CEC Competition Research Articles

Revolutionizing optimization: An innovative nutcracker optimizer for single and multi-objective problems

Nutcracker Optimization Algorithm (NOA) is a recently proposed meta-heuristic algorithm inspired by foraging and storing behavior of nutcracker birds. NOA demonstrates strong performance across various test sets and optimization problems. However, it faces challenges in effectively balancing exploration and exploitation, particularly in high-dimensional and complex applications. In this paper, an improved variant of NOA based on Bernoulli map strategy and seasonal behavior strategy, called INOA, is proposed. Firstly, the Bernoulli map strategy enhances the quality of the initial population during the initialization process. Secondly, the seasonal behavior strategy is employed to balance the exploration and exploitation of NOA, enabling it to effectively handle high-dimensional problems by improving convergence and exploration capabilities. Additionally, this paper extends INOA to a multi-objective version called MONOA, enabling the algorithm to solve multi-objective problems. The proposed algorithm, INOA, undergoes evaluation using 30 classical benchmark problems, CEC-2014, CEC-2017, CEC-2019 test suites, and two real-world engineering design problems. INOA’s performance is compared with three categories of optimization methods: (1) recently-developed algorithms, i.e., NOA, BWO, DBO, RIME, MGO, HBA, and SO, (2) highly-cited algorithms, i.e., SMA, MPA, GWO, and (3) high-performing optimizers and winners of CEC competition, i.e., CJADE, L-SHADE-RSP, L-SHADE, and EBOwithCMAR. The proposed algorithm, MONOA, undergoes evaluation using well-known ZDT and DTLZ suites, as well as six constrained and engineering design problems. MONOA’s performance is compared with some state-of-the-art approaches such as MOPSO, NSSO, MOGOA, MOSMA, and MOMGA. Five performance indicators are employed for comparison purposes. Experimental results and comparisons affirm the efficacy of INOA in solving complex and higher-dimensional optimization problems. Similarly, the findings underscore the effectiveness of MONOA in solving diverse multi-objective problems with distinct characteristics.

Hippopotamus optimization algorithm: a novel nature-inspired optimization algorithm

The novelty of this article lies in introducing a novel stochastic technique named the Hippopotamus Optimization (HO) algorithm. The HO is conceived by drawing inspiration from the inherent behaviors observed in hippopotamuses, showcasing an innovative approach in metaheuristic methodology. The HO is conceptually defined using a trinary-phase model that incorporates their position updating in rivers or ponds, defensive strategies against predators, and evasion methods, which are mathematically formulated. It attained the top rank in 115 out of 161 benchmark functions in finding optimal value, encompassing unimodal and high-dimensional multimodal functions, fixed-dimensional multimodal functions, as well as the CEC 2019 test suite and CEC 2014 test suite dimensions of 10, 30, 50, and 100 and Zigzag Pattern benchmark functions, this suggests that the HO demonstrates a noteworthy proficiency in both exploitation and exploration. Moreover, it effectively balances exploration and exploitation, supporting the search process. In light of the results from addressing four distinct engineering design challenges, the HO has effectively achieved the most efficient resolution while concurrently upholding adherence to the designated constraints. The performance evaluation of the HO algorithm encompasses various aspects, including a comparison with WOA, GWO, SSA, PSO, SCA, FA, GOA, TLBO, MFO, and IWO recognized as the most extensively researched metaheuristics, AOA as recently developed algorithms, and CMA-ES as high-performance optimizers acknowledged for their success in the IEEE CEC competition. According to the statistical post hoc analysis, the HO algorithm is determined to be significantly superior to the investigated algorithms. The source codes of the HO algorithm are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/160088-hippopotamus-optimization-algorithm-ho.

Quadruple parameter adaptation growth optimizer with integrated distribution, confrontation, and balance features for optimization

Growth optimizer is a novel metaheuristic algorithm that has powerful numerical optimization capabilities. However, its parameters and search operators become crucial factors that significantly impact its optimization capability for engineering problems and benchmarks. Therefore, this paper proposes a quadruple parameter adaptation growth optimizer (QAGO) integrated with distribution, confrontation, and balance features. In QAGO, the quadruple parameter adaptation mechanism aims to reduce the algorithmic sensitivity for parameter setting and enhance the algorithmic adaptability. By employing parameter sampling that adheres to specific probability distributions, the parameter adaptation mechanism achieves dynamic tuning of the algorithm hyperparameters. Moreover, one-dimensional mapping and fitness difference methods are designed in the triple parameter self-adaptation mechanism based on the contradictory relationship to adjust the operator’s parameters. After that, ”spear” and ”shield” are balanced based on the Jensen–Shannon divergence in information theory. Furthermore, the topological structure of the operators is redesigned, and by combining the parameter adaptation mechanism, operator refinement is achieved. Refined operators can effectively utilize different evolutionary information to improve the quality of the solution. The experiment evaluates the performance of QAGO on distinct optimization problems on the CEC 2017 and CEC 2022 test suites. To demonstrate the capability of QAGO in solving real-world applications, it was applied to tackle two specific problems: multilevel threshold image segmentation and wireless sensor network node deployment. The results demonstrated that QAGO delivers highly promising optimization results compared to seventy-one high-performance competing algorithms, including the five IEEE CEC competition winners. The source code of the QAGO algorithm is publicly available at https://github.com/tsingke/QAGO.

Robust optimization of the design of monopropellant propulsion control systems using an advanced teaching-learning-based optimization method

This research proposes a novel approach for the robust optimization of the design of hydrogen peroxide propulsion control systems using the efficient and advanced Teaching-Learning-Based Optimization (TLBO) method. This study adopts a robust design optimization (RDO) formulation that considers both epistemic and aleatory uncertainties, including sparse points and interval data, and uses the Johnson distribution family for uncertainty representation. The maximum likelihood estimation method is applied to determine the distribution parameters, also considering interval data with a nested optimization technique. A novel advanced TLBO method with high accuracy and convergence rate is employed to optimization of this robust design approach. The method’s originality and advancement come from two categories of modifications to the original framework: the structure of the teaching and learning phases and the initialization and search approach. The efficacy and applicability of the proposed Ad-TLBO, respectively, were evaluated using benchmark problems from the CEC2020 competition and three real-world engineering problems, with a comparison to some recently published and the CEC competition’s top-ranked algorithms. The results and statistical analyses of the Quade test, Wilcoxon signed-rank test, and Friedman test show that the proposed Ad-TLBO method outperforms the other algorithms. The proposed optimization method is eventually applied to design a monopropellant propulsion system as the control actuator of a satellite orbital transfer system. It is found that the proposed advanced TLBO is effective in handling uncertainty in real design problems and improves both the convergence rate and accuracy of the optimization process.

Manta ray foraging optimization based on mechanics game and progressive learning for multiple optimization problems

Metaheuristic algorithms are currently being studied in depth by many scholars, and it is an important task to improve the learning and adaptive capabilities of the algorithms so that they can be of great use in a wide range of optimization problems. The Manta ray foraging optimization (MRFO) has made certain achievements in optimization problems, but it still has shortcomings, such as its insufficient intra-population communication and poor learning ability, so the optimization capability of MRFO needs further improvement. To address these shortcomings, this paper proposes a manta ray foraging optimization based on mechanics game and progressive learning for multiple optimization problems, which is abbreviated as MGL-MRFO, introducing variable spiral factors and dynamic adjustment of internal parameters; then proposes progressive learning to enhance the learning ability of MRFO; and finally proposes a matching game-based update mechanism to eliminate intra-population repetition as a feasible solution. It is validated in terms of move step size and time complexity. The results are compared with variants of the algorithm proposed in recent years in 18 benchmark test functions and the CEC 2022 test set, as well as with the TOP algorithm in the CEC competition, and show that MGL-MRFO has strong advantages, validating the novelty and competitiveness of MGL-MRFO. At the end of the paper, the feasibility and practicality of MGL-MRFO is further validated by three engineering optimization problems.

3-D gravity inversion for the basement relief reconstruction through modified success-history-based adaptive differential evolution

SUMMARY A gravity inversion procedure using the success-history-based adaptive differential evolution (SHADE) algorithm is presented to reconstruct the 3-D basement relief geometry in sedimentary basins. We introduced exponential population size (number) reduction (EPSR) to reduce the computational cost and used self-adaptive control parameters to solve this highly nonlinear inverse problem. Model parametrization was carried out by discretizing the sedimentary cover via juxtaposed right prisms, each placed below each observation point. Resolvability characteristics of the 3-D inverse problem were revealed through some cost function topography landscapes. The fine-tuned control parameter namely, population number allowed us to get best benefit from the algorithm. Additionally, a stabilizing function as a relative constraint was used to avoid undesired effects originated from the ill-posedness of the problem. In the synthetic data cases, the strategy we propose outperformed the linear population number reduction strategy which has won various IEEE–CEC competitions so far. Thorough uncertainty assessments via probability density function and principal component analysis demonstrated the solidity of the obtained inverse models. In the real data case, residual gravity anomalies of two well-known major grabens of Aegean Graben System (Türkiye), calculated thanks to the finite element method, were inverted. It was determined that the inverse solutions obtained for these basement reliefs, whose depths are still controversial, are statistically reliable. Moreover, these depths were found to be less than the depths reported in most previous studies. We conclude that the SHADE using EPSR strategy that we propose is a powerful alternative inversion tool for highly nonlinear geophysical problems.

Fans Optimizer: A human-inspired optimizer for mechanical design problems optimization

This paper proposes a human-inspired algorithm for optimizing various practical engineering problems, specifically, the Fans Optimization (FO) algorithm that is inspired by the Fans economy fused in the entertainment domain. Opposing current algorithms, the FO algorithm introduces a Multi-groups mechanism (Cooperation–Competition) and a Two-characteristic individual update mechanism to balance the exploration and exploitation (E&E). Additionally, the multi-phase optimization algorithm includes Roles information and Fans-community, Fans-community Switching, Resource Competition, Information Sharing, and K-Update. In the experiments, the FO algorithm is first compared with 12 meta-heuristic algorithms in four groups of benchmark functions (selected from the IEEE CEC and GECCO competitions), demonstrating that the FO algorithm has a superior convergence performance and E&E. Moreover, the Williams test prove the superiority of the FO algorithm over the competitor algorithms. Additionally, eight class practical engineering problems verify the FO’s practical engineering applicability. Finally, the FO algorithm solves the inverse kinematic solution problem of the 9-degree of freedom serial robot arm (9-DFSRA) , demonstrating superior results over the competitor schemes. Overall, the test results prove that the FO algorithm is superior to its competitor algorithms for complex engineering problems.

A novel ensemble estimation of distribution algorithm with distribution modification strategies

The canonical estimation of distribution algorithm (EDA) easily falls into a local optimum with an ill-shaped population distribution, which leads to weak convergence performance and less stability when solving global optimization problems. To overcome this defect, we explore a novel EDA variant with an ensemble of three distribution modification strategies, i.e., archive-based population updating (APU), multileader-based search diversification (MSD), and the triggered distribution shrinkage (TDS) strategy, named E3-EDA. The APU strategy utilizes historical population information to rebuild the search scope and avoid ill-shaped distributions. Moreover, it continuously updates the archive to avoid overfitting the distribution model. The MSD makes full use of the location differences among populations to evolve the sampling toward promising regions. TDS is triggered when the search stagnates, shrinking the distribution scope to achieve local exploitation. Additionally, the E3-EDA performance is evaluated using the CEC 2014 and CEC 2018 test suites on 10-dimensional, 30-dimensional, 50-dimensional and 100-dimensional problems. Moreover, several prominent EDA variants and other top methods from CEC competitions are comprehensively compared with the proposed method. The competitive performance of E3-EDA in solving complex problems is supported by the nonparametric test results.

Learning unified mutation operator for differential evolution by natural evolution strategies

Differential evolution (DE) is one of the widely studied algorithms in evolutionary computation. Recently, many adaptive mechanisms have been proposed for DE including adaptive operator selection and adaptive parameter control. Existing studies consider the two kinds of mechanisms independently. In this paper, we first propose a unified mutation operator with learnable parameters. With different parameter settings, the unified mutation operator degenerates into various classic mutation operators. As a result, by adapting the control parameters of the unified mutation operator, we can realize parameter control and operator selection simultaneously. We then present how to use a neural network to adaptively determine the control parameters. We use natural evolution strategies to train the neural network by modeling the evolutionary process as a Markov decision process. We then embed it into three DEs including classic DE, JADE and LSHADE. Experimental studies show that by embedding the learned unified mutation operator, the performances of these backbone DEs can be improved. Particularly, by embedding the unified mutation operator, LSHADE can perform competitively among state-of-the-art EAs including the winner algorithms in the past CEC competitions. Furthermore, we verify the effectiveness of the unified mutation operator through analyzing the population diversity theoretically.

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.

Chaotic marine predators algorithm for global optimization of real-world engineering problems

A novel metaheuristic called Chaotic Marine Predators Algorithm (CMPA) is proposed and investigated for the optimization of engineering problems. CMPA integrates the exploration merits of the recently proposed Marine Predators Algorithm (MPA) with the chaotic maps exploitation capabilities. Several chaotic maps were applied in the proposed CMPA to govern MPA parameters that eventually led to controlled exploration and exploitation of search. This study makes an initial attempt to explore and employ CMPA in decoding complex and challenging design and manufacturing problems. For performance evaluation of the proposed algorithm, CEC 2020 numerical problems having different dimensions and five widely adopted constrained design problems were solved. For all problems, both qualitative and qualitative results are examined and discussed. Moreover, two case studies of multi-pass turning were examined by the proposed CMPA algorithm to optimize the cutting operation with a minimum cost of production per unit objective. Furthermore, the suggested CMPA algorithm has been investigated for solving a real-world structural topology optimization problem. Statistical analysis is performed, and the results of CMPA are compared with twelve distinguished algorithms. Outcomes of the proposed variant algorithm on the benchmarks demonstrate its significantly improved performance relative to other optimizers including a variant of MPA and two state-of-the-art IEEE CEC competitions winners algorithms. Findings from the manufacturing process exhibit CMPA proficiency in solving arduous real-world design problems.

Impact of Boundary Control Methods on Bound-Constrained Optimization Benchmarking

Benchmarking various metaheuristics and their new enhancements, strategies, and adaptation mechanisms has become standard in computational intelligence research. Recently, many challenges and issues regarding fair comparisons and recommendations toward good practices for benchmarking of metaheuristic algorithms, have been identified. This article is aimed at an important issues in metaheuristics design and benchmarking, which are boundary strategies or boundary control methods (BCMs). This work aims to investigate whether the choice of a BCM could significantly influence the performance of competitive algorithms. The experiments encompass the top three performing algorithms from IEEE CEC competitions 2017 and 2020 with six different BCMs. We provide extensive statistical analysis and rankings resulting in conclusions and recommendations for metaheuristics researchers and possibly also for the future direction of benchmark definitions. We conclude that the BCM should be considered another vital metaheuristics input variable for unambiguous reproducibility of results in benchmarking and for a better understanding of population dynamics, since the BCM setting could impact the optimization method performance.

Evolving chimp optimization algorithm by weighted opposition-based technique and greedy search for multimodal engineering problems

This paper presents an evolved chimp optimization algorithm (ChOA) that uses greedy search (GS) and opposition-based learning (OBL) to respectively increase the ChOA’s capabilities for exploration and exploitation in addressing real practical engineering-constrained problems. In order to investigate the efficiency of the GSOBL-ChOA, its performance is evaluated by twenty-three standard benchmark functions, 10 benchmark functions from CEC06-2019, a randomly generated landscape, and 12 real practical Constrained Optimization Problems (COPs-2020) from a wide variety of engineering fields, including power system design, synthesis and process design, industrial chemical producer, power-electronic design, mechanical design, and animal feed ratio. The findings are compared to those obtained using benchmark optimizers such as CMA-ES and SHADE as state-of-the-art optimization techniques and CEC competition winners; standard ChOA; OBL-GWO, OBL-SSA, and OBL-CSA as the best benchmark OBL-based algorithms. In order to perform a comprehensive assessment, three non-parametric statistical tests, including the Wilcoxon rank-sum, Bonferroni–Dunn and Holm, and Friedman average rank tests, are utilized. The top two algorithms are GSOBL-ChOA and CMA-ES, with scores of forty and eleven, respectively, among 27 mathematical functions. jDE100 obtained the highest score of 100 in the 100-digit challenge, followed closely by DISHchain1e+12, which achieved the highest possible score of 97, and GSOBL-ChOA obtained the fourth-highest score of 93. Finally, GSOBL-ChOA and CMA-ES outperform other benchmarks in five and four real practical COPs, respectively. The source code of the paper can be downloaded using the following link: https://se.mathworks.com/matlabcentral/fileexchange/119108-evolving-chimp-optimization-algorithm-by-weighted-opposition.

Comparative Performance Analysis of Differential Evolution Variants on Engineering Design Problems

Because of their superior problem-solving ability, nature-inspired optimization algorithms are being regularly used in solving complex real-world optimization problems. Engineering academics have recently focused on meta-heuristic algorithms to solve various optimization challenges. Among the state-of-the-art algorithms, Differential Evolution (DE) is one of the most successful algorithms and is frequently used to solve various industrial problems. Over the previous 2 decades, DE has been heavily modified to improve its capabilities. Several DE variations secured positions in IEEE CEC competitions, establishing their efficacy. However, to our knowledge, there has never been a comparison of performance across various CEC-winning DE versions, which could aid in determining which is the most successful. In this study, the performance of DE and its eight other IEEE CEC competition-winning variants are compared. First, the algorithms have evaluated IEEE CEC 2019 and 2020 bound-constrained functions, and the performances have been compared. One unconstrained problem from IEEE CEC 2011 problem suite and five other constrained mechanical engineering design problems, out of which four issues have been taken from IEEE CEC 2020 non-convex constrained optimization suite, have been solved to compare the performances. Statistical analyses like Friedman's test and Wilcoxon's test are executed to verify the algorithm’s ability statistically. Performance analysis exposes that none of the DE variants can solve all the problems efficiently. Performance of SHADE and ELSHADE-SPACMA are considerable among the methods used for comparison to solve such mechanical design problems.

A covariance-based Moth–flame optimization algorithm with Cauchy mutation for solving numerical optimization problems

Moth–Flame Optimization (MFO) algorithm, which is inspired by the navigation method of moths, is a nature-inspired optimization algorithm. The MFO is easy to implement and has been used to solve many real-world optimization problems. However, the MFO cannot balance exploration and exploitation well, and the information exchange between individuals is limited, especially in solving some complex numerical problems. To overcome these disadvantages of the MFO in solving the numerical optimization problems, a covariance-based Moth–Flame Optimization algorithm with Cauchy mutation (CCMFO) is proposed in this paper. In the CCMFO, the concept of covariance is used to transform the individuals of the moths and flames from the original space to the eigenspace and update the positions of moths, which can better improve the information exchange ability of the flames and moths in the eigenspace. In addition, Cauchy mutation is utilized to improve the exploration. And the CCMFO is compared with the other 22 algorithms on CEC 2020 test suite. The test results show that the CCMFO is better than other population-based optimization algorithms and MFO variants in search performance, while its performance is statistically similar to CEC competition algorithms. Furthermore, the CCMFO is compared with the other 12 algorithms on CEC 2020 real-world constrained optimization problems, and the results show that the CCMFO can effectively solve real-world constrained optimization problems. Finally, the CCMFO is used to optimize the tracking controller parameters of continuous casting mold vibration displacement. The experimental results based on the experimental platform show that the CCMFO can effectively reduce the difficulty of parameter selection and improve the tracking accuracy.

An intelligent chaotic clonal optimizer

Increasing complexity of real world problems motivated an area to explore efficient optimization methods to solve such problems. Existing optimization algorithms cannot solve all type of problems efficiently (NFL theorem), so new algorithms are proposed to find the better solutions for such complex optimization problems. However, their efficiency and performance can be still improved. Therefore, to follow this vital purpose, in this paper, a novel metaheuristic algorithm, called intelligent clonal optimizer (ICO), is proposed to solve continuous optimization problems. In the proposed algorithm, the initial population is generated through the chaos theory to enhance its exploration capability. It lacks any crossover operator. Instead, a novel clonal operator copying candidate solutions according to their fitness in a self-adaptive way is proposed. Cloning each parent is carried out by two methods, and according to these methods, each offspring is located near the parent or in direction of temporary target. The offsprings are classified to two classes. In addition, a novel conservative selection operator is proposed. According to this operator, the new population is selected from two classes of offsprings and current population by maintaining population diversity. The performance of the ICO algorithm is assessed on 39 well-known unimodal, multimodal, fixed-dimensional multimodal, composite and CEC2019 benchmark functions as well as three engineering application problems. Results of the proposed ICO are compared to sixteen state-of-art metaheuristic algorithms in three categories including the most well-known and recently developed algorithms and the best performer of IEEE CEC competitions using statistical analysis, scalability analysis, Wilcoxon Signed-Rank Test, Friedman test, computational time analysis and convergence analysis. The obtained results proved that ICO performs better than state-of-art metaheuristics in sense of scalability and accurate convergence. According to average rank of Friedman test, the proposed ICO is firstly ranked among others.

Evolutionary-Mean shift algorithm for dynamic multimodal function optimization

Recently, many dynamic optimization algorithms based on metaheuristic methods have been proposed. Although these schemes are highly efficient in determining a single global optimum, they fail in locating multiple optimal solutions. The central goal of dynamic multimodal optimization is to detect multiple optimal solutions for an optimization problem where its objective function is modified over time. Locating many optimal solutions (global and local) in a dynamic multimodal optimization problem is particularly crucial for several applications since the best solution could not always be the best implementable alternative due to various practical limitations. In spite of its importance, the problem of dynamic multimodal optimization through evolutionary principles has been scarcely considered in the literature. On the other hand, mean shift is a non-parametric and iterative process for detecting local maxima in a density function represented by a set of samples. Mean shift maintains interesting adaptive characteristics that allow it to find local maxima under dynamic environments. In this paper, the mean shift scheme is proposed to detect global and local optima in dynamic optimization problems. In the proposed method, the search strategy of the mean shift is modified to consider not only the density but also the fitness value of the candidate solutions. A competitive memory, along with a dynamic strategy, has also been added to accelerate the convergence process by using important information from previous environments. As a result, the proposed approach can effectively identify most of the global and local optima in dynamic environments. To demonstrate the performance of the proposed algorithm, a set of comparisons with other well-known dynamic optimization methods has been conducted. The study considers the benchmark generator of the CEC competition for dynamic optimization. The experimental results suggest a very competitive performance of the proposed scheme in terms of accuracy and robustness.

Improved ensemble of differential evolution variants.

In the field of Differential Evolution (DE), a number of measures have been used to enhance algorithm. However, most of the measures need revision for fitting ensemble of different combinations of DE operators—ensemble DE algorithm. Meanwhile, although ensemble DE algorithm may show better performance than each of its constituent algorithms, there still exists the possibility of further improvement on performance with the help of revised measures. In this paper, we manage to implement measures into Ensemble of Differential Evolution Variants (EDEV). Firstly, we extend the collecting range of optional external archive of JADE—one of the constituent algorithm in EDEV. Then, we revise and implement the Event-Triggered Impulsive (ETI) control. Finally, Linear Population Size Reduction (LPSR) is used by us. Then, we obtain Improved Ensemble of Differential Evolution Variants (IEDEV). In our experiments, good performers in the CEC competitions on real parameter single objective optimization among population-based metaheuristics, state-of-the-art DE algorithms, or up-to-date DE algorithms are involved. Experiments show that our IEDEV is very competitive.

On Selection of a Benchmark by Determining the Algorithms’ Qualities

The authors got the motivation for writing the article based on an issue, with which developers of the newly developed nature-inspired algorithms are usually confronted today: How to select the test benchmark such that it highlights the quality of the developed algorithm most fairly? In line with this, the CEC Competitions on Real-Parameter Single-Objective Optimization benchmarks that were issued several times in the last decade, serve as a testbed for evaluating the collection of nature-inspired algorithms selected in our study. Indeed, this article addresses two research questions: (1) How the selected benchmark affects the ranking of the particular algorithm, and (2) If it is possible to find the best algorithm capable of outperforming all the others on all the selected benchmarks. Ten outstanding algorithms (also winners of particular competitions) from different periods in the last decade were collected and applied to benchmarks issued during the same time period. A comparative analysis showed that there is a strong correlation between the rankings of the algorithms and the benchmarks used, although some deviations arose in ranking the best algorithms. The possible reasons for these deviations were exposed and commented on.

How Does the Number of Objective Function Evaluations Impact Our Understanding of Metaheuristics Behavior?

Comparing various metaheuristics based on an equal number of objective function evaluations has become standard practice. Many contemporary publications use a specific number of objective function evaluations by the benchmarking sets definitions. Furthermore, many publications deal with the recurrent theme of late stagnation, which may lead to the impression that continuing the optimization process could be a waste of computational capabilities. But is it? Recently, many challenges, issues, and questions have been raised regarding fair comparisons and recommendations towards good practices for benchmarking metaheuristic algorithms. The aim of this work is not to compare the performance of several well-known algorithms but to investigate the issues that can appear in benchmarking and comparisons of metaheuristics performance (no matter what the problem is). This article studies the impact of a higher evaluation number on a selection of metaheuristic algorithms. We examine the effect of a raised evaluation budget on overall performance, mean convergence, and population diversity of selected swarm algorithms and IEEE CEC competition winners. Even though the final impact varies based on current algorithm selection, it may significantly affect the final verdict of metaheuristics comparison. This work has picked an important benchmarking issue and made extensive analysis, resulting in conclusions and possible recommendations for users working with real engineering optimization problems or researching the metaheuristics algorithms. Especially nowadays, when metaheuristic algorithms are used for increasingly complex optimization problems, and meet machine learning in AutoML frameworks, we conclude that the objective function evaluation budget should be considered another vital optimization input variable.