search (CLS) mechanisms to effectively balance exploration and exploitation. The implementation of QOBL improves convergence accuracy and exploration rate, while the inclusion of a CLS strategy with ten chaotic maps improves exploitation by enhancing local search ability around the most prospective regions. Thus, the QOCTSA significantly enhances convergence accuracy while maintaining TSA diversification. The experimentations are conducted on a set of thirty-three diverse functions: CEC2005 and CEC2019 test functions, as well as several real-world engineering problems. The statistical and graphical outcomes indicate that QOCTSA is superior to TSA and exhibits a faster rate of convergence. Furthermore, the statistical tests, specifically the Wilcoxon rank-sum test and t-test, reveal that the QOCTSA method outperforms the other competing algorithms in the domain of real-world engineering design problems.

Enhancing population diversity based gaining-sharing knowledge based algorithm for global optimization and engineering design problems

Gaining-sharing knowledge based algorithm (GSK) is a recently emerged meta-heuristic algorithm based on human behavior and has been successfully applied to solve various optimization problems. However, GSK tends to get trapped in local optimum due to the rapid loss of population diversity during the optimization process, resulting in an imbalance between exploration and exploitation. To overcome this deficiency, this paper proposes an enhancing population diversity based GSK (EPD-GSK) framework. The proposed EPD-GSK framework incorporates three components: (1) The utilization of Sobol sequence with low divergence to initialize the population, enhancing the diversity of initial solutions. (2) The integration of the Cauchy mutation strategy in the junior phase to perturb individuals and expand the search space. (3) The application of the reverse learning update mechanism in the senior phase, increasing the likelihood of escaping local optimum. These techniques promote population diversity throughout the exploration and exploitation stages. The proposed EPD-GSK framework was evaluated on CEC2017, CEC2020, and the latest CEC2022 test suites as well as on four constrained real-world engineering design problems. The experimental results demonstrate that EPD-GSK can effectively improve the performance of various existing GSK algorithms. Furthermore, EPD-GSK also exhibits better performance compared with other state-of-the-art algorithms.

Bayesian Optimization via Exact Penalty

Constrained optimization problems pose challenges when the objective function and constraints are nonconvex and their evaluation requires expensive black-box simulations. Recently, hybrid optimization methods that integrate statistical surrogate modeling with numerical optimization algorithms have shown great promise, as they inherit the properties of global convergence from statistical surrogate modeling and fast local convergence from numerical optimization algorithms. However, the computational efficiency is not satisfied by practical needs under limited budgets and in the presence of equality constraints. In this article, we propose a novel hybrid optimization method, called exact penalty Bayesian optimization (EPBO), which employs Bayesian optimization within the exact penalty framework. We model the composite penalty function by a weighted sum of Gaussian processes, where the qualitative components of the constraint violations are smoothed by their predictive means. The proposed method features (i) closed-form acquisition functions, (ii) robustness to initial designs, (iii) the capability to start from infeasible points, and (iv) effective handling of equality constraints. We demonstrate the superiority of EPBO to state-of-the-art competitors using a suite of benchmark synthetic test problems and two real-world engineering design problems.

Multi-objective liver cancer algorithm: A novel algorithm for solving engineering design problems

This research introduces the Multi-Objective Liver Cancer Algorithm (MOLCA), a novel approach inspired by the growth and proliferation patterns of liver tumors. MOLCA emulates the evolutionary tendencies of liver tumors, leveraging their expansion dynamics as a model for solving multi-objective optimization problems in engineering design. The algorithm uniquely combines genetic operators with the Random Opposition-Based Learning (ROBL) strategy, optimizing both local and global search capabilities. Further enhancement is achieved through the integration of elitist non-dominated sorting (NDS), information feedback mechanism (IFM) and Crowding Distance (CD) selection method, which collectively aim to efficiently identify the Pareto optimal front. The performance of MOLCA is rigorously assessed using a comprehensive set of standard multi-objective test benchmarks, including ZDT, DTLZ and various Constraint (CONSTR, TNK, SRN, BNH, OSY and KITA) and real-world engineering design problems like Brushless DC wheel motor, Safety isolating transformer, Helical spring, Two-bar truss and Welded beam. Its efficacy is benchmarked against prominent algorithms such as the non-dominated sorting grey wolf optimizer (NSGWO), multiobjective multi-verse optimization (MOMVO), non-dominated sorting genetic algorithm (NSGA-II), decomposition-based multiobjective evolutionary algorithm (MOEA/D) and multiobjective marine predator algorithm (MOMPA). Quantitative analysis is conducted using GD, IGD, SP, SD, HV and RT metrics to represent convergence and distribution, while qualitative aspects are presented through graphical representations of the Pareto fronts. The MOLCA source code is available at: https://github.com/kanak02/MOLCA.

Elk herd optimizer: a novel nature-inspired metaheuristic algorithm

This paper proposes a novel nature-inspired swarm-based optimization algorithm called elk herd optimizer (EHO). It is inspired by the breeding process of the elk herd. Elks have two main breeding seasons: rutting and calving. In the rutting season, the elk herd splits into different families of various sizes. This division is based on fighting for dominance between bulls, where the stronger bull can form a family with large numbers of harems. In the calving season, each family breeds new calves from its bull and harems. This inspiration is set in an optimization context where the optimization loop consists of three operators: rutting season, calving season, and selection season. During the selection season, all families are merged, including bulls, harems, and calves. The fittest elk herd will be selected for use in the upcoming rutting and calving seasons. In simple words, EHO divides the population into a set of groups, each with one leader and several followers in the rutting season. The number of followers is determined based on the fitness value of its leader group. Each group will generate new solutions based on its leader and followers in the calving season. The members of all groups including leaders, followers, and new solutions are combined and the fittest population is selected in the selection season. The performance of EHO is assessed using 29 benchmark optimization problems utilized in the CEC-2017 special sessions on real-parameter optimization and four traditional real-world engineering design problems. The comparative results were conducted against ten well-established metaheuristic algorithms and showed that the proposed EHO yielded the best results for almost all the benchmark functions used. Statistical testing using Friedman’s test post-hocked by Holm’s test function confirms the superiority of the proposed EHO when compared to other methods. In a nutshell, EHO is an efficient nature-inspired swarm-based optimization algorithm that can be used to tackle several optimization problems.

An Interactive Knowledge-Based Multiobjective Evolutionary Algorithm Framework for Practical Optimization Problems

Experienced users often have useful knowledge and intuition in solving real-world optimization problems. User knowledge can be formulated as inter-variable relationships to assist an optimization algorithm in finding good solutions faster. Such inter-variable interactions can also be automatically learned from high-performing solutions discovered at intermediate iterations in an optimization run – a process called innovization. These relations, if vetted by the users, can be enforced among newly generated solutions to steer the optimization algorithm towards practically promising regions in the search space. Challenges arise for large-scale problems where the number of such variable relationships may be high. This paper proposes an interactive knowledge-based evolutionary multi-objective optimization () framework that extracts hidden variable-wise relationships as knowledge from evolving high-performing solutions, shares them with users to receive feedback, and applies them back to the optimization process to improve its effectiveness. The knowledge extraction process uses a systematic and elegant graph analysis method which scales well with number of variables. The working of the proposed is demonstrated on three large-scale real-world engineering design problems. The simplicity and elegance of the proposed knowledge extraction process and achievement of high-performing solutions quickly indicate the power of the proposed framework. The results presented should motivate further such interaction-based optimization studies for their routine use in practice.

Multi-objective exponential distribution optimizer (MOEDO): a novel math-inspired multi-objective algorithm for global optimization and real-world engineering design problems

The exponential distribution optimizer (EDO) represents a heuristic approach, capitalizing on exponential distribution theory to identify global solutions for complex optimization challenges. This study extends the EDO's applicability by introducing its multi-objective version, the multi-objective EDO (MOEDO), enhanced with elite non-dominated sorting and crowding distance mechanisms. An information feedback mechanism (IFM) is integrated into MOEDO, aiming to balance exploration and exploitation, thus improving convergence and mitigating the stagnation in local optima, a notable limitation in traditional approaches. Our research demonstrates MOEDO's superiority over renowned algorithms such as MOMPA, NSGA-II, MOAOA, MOEA/D and MOGNDO. This is evident in 72.58% of test scenarios, utilizing performance metrics like GD, IGD, HV, SP, SD and RT across benchmark test collections (DTLZ, ZDT and various constraint problems) and five real-world engineering design challenges. The Wilcoxon Rank Sum Test (WRST) further confirms MOEDO as a competitive multi-objective optimization algorithm, particularly in scenarios where existing methods struggle with balancing diversity and convergence efficiency. MOEDO's robust performance, even in complex real-world applications, underscores its potential as an innovative solution in the optimization domain. The MOEDO source code is available at: https://github.com/kanak02/MOEDO.

A Comparative Study of Metaheuristic Optimization Algorithms for Solving Real-World Engineering Design Problems

A Comparative Study of Metaheuristic Optimization Algorithms for Solving Real-World Engineering Design Problems

Physics-Constrained Bayesian Optimization for Optimal Actuators Placement in Composite Structures Assembly

Complex constrained global optimization problems such as optimal actuators placement are extremely challenging. Such challenges, including nonlinearity and nonstationarity of engineering response surfaces, hinder the use of ordinary constrained Bayesian optimization (CBO) techniques with standard Gaussian processes as surrogate models. To overcome those challenges, we propose a physics-constrained Bayesian optimization with multi-layer deep structured Gaussian processes, <i>MGP-CBO</i>. Specifically, we introduce a surrogate model with a multi-layer deep Gaussian process (MGP) mean function. The hierarchical structure of our model enables the applicability of constrained Bayesian optimization to complex nonlinear and nonstationary processes. The deep Gaussian process regression model, <i>MGP</i>, can efficiently and effectively represent the response surface function between actuators and dimensional deformations, thus yielding a better estimated global optimum in a shorter computational time. The proposed <i>MGP-CBO</i> model can realize faster convergence to the global optimum with lower constraint violations. Through extensive evaluations carried out on synthetic problems and a real-world engineering design problem, we show that <i>MGP-CBO</i> outperforms existing benchmarks. Although we use the optimal actuators placement as a demonstration example, the proposed <i>MGP-CBO</i> model can be applied to other complex nonstationary engineering optimization problems. <i>Note to Practitioners</i>&#x2014;Bayesian optimization is a widely used sequential design strategy for engineering optimization because it does not rely on functional forms of response surfaces. This paper helps address two questions in practice: (i) how to incorporate physics constraints into Bayesian optimization. (ii) How to do Bayesian optimization when the systems have hierarchical structures. In practice, the hierarchical system structure is ubiquitous, and the engineering optimization is constrained by physical laws or special requirements. Therefore, the proposed physics-constrained Bayesian optimization with a multi-layer Gaussian process could provide a new tool for engineering design optimization problems. The computational convergence and complexity have been investigated. The proposed method is applicable to broad complex and nonstationary engineering optimization problems.

Meta-heuristic search algorithms in truss optimization: Research on stability and complexity analyses

Although they are among the most researched real world engineering design problems, it is encountered with significant problems in the optimization of structural truss bar problems (TPs). The main reasons for these problems are (i) the studies on the optimization of TPs being carried out with different experimental settings, (ii) the competitor algorithms used in the optimization process being insufficient, and (iii) the stability analysis and computational complexity information of the algorithms are not investigated. It is designed a simulation environment with defined standards and a benchmarking suite consisting of nine TPs of three different types in order to eliminate these problems. It is found optimum solutions for all problems in the benchmark suite and it is introduced feasible solutions for the first time. According to the statistical analysis results, among the seventy-seven competing algorithms, the best ten algorithms showed competitive performance in the optimization of TPs are LSHADE-EpSin, LSHADE-CnEpSin, SHADE, LSHADE, GSK, FDB-AGDE, MPA, LRFDB-COA and BES. According to the results of the stability analysis carried out on feasible solutions, it has been determined the algorithms with the best success rate for planar type; LSHADE, LSHADE-CnEpSin, LSHADE-EpSin and GSK with 100% success rate, LSHADE-CnEpSin, LSHADE-EpSin, LSHADE and SHADE for Space type with 100% success rate, and LSHADE-EpSin with 69% success rate for frequency constrained type. When the performances of the algorithms are evaluated regardless of the problem type, LSHADE-EpSin has been the most stable algorithm with an overall success rate of 90% on the TPs.Click here for the simulation environment containing the source codes of the ten competitive algorithms and the TP benchmark suite proposed in the article: https://www.mathworks.com/matlabcentral/fileexchange/131668-structural-truss-problems-benchmark-suite.

Improved dwarf mongoose optimization algorithm using novel nonlinear control and exploration strategies

The Dwarf Mongoose Optimization Algorithm (DMO) is a popular metaheuristic algorithm utilized to solve real-world problems. However, DMO has limitations such as slow convergence rate, susceptibility to local optima, and poor performance in high-dimensional problems. Aiming at the defects of the DMO, we propose an improved version called IDMO. This paper introduces the best leader and proposes a novel nonlinear control strategy based on the sine function, significantly enhancing the convergence rate while ensuring accuracy. Moreover, we propose a novel exploration strategy to solve the global optimization and high-dimensional problem. To demonstrate the performance of the proposed IDMO, we test on 65 test functions, including CEC2017, CEC2020, CEC2022, and CEC2013 large-scale global optimization. IDMO is compared with three classes of widely recognized algorithms: (1) highly-cited algorithms, namely, GSA, GWO, WOA, and HHO, (2) advanced algorithms, such as CPSOGSA, CSA, AVOA, and SO, (3) high-performance optimizers including L-SHADE, AL-SHADE, LSHADE-SPACMA, and LSHADE-cnEpSin. Moreover, we also compare with the original DMO and variants such as GDNNMOA, CO-DWO, and BDMOSAO. Meanwhile, we apply IDMO to solve 19 engineering design problems from the CEC2020 real-world optimization suite. Experimental results demonstrate that IDMO outperforms other algorithms, exhibiting excellent convergence rate, stability, and accuracy. The effectiveness of IDMO is confirmed by the Friedman mean ranking, showcasing its potential for metaheuristic optimization and real-world engineering design problems.

DETDO: An adaptive hybrid dandelion optimizer for engineering optimization

Dandelion Optimizer (DO) is a recently proposed swarm intelligence algorithm that coincides with the process of finding the best reproduction site for dandelion seeds. Compared with the classical Meta-heuristic algorithms, DO exhibits strong competitiveness, but it also has some drawbacks. In this paper, we proposed an adaptive hybrid dandelion optimizer called DETDO by combining three strategies of adaptive tent chaotic mapping, differential evolution (DE) strategy, and adaptive t-distribution perturbation to address the shortcomings of weak DO development, easy to fall into local optimum and slow convergence speed. Firstly, the adaptive tent chaos mapping is used in the initialization phase to obtain a uniformly distributed high-quality initial population, which helps the algorithm to enter the correct search region quickly. Secondly, the DE strategy is introduced to increase the diversity of dandelion populations to avoid algorithm stagnation, which improves the exploitation capability and the accuracy of the optimal solution. Finally, adaptive t-distribution perturbation around the elite solution successfully balances the exploration and exploitation phases while improving the convergence speed through a reasonable conversion from Cauchy to Gaussian distribution. The proposed DETDO is compared with classical or advanced optimization algorithms on CEC2017 and CEC2019 test sets, and the experimental results and statistical analysis demonstrate that the algorithm has better optimization accuracy and speed. In addition, DETDO has obtained the best results in solving six real-world engineering design problems. Finally, DETDO is applied to two bar topology optimization cases. Under a series of complex constraints, DETDO produces a lighter bar structure than the current scheme. It further illustrates the effectiveness and applicability of DETDO in practical problems. The above results mean that DETDO with strong competitiveness will become a preferred swarm intelligence algorithm to cope with optimization problems.

ESO: An enhanced snake optimizer for real-world engineering problems

Meta-heuristic algorithms are an essential way to solve realistic optimization problems. Developing effective, accurate, and stable meta-heuristic algorithms has become the goal of optimization research. Snake Optimizer (SO) is a novel algorithm with good optimization results. However, due to the limitations of natural laws, the parameters are more fixed values in the exploration and exploitation phase, so the SO algorithm quickly falls into local optimization and slowly converges. This paper proposes an Enhanced Snake Optimizer (ESO) by introducing a novel opposition-based learning strategy and new dynamic update mechanisms (parameter dynamic update strategy, sine–cosine composite perturbation factors, Tent-chaos & Cauchy mutation) to achieve better performance. The effectiveness of ESO has been tested on 23 classic benchmark functions and the CEC 2019 function set. 13 functions of 23 classic benchmark functions have variants that belong to multiple dimensions (Dim = 30, 100, 500, 1000, and 2000). In addition, ESO is also used to solve four real-world engineering design problems. Experimental results and two statistical tests show that the proposed ESO performs better than the other 13 state-of-the-art algorithms, including SO. The MATLAB code of ESO is available from: https://ww2.mathworks.cn/matlabcentral/fileexchange/120173-eso-an-enhanced-snake-optimizer.

MOCOVIDOA: a novel multi-objective coronavirus disease optimization algorithm for solving multi-objective optimization problems

A novel multi-objective Coronavirus disease optimization algorithm (MOCOVIDOA) is presented to solve global optimization problems with up to three objective functions. This algorithm used an archive to store non-dominated POSs during the optimization process. Then, a roulette wheel selection mechanism selects the effective archived solutions by simulating the frameshifting technique Coronavirus particles use for replication. We evaluated the efficiency by solving twenty-seven multi-objective (21 benchmarks & 6 real-world engineering design) problems, where the results are compared against five common multi-objective metaheuristics. The comparison uses six evaluation metrics, including IGD, GD, MS, SP, HV, and delta p (Delta mathrm{P}). The obtained results and the Wilcoxon rank-sum test show the superiority of this novel algorithm over the existing algorithms and reveal its applicability in solving multi-objective problems.

A modified seahorse optimization algorithm based on chaotic maps for solving global optimization and engineering problems

Metaheuristic optimization algorithms are global optimization approaches that manage the search process to efficiently explore search spaces associated with different optimization problems. Seahorse optimization (SHO) is a novel swarm-based metaheuristic optimization method inspired by certain behaviors of sea horses. The SHO algorithm mimics the movement, hunting, and breeding behavior of sea horses in nature. Chaotic maps are effectively used to improve the performance of metaheuristic algorithms by avoiding the local optimum and increasing the speed of convergence. In this study, 10 different chaotic maps have been employed for the first time to produce chaotic values rather than random values in SHO, increasing the performance of the method. The purpose of using chaotic maps that generate chaotic values to their random values in SHO is to increase the convergence speed of the original SHO algorithm and avoid the local optimum. 33 different benchmark functions, consisting of unimodal, multimodal, fixed-dimension multimodal, and CEC2019, have been utilized to assess the performance of Chaotic SHO (CSHO), which is first introduced in this study. In addition, the proposed CSHO has been compared with four metaheuristic algorithms in the literature, namely Sine Cosine Algorithm, Salp Swarm Algorithm, Whale Optimization Algorithm, and Particle Swarm Optimization. Statistical analyses of the obtained results have been also performed. The proposed CSHO is then implemented to 4 different real-world engineering design problems, including the welded beam, pressure vessel, tension/compression spring, and speed reducer. The results obtained with CSHO are compared with popular metaheuristic methods in the literature. Experimental results show that it gives successful and promising results compared to the original SHO algorithm.

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

&lt;p&gt;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.&lt;/p&gt;

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.