Benchmark Test Suite Research Articles

An inverse reinforcement learning framework with the Q-learning mechanism for the metaheuristic algorithm

A reward function is learned from the expert examples by inverse reinforcement learning (IRL), which is more reliable than an artificial method. The moth–flame optimization algorithm (MFO), which is based on the navigation mechanism of a moth flying at night, has been extensively employed to address the complex optimization problem. An inverse reinforcement learning framework with the Q-learning mechanism (IRLMFO) is designed to strengthen the performance of the MFO algorithm in a large-scale real-parameter optimization problem. The right strategy is chosen by the Q-learning mechanism, using historical data provided by the relevant approach in the strategy pool, which stores strategies that include diverse functions. The competition mechanism is designed to strengthen the exploitation capability of the IRLMFO algorithm. The performance of the IRLMFO is verified on the benchmark test suite in CEC 2017. Experimental results illustrate that the IRLMFO outperforms state-of-the-art algorithms.

Orthogonal Transfer for Multitask Optimization

Knowledge transfer (KT) plays a key role in multitask optimization. However, most of the existing KT methods still face two challenges. First, the tasks may commonly have different dimensionalities (DDs), making the KT between heterogeneous search spaces very difficult. Second, the tasks may have different degrees of similarity in different dimensions, making that treating all dimensions with equal importance may be harmful to the KT process. To address these two challenges, this article proposes a novel orthogonal transfer (OT) method that is enabled by a cross-task mapping (CTM) strategy, which can achieve high-quality KT among heterogeneous tasks. For the first challenge, the CTM strategy maps the global best individual of one task from its original search space to the search space of the target task via an optimization process, which can handle the difference in task dimensionality. For the second challenge, the OT method is performed on the CTM-obtained individual and a random individual of the target task to find the best combination of different dimensions in these two individuals rather than treating all the dimensions equally, so as to achieve high-quality KT. To verify the effectiveness of the proposed OT method and the resulted OT-based multitask optimization (OTMTO) algorithm, this article not only uses the existing multitask optimization benchmark but also proposes a new benchmark test suite named multitask optimization problems (MTOPs) with DDs. Comprehensive experimental results on the existing and the proposed benchmarks show that the proposed OT method and the OTMTO algorithm are very advantageous in providing high-quality KT and in handling the heterogeneity of search space in MTOPs compared to the existing competitive evolutionary multitask optimization (EMTO) algorithms.

Dynamic Candidate Solution Boosted Beluga Whale Optimization Algorithm for Biomedical Classification

In many fields, complicated issues can now be solved with the help of Artificial Intelligence (AI) and Machine Learning (ML). One of the more modern Metaheuristic (MH) algorithms used to tackle numerous issues in various fields is the Beluga Whale Optimization (BWO) method. However, BWO has a lack of diversity, which could lead to being trapped in local optimaand premature convergence. This study presents two stages for enhancing the fundamental BWO algorithm. The initial stage of BWO’s Opposition-Based Learning (OBL), also known as OBWO, helps to expedite the search process and enhance the learning methodology to choose a better generation of candidate solutions for the fundamental BWO. The second step, referred to as OBWOD, combines the Dynamic Candidate Solution (DCS) and OBWO based on the k-Nearest Neighbor (kNN) classifier to boost variety and improve the consistency of the selected solution by giving potential candidates a chance to solve the given problem with a high fitness value. A comparison study with present optimization algorithms for single-objective bound-constraint optimization problems was conducted to evaluate the performance of the OBWOD algorithm on issues from the 2022 IEEE Congress on Evolutionary Computation (CEC’22) benchmark test suite with a range of dimension sizes. The results of the statistical significance test confirmed that the proposed algorithm is competitive with the optimization algorithms. In addition, the OBWOD algorithm surpassed the performance of seven other algorithms with an overall classification accuracy of 85.17% for classifying 10 medical datasets with different dimension sizes according to the performance evaluation matrix.

Evolutionary competitive multitasking optimization via improved adaptive differential evolution

Competitive multitasking optimization (CMTO) is a special multitasking optimization paradigm that has been recently proposed. In the CMTO problems, the objective values of all tasks are competitive, and the purpose of CMTO is to find an optimal solution for multiple tasks. However, existing algorithms designed for the CMTO problems perform poorly since their resource allocation strategies are prone to incorrect task selection. To remedy this drawback, this paper proposes an improved multitasking adaptive differential evolution, which can be featured as: (i) a success-history based resource allocation strategy is proposed; (ii) an adaptive random mating probability control strategy is devised to adapt to different task combinations; (iii) an adaptive multitasking differential evolution operator is designed to enhance the searchability. To evaluate the performance of the proposed method, three CMTO benchmark test suites and two real-world optimization problems are chosen. Compared with other related methods, the results show that the proposed method achieved better performance empirically.

Benchmarking large-scale subset selection in evolutionary multi-objective optimization

In the field of evolutionary multi-objective optimization (EMO), the standard practice is to present the final population of an EMO algorithm as the output. However, it has been shown that the final population often includes solutions which are dominated by other solutions generated and discarded in previous generations. Recently, a novel EMO framework has been developed to solve this issue by storing all the non-dominated solutions generated during the evolution in an archive, and selecting a subset of solutions from the archive as the output. The key component of this framework is the subset selection from the archive, which typically stores a large number of candidate solutions. However, most relevant studies have focused on small candidate solution sets for environmental selection. There is no benchmark test suite for large-scale subset selection. This study aims to fill this research gap by proposing a benchmark test suite for large-scale subset selection, and providing a comparison between several representative subset selection algorithms using the proposed test suite. The proposed test suite together with the benchmarking studies provides a baseline for researchers to understand, use, compare, and develop large-scale subset selection algorithms in the EMO field.

Visualizing Population Dynamics to Examine Algorithm Performance

This work assesses the efficacy of evolutionary algorithms (EAs) using an intuitive multidimensional scaling (MDS) visualization of the evolution of a population. We propose the use of landmark MDS (LMDS) to overcome computational challenges inherent to visualizing many-objective and complex problems with MDS. For the benchmark problems we tested, LMDS is akin to MDS visually, whilst requiring less than 1% of the time and memory necessary to produce an MDS visualization of the same objective space solutions, leading to the possibility of online visualizations for multi- and many-objective optimization evaluation. Using multi- and many-objective problems from the DTLZ and WFG benchmark test suites, we analyze how Landmark MDS visualizations can offer far greater insight into algorithm performance than using traditional algorithm performance metrics such as hypervolume alone, and can be used to complement explicit performance metrics. Ultimately, this visualization allows the visual identification of problem features and assists the decision maker in making intuitive recommendations for algorithm parameters/operators for creating and testing better EAs to solve multi- and many-objective problems.

An offline learning co-evolutionary algorithm with problem-specific knowledge

• An offline learning co-evolutionary algorithm is proposed. • The fitness landscape analysis technique is embedded in OLCA to extract knowledge. • The random forest is introduced to establish the problem-algorithm mapping. • EDA and DE are introduced to enhance the search ability of OLCA. • OLCA has a fast convergence rate and achieves better solutions than state-of-the-art algorithms. The meta-heuristics is an effective way to solve the complex optimization problems. However, the applicability of meta-heuristic is restricted in real applications due to the various characteristics of the corresponding problems. An offline learning co-evolutionary algorithm (OLCA) based on the fitness landscape analysis that introduces the Gaussian estimation of distribution algorithm (EDA) and a variant of differential evolution (DE) for enhancing the search ability, is proposed for complex continuous real-valued problems. The relationship between strategies and fitness landscapes is established by using offline learning of a random forest. The suitable strategy is determined based on the properties of the fitness landscape trained by a random forest before the beginning of the evolutionary process. The proposed OLCA is tested by using the CEC 2017 benchmark test suite and is compared with several state-of-the-art algorithms. The results show that the proposed OLCA is efficient and competitive for solving complex continuous optimization problems. In addition, the effectiveness of the proposed OLCA is also verified by using 19 IEEE CEC 2011 benchmark problems for tackling real-world problems.

Variable surrogate model-based particle swarm optimization for high-dimensional expensive problems

Many industrial applications require time-consuming and resource-intensive evaluations of suitable solutions within very limited time frames. Therefore, many surrogate-assisted evaluation algorithms (SAEAs) have been widely used to optimize expensive problems. However, due to the curse of dimensionality and its implications, scaling SAEAs to high-dimensional expensive problems is still challenging. This paper proposes a variable surrogate model-based particle swarm optimization (called VSMPSO) to meet this challenge and extends it to solve 200-dimensional problems. Specifically, a single surrogate model constructed by simple random sampling is taken to explore different promising areas in different iterations. Moreover, a variable model management strategy is used to better utilize the current global model and accelerate the convergence rate of the optimizer. In addition, the strategy can be applied to any SAEA irrespective of the surrogate model used. To control the trade-off between optimization results and optimization time consumption of SAEAs, we consider fitness value and running time as a bi-objective problem. Applying the proposed approach to a benchmark test suite of dimensions ranging from 30 to 200 and comparisons with four state-of-the-art algorithms show that the proposed VSMPSO achieves high-quality solutions and computational efficiency for high-dimensional problems.

A random forest‐regression‐based inverse‐modeling evolutionary algorithm using uniform reference points

The model-based evolutionary algorithms are divided into three groups: estimation of distribution algorithms, inverse modeling, and surrogate modeling. Existing inverse modeling is mainly applied to solve multi-objective optimization problems and is not suitable for many-objective optimization problems. Some inversed-model techniques, such as the inversed-model of multi-objective evolutionary algorithm, constructed from the Pareto front (PF) to the Pareto solution on nondominated solutions using a random grouping method and Gaussian process, were introduced. However, some of the most efficient inverse models might be eliminated during this procedure. Also, there are challenges, such as the presence of many local PFs and developing poor solutions when the population has no evident regularity. This paper proposes inverse modeling using random forest regression and uniform reference points that map all nondominated solutions from the objective space to the decision space to solve many-objective optimization problems. The proposed algorithm is evaluated using the benchmark test suite for evolutionary algorithms. The results show an improvement in diversity and convergence performance (quality indicators).

A benchmark generator for online dynamic single-objective and multi-objective optimization problems

In the past years, a number of benchmarks have been developed to characterize dynamic optimization problems (DOPs) consisting of a series of static problems over time. The solutions found for a static problem in a previous environment are required to be completely implemented so that the static problems in future environments are independent of the implementation of the solutions in the previous environment. Nevertheless, there is a wide range of real-world DOPs in which the problems in future environments are considerably influenced by the components of the solutions that are not implemented in previous environments, since the optimization for the problem in each environment continuously proceeds while the solutions are continuously implemented until the end of a working day or makespan. This type of DOPs can be termed as an online DOP (OL-DOP). To compensate for the lack of a systematical OL-DOP test suite, in this study we propose a benchmark generator for online dynamic single-objective and multi-objective optimization problems. Specifically, different types of influences of the solutions found in each environment on the problems in the next environment can be adjusted by different types of functions, and the dynamism degree can be tuned by a set of predefined parameters in these functions. Based on the proposed generator, we suggest a test suite consisting of ten continuous OL-DOPs and two discrete OL-DOPs. The empirical results demonstrate that the suggested OL-DOP test suite is characterized by time-deception in comparison with existing DOP benchmark test suites, and is able to analyze the ability of dynamic optimization algorithms in tackling the influence of the solutions found in each environment on the problem in the succeeding environment.

Parallel computing strategies for Sanitized Teaching Learning Based Optimization

Teaching-Learning-Based Optimization is a metaheuristic technique that imitates the knowledge transfer in a classroom. The competitive performance with other state-of-the-art metaheuristic algorithms, innate simplicity, and the requirement of only two user-defined parameters are the primary reason behind the popularity of this algorithm. However, due to the inherent nature of the Teaching Learning Based Optimization, it is not amenable to parallel computing for the multiple evaluations of the fitness function, thereby limiting its application to computationally intensive problems. This article considers the Teaching Learning Based Optimization algorithm without the duplicate removal step as Sanitized Teaching Learning Based Optimization. In this work, three competitive parallelized strategies of Sanitized Teaching Learning Based Optimization are suggested that can harness the benefits of parallel computing. The efficacies of the proposed strategies are demonstrated on 14 benchmark problems and the CEC’14 real parameter benchmark test suite. Additionally, the impact on the computational time with respect to the computational complexity of the objective function and the number of resources has been studied. It is observed that the proposed strategies can lead up to a 90% reduction in computational time over Sanitized Teaching Learning Based Optimization algorithm.

Multiple dynamic penalties based on decomposition for constrained optimization

When solving constrained optimization problems by constraint-handling techniques, the core idea is to balance constraint violation and objective function during the search process. Although many constraint-handling techniques have proposed to deal with this problem, it is difficult to reduce the risk of falling into the local optimums and maintain good population diversity. To tackle these issues, this paper proposes an evolutionary algorithm using multiple dynamic penalties based on decomposition for constrained optimization. Specifically, a constrained optimization problem is decomposed into a number of unconstrained optimization subproblems, and each subproblem is assigned a penalty coefficient to balance constraint and objective function. Then, these subproblems are solved simultaneously, which can improve global search ability and population diversity. In order to generate proper penalty coefficients, a penalty coefficient adjusting strategy is designed, and the penalty coefficient value increases with the number of evolutionary generations to balance the exploration and exploitation. The experimental results on two benchmark test suites and six real-world application problems demonstrate the proposed algorithm is efficient and competitive.

Quantum Nelder‐Mead Hunger Games Search for optimizing photovoltaic solar cells

The inherent multimodal and nonlinear characteristics of solar photovoltaic (PV) systems make it challenging to accurately extract PV parameters. Therefore, this study proposes an efficient and accurate optimization technique, improved Hunger Games Search, to identify unknown parameters in PV systems named IHGS. IHGS makes full use of the population information generated by the differential vectors while incorporating the quantum rotation gate strategy and the Nelder-Mead simplex method (NMs) are fused to further increase the population diversity while rotating the corresponding positions of the search agents, thus efficiently exploring the neighborhood of the optimal solution in the decision space and improving the stability of the algorithm in developing the global optimal solution. The first part of the experiments is to simply verify the effectiveness and the stable merit-seeking ability of the IHGS to handle complex functions by putting the proposed IHGS to test on the IEEE CEC 2017 benchmark test suite. The efficiency of IHGS is verified based on Wilcoxon singed-rank test and Friedman tests. Next, we apply IHGS to three different PV module models (single-diode, double-diode, and PV module) for PV parameter extraction experiments to verify the efficiency and accuracy of IHGS in extracting PV parameters. The root mean square error produced by the IHGS proposed in this study is 9.8602E-04, 9.8248E-04, and 2.4251E-03 for SDM, DDM, and PV modules, respectively. Examples show that IHGS outperforms HGS and other advanced algorithms in terms of convergence speed, data fitting, consistency, and stability. Finally, we perform the PV module parameter extraction problem on three commercial PV models (thin-film ST40, monocrystalline SM55, and multicrystalline KC200GT). We observe that IHGS can still maintain high accuracy when dealing with commercial PV models under complex environments such as different irradiation and temperature. The results show that IHGS is a valuable optimization technique for solar PV parameter estimation based on multi-model prediction.

A two-stage cooperative scatter search algorithm with multi-population hierarchical learning mechanism

Scatter search (SS) is a population-based metaheuristic algorithm, which has been proved high efficiency and effective optimizer for complex continuous real value problems. A two-stage cooperative SS guided with the multi-population hierarchical learning mechanism (TCSSMH) to overcome the slow convergence speed of the original SS is proposed. Three strategies are applied to the original SS. Firstly, TCSSMH adopts an adaptive two-way selection search strategy based on the elite reference set (RefSet), which is elite-oriented and ensures the quality of the population. Secondly, the multi-group hierarchical learning mechanism is embedded in the updating process of the RefSet, and the population of the candidates is divided into three levels including excellent candidates, medium candidates, and inferior candidates according to the fitness value of the function. These three subpopulations cooperate to balance the exploration and exploitation ability of the algorithm in the process of evolution. Finally, each subpopulation adopts an interactive learning strategy to increase the diversity of the population and avoid premature convergence of solutions. The optimum of each subpopulation with high accuracy is obtained by the pattern search (PS) optimization. The stronger search ability and higher search efficiency of these additional proposed strategies are verified by extensive experiments. The TCSSMH algorithm is tested on the CEC2017 benchmark test suite and practical engineering problems. The experimental results show that the TCSSMH algorithm is superior to other state-of-the-art algorithms in global search ability and convergence on the benchmark problems.

A reinforcement learning level-based particle swarm optimization algorithm for large-scale optimization

Large-scale optimization problems (LSOPs) have drawn researchers’ increasing attention since their resemblance to real-world problems. However, due to the complex search space and massive local optima, it is challenging to simultaneously guarantee the diversity and convergence of the algorithms. As a widely used evolutionary algorithm with fast convergence, particle swarm optimization (PSO) shows competitive performances on some LSOPs. Nevertheless, it can easily get trapped into local optima. Overcoming the complexity of LSOPs and improving search efficiency have become vital issues. The reinforcement learning method has proven to be an effective technique in self-adaptive adjustment, which can help search for better results in large-scale solution space more effectively. In this paper, we propose a large-scale optimization algorithm called reinforcement learning level-based particle swarm optimization algorithm (RLLPSO). In RLLPSO, a level-based population structure is constructed to improve population diversity. A reinforcement learning strategy for level number control is employed to help improve the search efficiency of RLLPSO. To further enhance the convergence ability of RLLPSO, a level competition mechanism is introduced. The experimental results from two large-scale benchmark test suites demonstrate that, compared with five state-of-the-art large-scale optimization algorithms, RLLPSO shows superiority in most cases.

Enhanced instance space analysis for the maximum flow problem

The Maximum Flow Problem (MFP) is a fundamental network flow theory problem, for which many algorithms, supported by strong theoretical worst-case analyses, have been proposed. However, their practical efficiency depends on the network structure, making it unclear which algorithm is best for a particular instance or a class of MFP. Instance Space Analysis (ISA) is a methodology that provides insights into such per-instance analysis. In this paper, the instance space of MFP is constructed and analysed for the first time. Novel features from the networks are extracted, capturing the performance of MFP algorithms. Additionally, this paper expands the ISA methodology by addressing the issue of how benchmark instances should be selected to reduce bias in the analysis. Using the enhanced ISA methodology with MFP as the case study, this paper demonstrates that the most important features can be detected, and machine learning methods can identify their impact on algorithm performance, whilst reducing the bias caused by over-representation within the selected sample of test instances. The enhanced methodology enables new insights into the performance of state-of-the-art general purpose MFP algorithms, as well as recommendations for the construction of comprehensive and unbiased benchmark test suites for MFP algorithm testing.

Evolutionary Many-Task Optimization Based on Multisource Knowledge Transfer

Multitask optimization aims to solve two or more optimization tasks simultaneously by leveraging intertask knowledge transfer. However, as the number of tasks increases to the extent of many-task optimization, the knowledge transfer between tasks encounters more uncertainty and challenges, thereby resulting in degradation of optimization performance. To give full play to the many-task optimization framework and minimize the potential negative transfer, this article proposes an evolutionary many-task optimization algorithm based on a multisource knowledge transfer mechanism, namely, EMaTO-MKT. Particularly, in each iteration, EMaTO-MKT determines the probability of using knowledge transfer adaptively according to the evolution experience, and balances the self-evolution within each task and the knowledge transfer among tasks. To perform knowledge transfer, EMaTO-MKT selects multiple highly similar tasks in terms of maximum mean discrepancy as the learning sources for each task. Afterward, a knowledge transfer strategy based on local distribution estimation is applied to enable the learning from multiple sources. Compared with the other state-of-the-art evolutionary many-task algorithms on benchmark test suites, EMaTO-MKT shows competitiveness in solving many-task optimization problems.

Micro multi-strategy multi-objective artificial bee colony algorithm for microgrid energy optimization

Multi-objective evolutionary algorithm (MOEA) has become a common and effective method to solve real-world multi-objective optimization problems. However, in some practical problems, such as the microgrid energy optimization problem (MEOP), the algorithm needs to run on the micro controller to control each distributed power supply in real time. Due limitation of hardware resources on the micro controller, the MOEAs are not suitable. The emerging micro population MOEAs are suitable for this scenario. But the micro population MOEA is vulnerable to lost diversity, resulting in its performance decline. Therefore, this paper proposes a new micro multi-strategy multi-objective ABC algorithm to solve MEOP, called μMMABC. Multi-strategy ABC optimizer is used to divide the population into multiple subgroups and produce offspring in parallel to balance the exploration and exploitation. In addition, an adaptive updating mechanism is proposed to renew the population adaptively. The mechanism can adaptively select more convergent and diverse solutions at different stages to balance the exploration and exploitation of the algorithm. Furthermore, in order to improve the performance of μMMABC on problems with irregular Pareto fronts, the reference point reconstruction with intermediate strategy is also proposed. Some benchmark test suites are used to test the performance of μMMABC. Finally, it is used to solve the MEOP. The experimental results show that the proposed algorithm is more competitive and effective than the traditional MOEAs and other micro population MOEAs in solving the MEOP.

Adaptive heterogeneous particle swarm optimization with comprehensive learning strategy

This paper proposes an adaptive heterogeneous particle swarm optimization with a comprehensive learning strategy for solving single-objective constrained optimization problems. In this algorithm, particles can use an exploration strategy and an exploitation strategy to update their positions. The historical success rates of the two strategies are used to adaptively control the adoption rates of strategies in the next iteration. The search strategy in the canonical particle swarm optimization algorithm is based on elite solutions. As a result, when no particles can discover better solutions for several generations, this algorithm is likely to fall into stagnation. To respond to this challenge, a new strategy is proposed to explore the neighbors of the elite solutions in this study. Finally, a constraint handling method is equipped to the proposed algorithm to make it be able to solve constrained optimization problems. The proposed algorithm is compared with the canonical particle swarm optimization, differential evolution, and several recently proposed algorithms on the benchmark test suite. The Wilcoxon signed-rank test results show that the proposed algorithm is significantly better on most of the benchmark problems compared with the competitors. The proposed algorithm is also applied to solve two real-world mechanical engineering problems. The experimental results show that the proposed algorithm performs consistently well on these problems.

Self-Organizing Migrating Algorithm with narrowing search space strategy for robot path planning

This article introduces a version of the Self-Organizing Migrating Algorithm with a narrowing search space strategy named iSOMA. Compared to the previous two versions, SOMA T3A and Pareto that ranked 3rd and 5th respectively in the IEEE CEC (Congress on Evolutionary Computation) 2019 competition, the iSOMA is equipped with more advanced features with notable improvements including applying jumps in the order, immediate update, narrowing the search space instead of searching on the intersecting edges of hyperplanes, and the partial replacement of individuals in the population when the global best improved no further. Moreover, the proposed algorithm is organized into processes named initialization, self-organizing, migrating, and replacement. We tested the performance of this new version by using three benchmark test suites of IEEE CEC 2013, 2015, and 2017, which, together contain a total of 73 functions. Not only is it superior in performance to other SOMAs, but iSOMA also yields promising results against the representatives of well-known algorithmic families such as Differential Evolution and Particle Swarm Optimization. Moreover, we demonstrate the application of iSOMA for path planning of a drone, while avoiding static obstacles and catching the target.