Solving Complex Optimization Problems Research Articles

Dual Elite Groups-Guided Differential Evolution for Global Numerical Optimization

Differential evolution (DE) has shown remarkable performance in solving continuous optimization problems. However, its optimization performance still encounters limitations when confronted with complex optimization problems with lots of local regions. To address this issue, this paper proposes a dual elite groups-guided mutation strategy called “DE/current-to-duelite/1” for DE. As a result, a novel DE variant called DEGGDE is developed. Instead of only using the elites in the current population to direct the evolution of all individuals, DEGGDE additionally maintains an archive to store the obsolete parent individuals and then assembles the elites in both the current population and the archive to guide the mutation of all individuals. In this way, the diversity of the guiding exemplars in the mutation is expectedly promoted. With the guidance of these diverse elites, a good balance between exploration of the complex search space and exploitation of the found promising regions is hopefully maintained in DEGGDE. As a result, DEGGDE expectedly achieves good optimization performance in solving complex optimization problems. A large number of experiments are conducted on the CEC’2017 benchmark set with three different dimension sizes to demonstrate the effectiveness of DEGGDE. Experimental results have confirmed that DEGGDE performs competitively with or even significantly better than eleven state-of-the-art and representative DE variants.

Efficient Harris Hawk Optimization (HHO)-Based Framework for Accurate Skin Cancer Prediction

The prediction of skin cancer poses a number of challenges due to the differences in visual characteristics between melanoma, basal cell carcinomas, and squamous cell carcinomas. These visual differences pose difficulties for models in discerning subtle features and patterns accurately. However, a remarkable breakthrough in image analysis using convolutional neural networks (CNNs) has emerged, specifically in the identification of skin cancer from images. Unfortunately, manually designing such neural architectures is prone to errors and consumes substantial time. It has become increasingly popular to design and fine-tune neural networks by using metaheuristic algorithms that are based on natural phenomena. A nature-inspired algorithm is a powerful alternative to traditional algorithms for solving problems, particularly in complex optimization tasks. One such algorithm, the Harris hawk optimization (HHO), has demonstrated promise in automatically identifying the most appropriate solution across a wide range of possibilities, making it suitable for solving complex optimization problems. The purpose of this study is to introduce a novel automated architecture called “HHOForSkin” that combines the power of convolutional neural networks with meta-heuristic optimization techniques. The HHOForSkin framework uses an innovative custom CNN architecture with 26 layers for the analysis of medical images. In addition, a Harris hawk optimization algorithm (HHO) is used to fine-tune the developed model for multiple skin cancer classification problems. The developed model achieves an average accuracy of 99.1% and 98.93% F1 score using a publicly available skin cancer dataset. These results position the developed optimization-based skin cancer detection strategy at the forefront, offering the highest accuracy for seven-class classification problems compared to related works.

A Novel Hybrid Firefly Algorithm with Double-Level Learning Strategy

The firefly algorithm (FA) is a swarm intelligence algorithm capable of solving global optimization problems exactly; it has been used to solve many practical problems. However, traditional firefly algorithms solve complex optimization problems with a simple update method, which leads to premature stagnation due to the limitation of firefly diversity. To overcome these drawbacks, a novel hybrid firefly algorithm (HFA-DLL) with a double-level learning strategy is proposed. In HFA-DLL, a double-level learning strategy is proposed to avoid premature convergence and enhance the algorithm’s global search capability. At the same time, a competitive elimination mechanism is introduced to increase the accuracy of solving complex optimization problems and improve the convergence rate of the algorithm. Moreover, a stochastic disturbance strategy is designed to help the best solution jump out of the local optimum and minimize the time cost in the wrong direction. To understand the advantages and disadvantages of HFA-DLL, experiments were conducted on the CEC 2017 benchmark suite. Experimental results show that HFA-DLL outperforms other state-of-art algorithms in terms of convergence rate and exploration efficiency.

A nonlinear programming algorithm for finite element limit analysis using feasible arc searching technique

AbstractThis article presents a nonlinear programming algorithm for finite element limit analysis (FELA) based on feasible arc searching technique (FAST). The proposed algorithm has the potential to significantly reduce the iteration numbers required for convergence, making it a valuable tool for solving complex optimization problems from FELA. The algorithm also introduces several new features to the existing methods, including: (i) a novel method for determining a reasonable updating step length; (ii) the avoidance of solving an additional “phase one problem” for finding an initial feasible point; and (iii) the proposition of an empirical criterion for detecting infeasibility problems. The effectiveness of the proposed approach has been demonstrated through several classic examples derived from geotechnical engineering. The initial two examples show the superior convergence speed of the novel approach compared to existing methods. Additionally, the third example highlights the efficacy of the feasibility detection criterion for problems involving both prescribed and unknown external forces.

Revolutionizing sustainable supply chain management: A review of metaheuristics

This paper reviews the application of metaheuristics for optimized sustainable supply chain management (SSCM). This paper explores the potential of metaheuristics to improve the supply chain’s sustainability while enhancing its efficiency and competitiveness. The paper provides an overview of the principles of SSCM and the challenges businesses face in achieving sustainable supply chain management. It then introduces the concept of metaheuristics and describes their use in solving complex optimization problems. The paper reviews various metaheuristics algorithms applied to sustainable supply chain management and analyzes their effectiveness in addressing the challenges of SSCM. The paper also identifies the key factors that influence the success of using metaheuristics for SSCM, such as the choice of algorithm, problem complexity, and data quality. Finally, the paper provides recommendations for future research in this area and highlights the potential of metaheuristics to promote sustainable supply chain management. The review suggests that metaheuristics can be a valuable tool for optimizing sustainable supply chain management and improving supply chain operations’ sustainability, efficiency, and competitiveness.

Research Progress of Nature-Inspired Metaheuristic Algorithms in Mobile Robot Path Planning

The research of mobile robot path planning has shifted from the static environment to the dynamic environment, from the two-dimensional environment to the high-dimensional environment, and from the single-robot system to the multi-robot system. As the core technology for mobile robots to realize autonomous positioning and navigation, path-planning technology should plan collision-free and smooth paths for mobile robots in obstructed environments, which requires path-planning algorithms with a certain degree of intelligence. Metaheuristic algorithms are widely used in various optimization problems due to their algorithmic intelligence, and they have become the most effective algorithm to solve complex optimization problems in the field of mobile robot path planning. Based on a comprehensive analysis of existing path-planning algorithms, this paper proposes a new algorithm classification. Based on this classification, we focus on the firefly algorithm (FA) and the cuckoo search algorithm (CS), complemented by the dragonfly algorithm (DA), the whale optimization algorithm (WOA), and the sparrow search algorithm (SSA). During the analysis of the above algorithms, this paper summarizes the current research results of mobile robot path planning and proposes the future development trend of mobile robot path planning.

A Modified Binary Arithmetic Optimization Algorithm for Feature Selection

Feature selection chooses the optimal subset from the feature set without scarifying the information carried by the dataset. It is considered a complex combinatorial problem, so classical optimization techniques fail to solve it when the feature set becomes larger. Meta-heuristic approaches are well known to solve complex optimization problems; hence these algorithms have been successfully applied to extract optimal feature subsets. The arithmetic Optimization Algorithm is a newly proposed mathematics-based meta-heuristic search algorithm successfully applied to solve optimization problems. However, it has been observed that AOA experiences a poor exploration phase. Hence in the present work, a Modified Binary Arithmetic Optimization Algorithm (MB-AOA) is proposed, which solves the poor exploration problem of standard AOA. In the MB-AOA, instead of utilizing a single best solution, an optimal solution set that gradually shrinks after each successive iteration is applied for better exploration during initial iterations. Also, instead of a fixed search parameter (μ), the MB-AOA utilizes a variable parameter suitable for binary optimization problems. The proposed method is evaluated over seven real-life datasets from the UCI repository as a feature selection wrapper method and compared with standard AOA over two performance metrics, Average Accuracy, F-score, and the generated feature subset size. MB-AOA has performed better in six datasets regarding F-score and average accuracy. The obtained results from the simulation process demonstrate that the MB-AOA can select the relevant features, thus improving the classification task’s overall accuracy levels.

A Compact Snake Optimization Algorithm in the Application of WKNN Fingerprint Localization.

Indoor localization has broad application prospects, but accurately obtaining the location of test points (TPs) in narrow indoor spaces is a challenge. The weighted K-nearest neighbor algorithm (WKNN) is a powerful localization algorithm that can improve the localization accuracy of TPs. In recent years, with the rapid development of metaheuristic algorithms, it has shown efficiency in solving complex optimization problems. The main research purpose of this article is to study how to use metaheuristic algorithms to improve indoor positioning accuracy and verify the effectiveness of heuristic algorithms in indoor positioning. This paper presents a new algorithm called compact snake optimization (cSO). The novel algorithm introduces a compact strategy to the snake optimization (SO) algorithm, which ensures optimal performance in situations with limited computing and memory resources. The performance of cSO is evaluated on 28 test functions of CEC2013 and compared with several intelligent computing algorithms. The results demonstrate that cSO outperforms these algorithms. Furthermore, we combine the cSO algorithm with WKNN fingerprint positioning and RSSI positioning. The simulation experiments demonstrate that the cSO algorithm can effectively reduce positioning errors.

A multi-leader Harris hawks optimizer with adaptive mutation and its application for modeling of silicon content in liquid iron of blast furnace

Aiming at the problem that Harris hawks optimizer (HHO) has poor population diversity and is easy to fall into local optimum when solving complex optimization problems, a multi-leader Harris Hawks optimizer with adaptive mutation (MLHHO-AM) is proposed, in which multiple leaders are used to guide the Harris hawks to improve the population diversity. An adaptive mutation is introduced to enhance the ability of the algorithm to jump out of the local optimum. The key feature of the strategy is that Gaussian mutation occurs in some dimensions of the optimal solution, and the number of mutation dimensions is adaptively changed. To verify the numerical optimization performance of MLHHO-AM, the parameter sensitivity, the role of two improved mechanisms, and population diversity are analyzed based on 23 classical test functions. Then, MLHHO-AM is compared with 12 state-of-the-art variants and 11 basic metaheuristic algorithms on IEEE CEC2017 and IEEE CEC2022 benchmark suites. The above test results show that the proposed MLHHO-AM is an effective algorithm with better numerical optimization performance than most competitors. In order to verify ability of MLHHO-AM to handle the practical problem, the parameters of the Elman neural network (ENN) used to build the prediction model of silicon content in liquid iron of blast furnace are optimized by MLHHO-AM. The simulation results based on actual data show that the ENN prediction model based on MLHHO-AM has higher prediction accuracy with R2=0.7563 and RMSE=0.0598. Therefore, the proposed MLHHO-AM has excellent numerical optimization performance and can be used to predict the silicon content in liquid iron of blast furnace.

A novel chaotic chimp sine cosine algorithm Part-I: For solving optimization problem

In the realm of solving complex optimization problems, it becomes crucial to fulfill multiple objectives to achieve optimal system performance while adhering to various conditions and limitations. Traditional optimization methods often face challenges such as sluggish convergence speed and confinement to local optima, making it difficult to find satisfactory solution. To tackle this challenge, the development of multi-objective programming is directed towards satisfying physical constraints. In line of the above problems and limitations, this work aims to contribute by proposing a hybrid optimization technique that can effectively address such optimization issues. The proposed algorithm, called the chaotic chimp sine cosine (C-CHOA-SC) algorithm, combines the chimp optimization algorithm (CHOA) and the sine cosine algorithm (SCA) to overcome problems of slow convergence and getting stuck in local optima. It does this by using the SCA after the CHOA and incorporating chaos to explore and exploit the search space effectively. This hybrid approach aims to improve the algorithm's performance (offers enhanced exploration capabilities, efficient exploitation of the search space, and improved convergence speed) and find better solutions to optimization problems. These features make the C-CHOA-SC algorithm well-suited for solving complex optimization problems with multiple objectives, providing a contemporary and effective solution. To evaluate the performance of the proposed C-CHOA-SC algorithm, three phases of analysis are conducted. In the first phase, the exploration, exploitation, and avoidance of local optima are tested using the CEC 2019 benchmark problems. The second phase involves tracking and validating the performance of C-CHOA-SC using multiple performance metrics on two-dimensional test functions. Finally, non-parametric alternative test i.e., the Wilcoxon rank sum test and Friedman test are performed. The results demonstrate that the proposed technique exhibits significantly better performance compared to other methods, with a 95 % significance level. As concerned to Friedman test, the C-CHOA-SC algorithm obtains a lower rank, it implies that it outperforms the other competing algorithms in terms of its overall performance.

Variational quantum non-orthogonal optimization

Current universal quantum computers have a limited number of noisy qubits. Because of this, it is difficult to use them to solve large-scale complex optimization problems. In this paper we tackle this issue by proposing a quantum optimization scheme where discrete classical variables are encoded in non-orthogonal states of the quantum system. We develop the case of non-orthogonal qubit states, with individual qubits on the quantum computer handling more than one bit classical variable. Combining this idea with Variational Quantum Eigensolvers (VQE) and quantum state tomography, we show that it is possible to significantly reduce the number of qubits required by quantum hardware to solve complex optimization problems. We benchmark our algorithm by successfully optimizing a polynomial of degree 8 and 15 variables using only 15 qubits. Our proposal opens the path towards solving real-life useful optimization problems in today’s limited quantum hardware.

Improved Teaching Learning Algorithm with Laplacian operator for solving nonlinear engineering optimization problems

Teaching Learning Algorithm (TLA) is a recently developed nature-inspired optimization technique applicable to complex optimization problems. This paper proposes an improved TLA version using the Laplacian operator of the Genetic Algorithm (GA), named LX-TLA. The proposed algorithm is tested on benchmark optimization problems, including unimodal and multimodal problems. The numerical results are obtained in the form of objective function values, and a t-test is applied to compare the performance of LX-TLA and basic TLA. Convergence plots are given to provide insight into the convergence behavior of LX-TLA. The results reveal that proposed algorithm provides effective and efficient performance in solving benchmark test functions. The proposed algorithm is also applied to engineering design problems, such as Tuned Mass Damper (TMD), truss structure, welded beam, tension string, and pressure vessel. The results obtained using LX-TLA are compared with other nature-inspired optimization algorithms. The results demonstrate that the proposed algorithm is a robust and effective tool for solving complex optimization problems.

Fast random opposition-based learning Golden Jackal Optimization algorithm

Nowadays, optimization techniques are required in various engineering domains in order to find optimal solutions for complex problems. As a result, there is a growing tendency among scientists to enhance existing nature-inspired algorithms using various evolutionary strategies and to develop new nature-inspired optimization methods that can properly explore the feature space. The recently designed nature-inspired metaheuristic, named the Golden Jackal Optimization​ (GJO) algorithm, was inspired by the collaborative hunting actions of the golden jackal in nature to solve various challenging problems. However, like other approaches, the GJO has the limitations of poor exploitation ability, ease to get stuck in a local optimal region, and an improper balancing of exploration and exploitation. To overcome these limitations, this paper proposes a novel contribution to GJO based on a new technique, namely the fast random opposition-based learning Golden Jackal Optimization algorithm (FROBL-GJO). The FROBL technique is mainly inspired by opposition-based learning (OBL) and random opposition-based learning (ROBL) techniques to enhance the optimization precision and convergence speed of the GJO algorithm. Furthermore, two other models, such as OBL-GJO and ROBL-GJO, are also proposed for comparison purposes. To examine the proficiency of the newly proposed FROBL-GJO algorithm, it has been examined with several well-known existing meta-heuristic algorithms while solving the CEC-2005 and CEC-2019 benchmark test functions and real-life engineering problems. The experimental outcomes and statistical tests reveal the superior performance of the proposed FROBL-GJO in solving both global optimization and engineering design problems. Hence, the findings of benchmark functions and engineering problems endorse that the proposed FROBL-GJO algorithm can be considered a promising method for solving complex optimization problems.

Neural Network Algorithm With Reinforcement Learning for Parameters Extraction of Photovoltaic Models.

This research focuses on the application of artificial neural networks (ANNs) on parameters extraction of photovoltaic (PV) models. Extracting parameters of the PV models accurately is crucial to control and optimize PV systems. Although many algorithms have been proposed to address this issue, how to extract the parameters of the PV models accurately and reliably is still a great challenge. Neural network algorithm (NNA) is a recently reported metaheuristic algorithm. NNA is inspired by ANNs. Benefiting from the unique structure of ANNs, NNA shows excellent global search ability. However, NNA faces the challenge of slow convergence rate and local optima stagnation in solving complex optimization problems. This article presents an improved NNA, named neural network algorithm with reinforcement learning (RLNNA), for extracting parameters of the PV models. In RLNNA, three strategies, namely modification factor with reinforcement learning (RL), transfer operator with historical population, and feedback operator, are designed to overcome the challenge of NNA. To verify the performance of RLNNA, it is employed to extract the parameters of the three PV models. Experimental results show that RLNNA can extract the parameters of the considered PV models with higher accuracy and stronger stability compared with NNA and the other 12 powerful algorithms, which fully indicates the effectiveness of the improved strategies.

An Improved Differential Evolution Algorithm for Numerical Optimization Problems

The differential evolution algorithm has gained popularity for solving complex optimization problems because of its simplicity and efficiency. However, it has several drawbacks, such as a slow convergence rate, high sensitivity to the values of control parameters, and the ease of getting trapped in local optima. In order to overcome these drawbacks, this paper integrates three novel strategies into the original differential evolution. First, a population improvement strategy based on a multi-level sampling mechanism is used to accelerate convergence and increase the diversity of the population. Second, a new self-adaptive mutation strategy balances the exploration and exploitation abilities of the algorithm by dynamically determining an appropriate value of the mutation parameters; this improves the search ability and helps the algorithm escape from local optima when it gets stuck. Third, a new selection strategy guides the search to avoid local optima. Twelve benchmark functions of different characteristics are used to validate the performance of the proposed algorithm. The experimental results show that the proposed algorithm performs significantly better than the original DE in terms of the ability to locate the global optimum, convergence speed, and scalability. In addition, the proposed algorithm is able to find the global optimal solutions on 8 out of 12 benchmark functions, while 7 other well-established metaheuristic algorithms, namely NBOLDE, ODE, DE, SaDE, JADE, PSO, and GA, can obtain only 6, 2, 1, 1, 1, 1, and 1 functions, respectively. Doi: 10.28991/HIJ-2023-04-02-014 Full Text: PDF

Significance of Linear Programming for Optimization

Linear programming (LP) is a powerful mathematical technique that has revolutionized optimization problems across various fields. This abstract highlights the significance of linear programming in optimization and its profound impact on decision-making, resource allocation, and efficiency enhancement. The primary objective of linear programming is to maximize or minimize a linear objective function, subject to a set of linear constraints. LP provides a systematic framework for modeling and solving complex optimization problems, enabling decision-makers to make informed choices and allocate resources optimally. The significance of linear programming lies in its ability to address a wide range of real-world challenges efficiently and effectively. In the realm of operations research, linear programming has found extensive applications in supply chain management, production planning, scheduling, and logistics optimization. By formulating decision problems into mathematical models, LP allows organizations to streamline their processes, minimize costs, optimize resource utilization, and maximize overall productivity. Linear programming has also made significant contributions in the field of economics. It has enabled economists to analyze and optimize economic systems, such as determining the optimal production levels for different goods, optimizing resource allocation in a market, and solving complex pricing problems. LP provides a quantitative framework for economic decision-making, facilitating the identification of optimal solutions and supporting policy development. Furthermore, linear programming plays a crucial role in the field of transportation and network optimization. It aids in solving problems related to route optimization, facility location, network design, and capacity planning. By efficiently allocating resources and optimizing transportation networks, LP helps reduce costs, improve service levels, and enhance overall efficiency in the transportation sector. In summary, the significance of linear programming for optimization is evident in its wide-ranging applications and its ability to tackle complex decision problems in various domains. By employing mathematical modeling and optimization techniques, LP allows decision-makers to make informed choices, allocate resources optimally, and achieve desired objectives. The ongoing advancements in LP algorithms and computing technologies further enhance its applicability and make it an indispensable tool for optimization in today's dynamic and competitive world.

Quantum-behaved particle swarm optimization with dynamic grouping searching strategy

The quantum-behaved particle swarm optimization (QPSO) algorithm, a variant of particle swarm optimization (PSO), has been proven to be an effective tool to solve various of optimization problems. However, like other PSO variants, it often suffers a premature convergence, especially when solving complex optimization problems. Considering this issue, this paper proposes a hybrid QPSO with dynamic grouping searching strategy, named QPSO-DGS. During the search process, the particle swarm is dynamically grouped into two subpopulations, which are assigned to implement the exploration and exploitation search, respectively. In each subpopulation, a comprehensive learning strategy is used for each particle to adjust its personal best position with a certain probability. Besides, a modified opposition-based computation is employed to improve the swarm diversity. The experimental comparison is conducted between the QPSO-DGS and other seven state-of-art PSO variants on the CEC’2013 test suit. The experimental results show that QPSO-DGS has a promising performance in terms of the solution accuracy and the convergence speed on the majority of these test functions, and especially on multimodal problems.

A Modified Simulated Annealing (MSA) Algorithm to Solve the Supplier Selection and Order Quantity Allocation Problem with Non-Linear Freight Rates

Economic Order Quantity (EOQ) is an important optimization problem for inventory management with an impact on various industries; however, their mathematical models may be complex with non-convex, non-linear, and non-differentiable objective functions. Metaheuristic algorithms have emerged as powerful tools for solving complex optimization problems (including EOQ). They are iterative search techniques that can efficiently explore large solution spaces and obtain near-optimal solutions. Simulated Annealing (SA) is a widely used metaheuristic method able to avoid local suboptimal solutions. The traditional SA algorithm is based on a single agent, which may result in a low convergence rate for complex problems. This article proposes a modified multiple-agent (population-based) adaptive SA algorithm; the adaptive algorithm imposes a slight attraction of all agents to the current best solution. As a proof of concept, the proposed algorithm was tested on a particular EOQ problem (recently studied in the literature and interesting by itself) in which the objective function is non-linear, non-convex, and non-differentiable. With these new mechanisms, the algorithm allows for the exploration of different regions of the solution space and determines the global optimum in a faster manner. The analysis showed that the proposed algorithm performed well in finding good solutions in a reasonably short amount of time.

Epigenetic opportunities for evolutionary computation

Evolutionary computation is a group of biologically inspired algorithms used to solve complex optimization problems. It can be split into evolutionary algorithms, which take inspiration from genetic inheritance, and swarm intelligence algorithms, that take inspiration from cultural inheritance. However, much of the modern evolutionary literature remains relatively unexplored. To understand which evolutionary mechanisms have been considered, and which have been overlooked, this paper breaks down successful bioinspired algorithms under a contemporary biological framework based on the extended evolutionary synthesis, an extension of the classical, genetics focused, modern synthesis. Although the idea of the extended evolutionary synthesis has not been fully accepted in evolutionary theory, it presents many interesting concepts that could provide benefits to evolutionary computation. The analysis shows that Darwinism and the modern synthesis have been incorporated into evolutionary computation but the extended evolutionary synthesis has been broadly ignored beyond: cultural inheritance, incorporated in the sub-set of swarm intelligence algorithms, evolvability, through covariance matrix adaptation evolution strategy (CMA-ES), and multilevel selection, through multilevel selection genetic algorithm (MLSGA). The framework shows a gap in epigenetic inheritance for evolutionary computation, despite being a key building block in modern interpretations of evolution. This leaves a diverse range of biologically inspired mechanisms as low hanging fruit that should be explored further within evolutionary computation and illustrates the potential of epigenetic based approaches through the recent benchmarks in the literature.

Distributed Differential Evolution With Adaptive Resource Allocation.

Distributed differential evolution (DDE) is an efficient paradigm that adopts multiple populations for cooperatively solving complex optimization problems. However, how to allocate fitness evaluation (FE) budget resources among the distributed multiple populations can greatly influence the optimization ability of DDE. Therefore, this article proposes a novel three-layer DDE framework with adaptive resource allocation (DDE-ARA), including the algorithm layer for evolving various differential evolution (DE) populations, the dispatch layer for dispatching the individuals in the DE populations to different distributed machines, and the machine layer for accommodating distributed computers. In the DDE-ARA framework, three novel methods are further proposed. First, a general performance indicator (GPI) method is proposed to measure the performance of different DEs. Second, based on the GPI, a FE allocation (FEA) method is proposed to adaptively allocate the FE budget resources from poorly performing DEs to well-performing DEs for better search efficiency. This way, the GPI and FEA methods achieve the ARA in the algorithm layer. Third, a load balance strategy is proposed in the dispatch layer to balance the FE burden of different computers in the machine layer for improving load balance and algorithm speedup. Moreover, theoretical analyses are provided to show why the proposed DDE-ARA framework can be effective and to discuss the lower bound of its optimization error. Extensive experiments are conducted on all the 30 functions of CEC 2014 competitions at 10, 30, 50, and 100 dimensions, and some state-of-the-art DDE algorithms are adopted for comparisons. The results show the great effectiveness and efficiency of the proposed framework and the three novel methods.