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This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

This paper introduces an improved differential evolution algorithm based on cooperative multi-population (CMp-DE for short), which combines diverse population collaboration mechanisms and catalytic factors into an improved differential evolution framework. By harnessing various population collaboration mechanisms, the algorithm enhances the diversity of individuals within populations during initial iterations and reduces it during later iterations, thereby harmonizing the algorithm's exploratory and exploitative capabilities. Furthermore, a novel mutation operator is proposed that divides the iterative process into exploration and exploitation phases, thereby augmenting the algorithm's global exploration prowess. Lastly, a catalytic operator is introduced to generate new individuals near post-crossover individuals based on a specified rule, which enhances the algorithm's ability to escape local optima and increasing stability. The proposed CMp-DE is benchmarked against the CEC2017 benchmark test functions and compared against 13 algorithms, including five differential evolution algorithms and their variants, as well as eight state-of-the-art metaheuristic optimization algorithms. This evaluation assesses the CMp-DE's solution accuracy, convergence, stability, and scalability. Finally, the applicability of CMp-DE is validated by addressing six practical optimization problems. The experimental results show that CMp-DE surpasses other algorithms in terms of both convergence accuracy and robustness. Moreover, integrating a catalytic operator with other optimization algorithms notably boosts performance in convergence accuracy and stability. The inclusion of the catalytic operator has significantly enhanced the performance of algorithms compared to their performance before its addition. This underscores the potential of the catalytic operator in improving the performance of various algorithms, particularly in terms of convergence accuracy and robustness. [ABSTRACT FROM AUTHOR]

• MMODE is developed as a new hybrid gene selection method for tumor identification. • MMODE combines multi-tasking and multi-objective frameworks. • MMODE uses a new elite strategy and a new guidance strategy. • MMODE selects a few genes and achieves high classification accuracy. A key preprocessing step in tumor recognition based on microarray expression profile data and machine learning is to identify tumor marker genes. Gene selection aims to select the most relevant gene subset from the original ultra-high dimensional microarray expression profile data to improve tumor identification performance. Inspired by evolutionary multitasking (EMT) and multi-objective optimization, this paper puts forward a novel multitasking multi-objective differential evolution gene selection algorithm (MMODE) which uses new elite and guidance strategies to select the best gene subsets. MMODE initializes two different populations according to different filtering criteria to increase the diversity of the search. These two populations guide their respective populations to search in the optimal direction through knowledge transfer in the evolutionary process. In addition, MMODE employs new elite and guidance strategies that enables individuals to narrow the search range and jump out of local optima. The proposed algorithm is validated on 13 publicly available microarray expression datasets in comparison with state-of-the-art gene selection algorithms. The experimental results show that MMODE can find smaller gene subsets and achieve higher classification accuracy compared with other algorithms. [ABSTRACT FROM AUTHOR]

The differential evolution (DE) algorithm is widely regarded as one of the most influential evolutionary algorithms for addressing complex optimization problems. However, the fixed mutation strategy limits the adaptive ability of DE, and the lack of utilization of historical information limits the optimization ability of DE. In this paper, an indicator-based self-learning differential evolution algorithm (ISDE) is proposed. A jump out mechanism based on deep reinforcement learning is adopted to control the mutation intensity of the population. The neural network in the jump out mechanism is designed as a decision maker. The mutation intensity of the population is controlled by the neural network, and the neural network are trained by a double deep Q network algorithm based on the continuous data generated during the evolution process. A population range indicator (PRI) is utilized to describe individual differences in the population. A diversity maintenance mechanism is designed to maintain individual differences according to the value of PRI. The experimental results reveal that the comprehensive performance of ISDE is superior to comparison algorithms on CEC 2017 real-parameter numerical optimization. [ABSTRACT FROM AUTHOR]

Nowadays, economic and environmental concerns in production have become increasingly significant. To address these issues, the Combined Economic and Emission Dispatch (CEED) problem has been introduced to optimize the power generation process by considering fuel cost and emitted substances. However, due to the nonlinearity and nonconvexity of the objective function, the optimization of CEED remains a challenge. In this paper, we develop a Reinforcement Learning-based Adaptive Differential Evolution (RLADE) algorithm to enhance the optimization performance. The mutation strategy and crossover probability of RLADE are optimized using Reinforcement Learning (RL) to respectively ensure better convergence speed and searchability. Additionally, two modifications of RL, namely the adaptive population size-based state division and fitness-ranking-based reward mechanism, are proposed to improve the accuracy of state division and reward calculation in RL. The experiments conducted in this paper consider two objective formulation methods of CEED problems, namely the quadratic and cubic criterion functions. The mean values and standard deviations of the obtained solutions were utilized to assess the performance of RLADE, as well as other comparative algorithms, namely DE algorithm and two RL-based DE variants. The results clearly demonstrate that RLADE surpasses its counterparts with proportion of 100%, 85.7%, and 100% for the 6-unit and 11-unit quadratic CEED problems, as well as cubic criterion functions, in terms of both search accuracy and convergence ability. Furthermore, the significance of RLADE's superiority is confirmed through the Wilcoxon's signed rank test. [ABSTRACT FROM AUTHOR]

Reducing the number of lower-level function evaluations (LFEs) is crucial to designing a bilevel evolutionary algorithm (BLEA) for bilevel optimization. Direct neighbor solution transfer (DST) is regularly used in BLEA because it can improve the lower-level search efficiency and reduce the number of LFEs. But this method still faces the challenge of misleading searches to make the algorithm converge to the wrong optimum. This paper proposes a bilevel improved multi-operator differential evolution algorithm (BL-IMODE) for bilevel optimization, which uses the knowledge transfer and adaptive coordinate systems approach. Specifically, this paper proposes a lower-level search knowledge transfer (LLS-KT) and a lower-level (LL) optimal solution distribution information transfer (LLO-DIT) mechanism to implement knowledge transfer. In LLS-KT, transferring LL solutions to the LL optimizer is similar to DST, but the LLS-KT transfers multiple solutions and thus has less possibility of misleading searches than DST. Moreover, the LLO-DIT transfers the LL optimal solution distribution information to the LL optimizer for generating promising offspring solutions. Since this method does not directly transfer LL solutions, it avoids misleading searches. Additionally, the adaptive coordinate systems (ACS) approach is used in two-level optimizers to suit different fitness landscapes and further reduce the number of LFEs. In ACS, three differential evolution mutation operators are produced in two coordinate systems. An adaptive strategy is used to select the suitable differential evolution mutation operator to generate promising offspring solutions in the Eigen coordinate or original coordinate system. Experimental studies on three test suites benchmark problems for comparison with seven state-of-the-art algorithms are conducted. The results show BL-IMODE has a significant advantage over the comparative algorithms. Finally, BL-IMODE is applied to tackle the inverse optimal control problem. • We propose a bilevel improved multi-operator differential evolution algorithm. • We propose a knowledge transfer approach to avoid misleading search. • We propose an adaptive coordinate systems approach to improve search efficiency. • We outperform all existing approaches in most test instances. [ABSTRACT FROM AUTHOR]

In this paper, we proposed a novel fitness-value-independent Differential Evolution to tackle complex real-parameter single-objective optimization. There were three innovations in the algorithm: First, dimension improvements based adaptation schemes for control parameters F and C R were advanced in this paper. Different from those fitness value improvements based parameter control in the recent winner DE variants, our algorithm has fitness-value-independent characteristic, therefore, it can be applied in much wider optimization scenarios especially for those that the exact fitness values of the objectives are unavailable. Second, a combined parabolic–linear reduction scheme for population size is employed in the algorithm based on the observation that the slower reduction of population size at the earlier stage of the evolution usually helps to get better perception of the objectives while a linear reduction of population size in the later stage helps to get better exploitation. Third, an indicator is proposed to monitor the diversity of the population and a corresponding population enhancement technique is launched when the diversity is detected bad. The first two innovations have the P arameter a daptive characteristic of the DE algorithm while the third innovation refers to p opulation e nhancement t echnique, therefore, we name our algorithm "the PaDE-pet algorithm". Then, the algorithm is validated under a larger test suite containing 88 benchmarks from CEC2013, CEC2014 and CEC2017 test suites for real-parameter single objective optimization, which may avoid over-fitting problem in comparison with employing a test suite containing a small number of benchmarks. The experiments support the superiority of the novel PaDE-pet algorithm in comparison with several recently proposed powerful DE variants. • A black-box model reflecting complex optimization without available fitness values. • The model reveals the fitness-value-dependent weakness of recent winner DE variants. • A novel fitness-value-independent DE algorithm was proposed to tackle the model. • New adaptation schemes for control parameters and population enhancement technique. • To avoid over-fitting, a larger test suite is employed in algorithm validation. [ABSTRACT FROM AUTHOR]

• An efficient radial-basis-function guided segmentation method is proposed to generate smooth and contiguous model partition based on surface attributes, which serves as the initial segmentation result. • A differential evolution based smoothing algorithm is introduced to optimize the cut interfaces of segmented parts constrained by the prescribed minimal printing thickness. • A refinement method for part extractability is designed to detect the infeasible segmented parts and compute division planes to further sub-divide them to ensure the extractability of all split parts. • The proposed technique is applied on a variety of models, and the experimental results shows its advantages over prior methods. Additionally, printed physical objects are provided as a proof of its reliability on current mainstream printers. [Display omitted] Volume segmentation based on surface attributes is an essential problem in multi-material fabrication and model packing. In practice, current mainstream fabrication techniques have difficulties in yielding models with diverse surface attributes in one pass owing to their craft limitations, making model segmentation a sensible choice for model realization. Partitioning 3D objects into single-attribute volumetric parts prevents fabricating models with different material in a single printing procedure, whereas the arisen challenge is to determine a reliable segmentation solution that is able to handle complicated models in various use scenarios. To achieve this goal, we propose a novel volume partition algorithm generating feasible volumetric parts, each of which is affiliated with one single surface attribute. Our technique enables model segmentation with least conflict and constrained wall thickness so that each volumetric segment can be realized independently by 3D-printing. Generally, it starts with computing a partition proposal guided by radial-based-function iso-surface, then optimizes segmentation interface with a prescribed minimal printing thickness to produce high-quality surface for every volumetric part, and finally splits unextractable volumetric parts into smaller sub-volumes to ensure assemblability of the whole model. As previous methods do not work well in optimizing segment interface for printing, we propose a differential evolution based smoothing algorithm to generate smooth and continuous interface, declining the risk of collision between adjacent volumetric parts. Extensive experimental results are provided in this paper to demonstrate the effectiveness and quality of our proposed technique, showing its advantages on model manufacture over prior methods. [ABSTRACT FROM AUTHOR]

In this study, an energy efficiency study has been carried out through the moment values of a quadrotor applied in the position control with the differential evolution algorithm (DE), which is under the evolutionary algorithms among meta-heuristic algorithms particle swarm optimization (PSO) which is among swarm-based algorithms and gravity search algorithm (GSA) among physics-based algorithms and charged system search (CSS) algorithm, which are all well-known in the literature. The efficient use of energy in electrically powered flying mechanisms is important in terms of completing its task. The aim of this study is to obtain proportional–integral–derivative (PID) coefficients that minimize the energy consumption caused by quadrotor moments. First of all, 12 PID coefficients calculated with traditional Ziegler Nicholes, and trying-error methods for the control of the quadrotor have been trained with DE, PSO, GSA and CSS algorithms and their cost values have been found for this problem. In the study, optimum PID coefficients have been found separately with each algorithm and torque data giving energy efficiency have been obtained by applying them to the state equations. Although the cost minimization convergence value obtained from DE does not look good compared to other algorithms, it has been observed that the moment values of the obtained PID coefficients in the control program are lower. In the study, it has been shown that the PID coefficients obtained from DE reach the target with approximately less energy than the maximum-moment value of the PSO, which provides the closest moment value. It can be thought that this value contributes to energy consumption in each orbital movement of the quadrotor. The simulation results show that the coefficients obtained from DE provide better energy efficiency and are superior to other algorithms compared in terms of energy efficiency. • PID coefficients for quadrotor control are optimized with DE,PSO,CSS,GSA algorithms • The torque values to be applied to each motor were adjusted with these coefficients • The total force applied with DEPID in the z direction is smaller than others • DEPID consumes less energy than the other algorithms in the paper [ABSTRACT FROM AUTHOR]

Differential evolution is one of the most powerful stochastic real-parameter optimization algorithms currently, and its performance depends heavily on control parameters and mutation strategy. In recent years, methods to select favorable parameters control and mutation strategy when solving various optimization problems have attracted increasing attention. To choose an appropriate mutation strategy and control parameters for a given optimization problem, in this paper, a Adaptive Differential Evolution Algorithm Based on Deeply-Informed Mutation Strategy and Restart Mechanism (ADEDMR) is proposed, and the ADEDMR algorithm has the following characteristics: First, a deeply-informed mutation strategy is proposed, which takes into account the information of suboptimal solutions discarded by selection and inherits the advantages of the powerful "DE/target-pbest/1/bin", aiming to obtain a better perceptual landscape of the target function and improve the candidate diversity of the trial vector. Second, according to the evolution process, the segmentation method is used to control F , which alleviates the scaling of F in the wrong direction, and makes the newly generated F fit more accurately. Third, a new population restart mechanism is adopted to further enhance population diversity by adaptively enhancing the search ability of hopeless individuals and randomly replacing some inferior individuals with wavelet walks. To evaluate the performance of our proposed algorithm, comparative experiments are conducted on 72 benchmark functions from the CEC2014, CEC2017 and CEC2022 test suites. Experimental results show that the proposed ADEDMR has higher convergence accuracy, better optimization ability when solving high-dimensional complex functions, and is competitive with six recent strong DE variants. [ABSTRACT FROM AUTHOR]

In this study, an energy efficiency study has been carried out through the moment values of a quadrotor applied in the position control with the differential evolution algorithm (DE), which is under the evolutionary algorithms among meta-heuristic algorithms particle swarm optimization (PSO) which is among swarm-based algorithms and gravity search algorithm (GSA) among physics-based algorithms and charged system search (CSS) algorithm, which are all well-known in the literature. The efficient use of energy in electrically powered flying mechanisms is important in terms of completing its task. The aim of this study is to obtain proportional–integral–derivative (PID) coefficients that minimize the energy consumption caused by quadrotor moments. First of all, 12 PID coefficients calculated with traditional Ziegler Nicholes, and trying-error methods for the control of the quadrotor have been trained with DE, PSO, GSA and CSS algorithms and their cost values have been found for this problem. In the study, optimum PID coefficients have been found separately with each algorithm and torque data giving energy efficiency have been obtained by applying them to the state equations. Although the cost minimization convergence value obtained from DE does not look good compared to other algorithms, it has been observed that the moment values of the obtained PID coefficients in the control program are lower. In the study, it has been shown that the PID coefficients obtained from DE reach the target with approximately less energy than the maximum-moment value of the PSO, which provides the closest moment value. It can be thought that this value contributes to energy consumption in each orbital movement of the quadrotor. The simulation results show that the coefficients obtained from DE provide better energy efficiency and are superior to other algorithms compared in terms of energy efficiency. • PID coefficients for quadrotor control are optimized with DE,PSO,CSS,GSA algorithms • The torque values to be applied to each motor were adjusted with these coefficients • The total force applied with DEPID in the z direction is smaller than others • DEPID consumes less energy than the other algorithms in the paper [ABSTRACT FROM AUTHOR]

Multi-UAV (unmanned aerial vehicle)-supported mobile edge computing system deploys multiple UAVs as flight edge clouds for large-scale users. In this system, how to optimize the deployment of UAVs is important for providing good service for all mobile users. Specifically, for each mobile user, we need to determine whether the task can be performed locally or on the drone (i.e., the unload decision) and how much resources should be allocated. In this paper, a new two-level optimization method is proposed for UAV deployment and task scheduling problem to minimize the system energy consumption. The proposed algorithm is named TSHGHSDE algorithm, in which a few features are designed to enhance the algorithm performance. Firstly, a two-stage optimization strategy is proposed based on HS-DE algorithm. In the early stage, HS algorithm is used for the local search in a limited space, and the DE algorithm is employed for the global search in the late stage. Secondly, we design an effective control parameter to adjust the search process, which aims to effectively combine the local search ability of HS algorithm and the global search ability of DE algorithm. Thirdly, a novel encoding mechanism is proposed in the process of the UAV deployment optimization. A global search strategy is designed to enhance the performance of the proposed algorithm. To assess the performance of the proposed algorithm, some well-known algorithms are used for comparison in experiments. The results demonstrate that the proposed algorithm performs better in terms of the search efficiency, search accuracy and stability. • A two-stage optimization strategy is proposed based on HS-DE algorithm. • An effective control parameter is designed to balance the local and global search ability. • A novel encoding mechanism is proposed in the process of the UAV deployment optimization. • A global search strategy is designed to enhance the performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In the phase-field model for fracture, material damage can be characterized by a variable called the crack phase-field. Usually-two sub-problems controlled by the equilibrium equation and the evolution equation, respectively, are needed to be solved in the whole domain. In this paper, an adaptive local algorithm is proposed for the unified phase-field model to solve the evolution equation in the local domain based on the fact that the value of phase-field is non-zero only around the crack. In the initial unified phase-field model, the boundedness and irreversibility conditions are not easy to be satisfied. In this paper, a history field is proposed to convert the inequality into equality in the evolution equation, and the boundedness and irreversibility conditions can be treated easily as in the classical phase-field model. To further obtain the local algorithm, some failure criteria are introduced to identify the damaged area, and the elements in the local domain are updated adaptively in each iteration step. The local algorithm can be implemented easily since the boundary conditions of the local domain are the same as in the non-local algorithm. Numerical examples have shown that the proposed local algorithm can obtain the same results as the non-local algorithm. [ABSTRACT FROM AUTHOR]

A Meta-evolutionary Selection of Constituents in Ensemble DE (MeSCEDE) framework is proposed in this paper to automate the design of high-level multi-population ensemble Differential Evolution (DE) algorithms. The automated design of high-level multi-population ensemble DE algorithms involves both automated selection of constituent DE algorithms for the ensemble and automated configuration of ensemble related parameters. Grammatical Evolution has been used as the meta-evolutionary algorithm in MeSCEDE to search the space of design choices so as to evolve effective ensemble design(s) for given problem(s). The simulation experiments carried out in this paper involve applying MeSCEDE to evolve ensemble DE designs for solving 30-dimensional CEC'17 benchmark functions. The effectiveness of the evolved designs are validated on 30 and 50-dimensional CEC'14 functions as well as on 22 real-world problem instances from CEC'11 benchmark suite. The MeSCEDE evolved designs have exhibited a competitive performance against state-of-the-art ensemble DE algorithms. In addition, the potential of MeSCEDE has been demonstrated against irace , a state-of-the-art algorithm configurator. All simulation experiments reiterate the potential of MeSCEDE towards evolving effective and robust ensemble DE designs. • Automated design of ensemble differential evolution (DE) algorithm is presented. • The proposed approach is Meta-evolutionary Selection of Constituents in Ensemble DE. • The approach uses grammatical evolution as the meta evolutionary algorithm. • The approach is demonstrated on CEC'17, CEC'14 and CEC'11 benchmark suites. • Relieves the practitioners from the difficult task of algorithm configuration. [ABSTRACT FROM AUTHOR]

This paper develops a robust strategy based on integrating three mutation phases and adapted control parameters into the Adaptive Guided Differential Evolution algorithm called (mAGDE) to improve diversity and exploration of the original AGDE. The mAGDE performance is evaluated using IEEE CEC'2020 test suite. Furthermore, the mAGDE is employed to identify the solid oxide fuel cell (SOFC) model optimal parameters. Two modes of SOFC operation are investigated, steady and transient states. The results obtained from the proposed mAGDE are compared with a number of recent, well-established and reputed meta-heuristics, including Particle swarm optimization, Teaching learning-based optimization, Whale optimization algorithm, Harris hawks optimization, Marine predators algorithm, Archimedes optimization algorithm, Differential evolution, and the original AGDE. Additionally, the statistical parameters that measure the performance of the proposed optimizer and the other competitors are calculated. The main finding demonstrated the preference and robustness of the suggested mAGDE in constructing the SOFC circuit that closely converges to the actual one. During the steady-state operation, the best fitness value obtained via the suggested mAGDE for operation at 1273 K is 2.2995E−06, while in the transient-state operation, the best SMSE is 1.04. The average cost function is decreased by 43.33% compared to the one obtained by the original AGDE. From the aforementioned assessments, it can be concluded that the proposed mAGDE is outstanding and promising. • This paper introduces a modified mAGDE based on the integration of a modified three-phases AGDE with the DE_SPA algorithm. • A modified three-phases AGDE has been introduced to maintain diversity and convergence of the evolutionary process. • The CEC'2020 test suite problems are used to demonstrate the performance mAGDE against other competitors. • Applying for first time mAGDE to identify the optimal parameters of SOFC model. • The robustness of the proposed strategy-based mAGDE is proved. [ABSTRACT FROM AUTHOR]

The population structure of differential evolution (DE) algorithm cannot maintain the diversity of the population to the greatest extent and help the population avoid to fall into the local optima in time. In this paper, a co-evolutionary multi-swarm adaptive differential evolution algorithm, namely ECMADE is proposed to solve the premature convergence and search stagnation. First of all, in terms of population structure, based on the parallel distributed framework, ECMADE randomly and evenly divides the population into exploration subpopulation, development subpopulation, and auxiliary subpopulation, and introduces an adaptive information exchange mechanism so that subpopulations can escape local optima in time. Then, a multi-operator parallel search strategy is proposed to keep population diversity and meet the optimization needs of different problems. Finally, an adaptive adjustment mechanism of control parameters is developed, through recent elite parameter archive and weight distribution to fully mine successful parameter information, and generate control parameters with a high success rate for the current evolutionary stage. In order to prove the effectiveness of the ECMADE, 10 test functions and portfolio optimization problem are selected in here. The experiment results show that the ECMADE can effectively solve these test functions, the accuracy and efficiency is superior to those of two classical DE algorithms. The actual application results show that the ECMADE can significantly improve the ability of portfolio to resist extreme losses, which proves the effectiveness and feasibility of the ECMADE once again. The ECMADE has better optimization performance by comparing with some well-known algorithms in term of the solution quality, robustness and space distribution. It provides a new algorithm for solving complex optimization problems. [ABSTRACT FROM AUTHOR]

The shape optimization of interpolation curves is a crucial and intractable technique in scientific visualization, data analysis, manufacturing and computer-aided design and is potentially used in many engineering fields involving geometric modeling. In this paper, an enhanced hybrid tunicate swarm algorithm (TSA) is used to optimize the shape of complex rational quartic interpolation spline (RQI-spline, for short) curves. Firstly, to modify the shape of the interpolation curve more flexibly, a novel multi-parameter RQI-spline curve with local and global shape parameters is presented. Then the corresponding combined RQI-spline curves with 2th-order parametric continuity denoted C 2 are constructed. In addition, considering that the optimization of shape parameters for RQI-spline curves is a complex optimization problem, an enhanced hybrid version of TSA called DQTSA is developed. The introduction of differential evolution and quadratic interpolation strategies enhances the ability of the TSA to jump out of local minima, thus effectively solving the shape parameter optimization of RQI-spline curves. DQTSA and some popular comparison algorithms are used to solve the set of 23 benchmark functions and CEC2019 test functions. The experimental results show that DQTSA performs the best in 7 (30.43%) of the 23 test problems, while DQTSA performs the best in 3 of the 10 CEC2019 suites. Meanwhile, applying DQTSA to three engineering optimization problems, the best value, mean and significantly better than other search algorithms are obtained from 20 optimized designs, which verifies the applicability and stability of DQTSA in solving engineering optimization problems. Finally, the proposed DQTSA is used to solve the shape optimization model for the combined C 2 RQI-spline curve. Numerical results find that DQTSA obtains the optimal RQI-spline curve with minimum energy. Some representative numerical examples illustrate that DQTSA is a potentially excellent algorithm for solving curve optimization. • A novel C2 rational quartic interpolation spline (RQI-spline, for short) curves are constructed. • An enhanced tunicate swarm algorithm called DQTSA is presented. • The superiority of DQTSA is verified by comparing with popular intelligent algorithms. • Shape optimization model of C2 RQI-spline curves is established. • The DQTSA algorithm is applied to the solutions of the established optimization model. [ABSTRACT FROM AUTHOR]

Multimodal multiobjective optimization problems (MMOPs) possess multiple equivalent Pareto optimal sets (PSs) corresponding to the same Pareto front (PF). Numerous multimodal multiobjective evolutionary algorithms (MMEAs) have been developed to solve MMOPs. However, how to locate multiple high quality equivalent PSs and obtain a uniformly distributed PF simultaneously remains a challenging task. This paper explores a novel multimodal multiobjective differential evolution algorithm, termed MMO_CDE, for solving MMOPs. In MMO_CDE, a neighborhood-based dual mutation strategy is proposed by developing two novel mutation operators. The two novel mutation operators provide a better tradeoff between exploration and exploitation in locating multiple equivalent PSs. In addition, a clustering-based environmental selection mechanism is designed by integrating an affinity propagation method. The affinity propagation method improves the distribution of solutions in decision and objective spaces, and a harmonic averaged distance is adopted to promote the diversity of a population. The proposed MMO_CDE is compared against state-of-the-art MMEAs on a test suite of CEC 2019 benchmark functions and a map-based practical application. Empirical results validate the superiority of the proposed MMO_CDE regarding locating multiple equivalent PSs and obtaining a well-distributed PF. • Propose a clustering differential evolution with neighborhood-based dual mutation. • Develop a neighborhood-based dual mutation for the proposed algorithm. • Develop a clustering-based environmental selection for the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we propose an improved version of JADE by h ybridizing the JADE algorithm with a G aussian t ail, a modified hunger games search (HGS) algorithm, and a distance-based multi-population (DbMP) approach named as HJADE-GT. In the proposed algorithm, two sets of operators (modified HGS operator and JADE operator with Gaussian tail) are utilized to generate offspring to further enhance the exploration and exploitation abilities. DbMP approach is proposed to make full use of feedback information from the whole population. In HJADE-GT, the main population is divided into three fixed-size subpopulations: exploration subpopulation, balanced subpopulation, and exploitation subpopulation. Secondly, a modified HGS operator is incorporated into the exploration subpopulation to improve global searchability. Thirdly, the JADE operator with a Gaussian tail is utilized to enhance the ability of exploitation subpopulation. Finally, the DbMP approach is utilized for the balanced subpopulation to choose an appropriate operator for current individuals to make full use of feedback information from the exploration subpopulation and exploitation subpopulation. In the experimental studies, it is demonstrated that the proposed algorithm presents competitive performance with 13 well-known algorithms, including jDE, SaDE, JADE, MPEDE, SHADE, CoDE, SaJADE, iLSHADE, jSO, CMAES, MGFPA, ESSA, and PPSO on CEC2017 benchmark functions. Four engineering problems and three dynamic economic emission dispatch (DEED) problems were utilized to verify the performance of HJADE-GT, and the experiments on DEED problems confirm that HJADE-GT is an efficient algorithm to solve engineering and large-scale constrained DEED problems. [ABSTRACT FROM AUTHOR]

Driver pathways have been acknowledged to play critical roles in the initiation and progression of cancers►hence it is essential for precision medicine related studies to develop accurate and efficient methods to identify them. Although previous approaches have shown promising results by integrating multi-omics data, their preset artificial parameters may decrease the convenience to use and limit the application scalability. In this paper, a novel integration approach is proposed to incorporate four omics data, i.e., construct a weighted non-binary mutation matrix without presetting artificial parameters. A parameter-free identification model is put forward based on it. It takes advantage of the association between genes in the PPI network as well as balances the contribution of coverage and mutual exclusivity with the harmonic mean. Furthermore, a cooperative co-evolution algorithm is proposed for solving this model. In the algorithm, a particle swarm optimization algorithm suitable for solving combinatorial problems is presented. Three cooperative operators are devised to construct the cooperation among the populations and the swarm to increase the population diversity. Both real biological datasets and simulated ones were exerted to perform experimental comparisons among the proposed method and six other state-of-the-art ones. The gene sets identified by the presented method generally contain more genes involved in known signaling pathways than those obtained by the other methods. Simultaneously, both high accuracy and high efficiency of the proposed method were verified in experiments, making it practical in realistic applications and an effective supplementary tool to identify driver pathways. • A non-binary mutation matrix is constructed without artificial adjustable parameters. • The model incorporates gene association and balances coverage and mutual exclusivity. • A PSO algorithm suitable for solving combinatorial problems is presented. • A co-operative co-evolution algorithm is put forward for solving the presented model. • The performance is compared among the proposed method and seven state of the art ones. [ABSTRACT FROM AUTHOR]

• The optimal mass design of the nonlinear energy sink is proposed. • The relations between damping and optimal mass of NESs is revealed. • The advantages of mass design of the bistable nonlinear energy sink are found. Nonlinear energy sink (NES) is attracting more attention because of its promising in the control of engineering structure vibration. This paper thoroughly reviews the selection of NES mass ratios in existing studies and finds the big difference. So there is still a lack of a unified and profound understanding of the mass design of the NES. To achieve decent vibration mitigation and reduce costs, the mass design of the NES is essential. This paper pioneers the optimal mass design of NESs. The non-dominated sorting differential evolution algorithm and parameter sensitivity analysis are adopted. The relations between the optimal mass and the vibration mitigation effects are discussed in different damping and harmonic excitation strength. The results show that different from the monostable NES, the bistable NES with a small mass ratio (no more than 0.7%) and small damping can reduce 30% of the resonance peak of the primary system in most situations. However, both these two NESs with large damping need larger mass ratios to achieve decent vibration mitigation. Smaller damping of the primary system will contribute to wider effective ranges of the mass ratio of the two NESs, while larger excitation will contribute to those of the monostable NES. To ensure the vibration mitigation effects in small mass ratio, the monostable and bistable NESs with small damping need large and small cubic stiffness, respectively. Besides, the bistable NES with small damping prefers small negative linear stiffness. In summary, this paper presents a detailed study of the mass design of the nonlinear energy sink. It will help researchers and engineers find the suitable mass and design NES in the vibration reduction of engineering structures. [ABSTRACT FROM AUTHOR]

In imperialist competition algorithm (ICA), the assimilation is an important step, which is responsible for exploring potential better position or solution for an optimization problem. In this paper, an improved ICA equipped with an adaptive differential mutation (ADM) assimilation strategy was proposed inspired by differential evolution (DE). The proposed algorithm is called ICA-ADM. The ADM assimilation strategy generates new positions for colonies in an empire using the "DE/best/1" mutation operator and crossover operator with adaptively varied mutation and crossover rate. Since the "DE/best/1" mutation and crossover can produce high quality solutions, ICA-ADM possesses good exploration capability. Meanwhile, since the mutation and crossover rates are adaptively varied, ICA-ADM also preserves a good population diversity. Thus, the performance of ICA-ADM is greatly increased. Optimization results on 16 well-known benchmark functions and comparisons verify that the proposed ICA-ADM exceeds the initial ICA and its several variants. • A new assimilation method was proposed for imperialist competitive algorithm. • The method generates new position using "DE/best/1" mutation and crossover operator. • The method has better global searching capability. • The method can maintain a good population diversity. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) algorithm is popular to tackle real-world optimization problems. The standard DE, however, is not able to solve constrained optimization problems (COPs) for their complicated linear or nonlinear constraints. The transformation of constraints, which is realized via constraint handling technique, has a great impact on dealing with constrained algorithms. In this paper, a lightweight and efficient variant of DE named C ε -LDE is proposed to solve constrained single-objective optimization problems. This study firstly introduces a combined constraint handling method, which is designed based on the difference and relationship between two different ε constrained methods and balances infeasible solution and feasible solution with rules from the perspective of probability allocation. In addition, an extra control parameter is redefined in terms of different initial ε level in consideration of the complexity and diversity of COPs. On the other hand, DE evolves by opposition-based learning initialization and modifications on mutation operator and crossover rate selection, respectively. Mutation strategies frequently named rand/1 and best/1 are adopted and Lévy flight is added to the mutation strategy as a multiplier with scale factor F for a long jump. The crossover rate CR tends to be a larger or smaller stochastic value according to the pros and cons of the selected vector. A set of 28 problems under different dimension settings (D = 10, 30, 50 and 100) used for the CEC 2017 Competition is employed to evaluate the performance of the proposed C ε -LDE. The computational results demonstrate the effectiveness and superiority of the proposed combined ε constrained method. A comparative study of C ε -LDE with state-of-art algorithms is conducted on the obtained experimental results under the rules of CEC 2017 Competition. The ranking outcomes reveal that C ε -LDE is equipped with high competitiveness. Furthermore, the applications in several standard real-life engineering problems verify the effectiveness and practicability of the proposed scheme. [ABSTRACT FROM AUTHOR]

• Optimal foraging algorithm with direction prediction & Gaussian oscillation is built. • New algorithm includes two update methods: prediction model and random model. • Prediction model mends exploitation ability by predicting the evolutionary direction. • Random model mends exploration by exploring the space with Gaussian distribution. • The superiority of algorithm is verified on benchmark set and engineering problems. Optimal foraging algorithm (OFA) is a newly stochastic optimization technique and is famous for its computational accuracy. However, the high computational accuracy leads to slow convergence speed. Experimental results demonstrate that OFA is good at unimodal functions but poor at multimodal functions. To improve these drawbacks, in this paper a novel modified OFA with direction prediction and Gaussian oscillation, named OFA/P&G is introduced. In OFA/P&G, a transition matrix is constructed when a new global optimum is found to generate the candidate individuals. If the current global optimum does not change, the Gaussian oscillation is employed in a low probability and OFA update method is used in a high probability to generate the candidate individuals. The superior performance of OFA/P&G is verified on the 12 CEC2017 benchmark functions, 13 constrained benchmark functions and 5 engineering problems. Experimental results demonstrate that OFA/P&G outperforms other comparative algorithms. Finally, a real-world problem, drilling path optimization, is solved by OFA/P&G. [ABSTRACT FROM AUTHOR]

• The proposed method can be applied for any non-linear ECM without pre-assumptions. • Parameters identification of battery was transformed into a LSOP. • A new m -decomposition method allots R 0 , R P and C P overlapped to each group. Parameters identification of battery is a significant task for lithium-ion batteries. Some widely used techniques usually simplify the electrical circuit model (ECM) with non-linearity to a linear model or local linear model. However, by using such a methodology, the parameters in ECMs are not globally optimal, since the parameters may be not consistent at different linearized points. To address this issue, this paper proposed a cooperative co-evolution differential evolution (CCDE) algorithm to identify parameters of lithium-ion battery, without any linearization or pre-assumption. First, to describe the dynamic behaviors of battery, we presented a first-order RC equivalent circuit model ECM. Without making any approximation, improved Euler's numerical method was utilized to solve the differential equations directly. Second, an optimizing objective function was built to minimize errors between the true and optimized terminal voltages. In that optimization model, parameters of battery (R 0 , R P and C P) and v OCV (t) at each sampling point were considered as variables to be optimized, resulting in a very high-dimension problem. Third, such an optimization problem was transformed into a large scale optimization problem (LSOP). Based on the character of parameters identification, we proposed a new m -decomposition method which is different from general grouping methods for benchmark functions and its corresponding differential evolution (DE) algorithm to solve this LSOP. Comprehensive experimental results demonstrated effectiveness of the proposed framework and methodology, compared with seven state-of-the-art cooperative co-evolution methods. [ABSTRACT FROM AUTHOR]

Search-based algorithms are a recent research hotspot for solving path coverage (PC), which is the most critical and challenging problem in the field of automated test case generation (ATCG). There remains a large research space for achieving ATCG-PC's goal of finding a set of test cases covering all possible paths with as little computational overhead as possible. In contrast to two existing research approaches of testing different search-based algorithms and developing different fitness functions, this paper proposes two learning strategies based on a hypercube (termed HBL and THBL), which are inspired by a problem-specific knowledge expressed by the mathematical formulas of different fitness functions for ATCG-PC. The hypercubes of HBL and THBL are developed via an opposition-based learning strategy around the current best solution. The two learning strategies can guide search-based algorithms to search for test cases that cover uncovered paths. Two improved differential evolutionary algorithms based on HBL and THBL are then proposed to solve ATCG-PC. Experimental studies on thirty instances generated by eight classical benchmark programs and six fog computing benchmark programs show that the proposed algorithms achieve highest path coverage with fewer test cases and less running time than some compared state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

Land readjustment and redistribution (LR) is an important approach used to realize development plans by converting rural lands to urban land and also providing urban infrastructure. The LR problem, which is a complex challenging real-world problem, is a discrete optimization problem because its structure is similar to TSP (Traveling Salesman Problem) and scheduling problems which are combinatorial optimization problems. Since classical mathematical methods are insufficient for solving NP (Nondeterministic Polynomial) optimization problems due to time limitations, meta-heuristic optimization algorithms are commonly utilized for solving these kinds of problems. In this paper, meta-heuristic algorithms including genetic, particle swarm, differential evolution, artificial bee, and tree seed algorithms are utilized for solving LR problems. The stated meta-heuristic algorithms are used by applying spatial-based crossover and mutation operators depending upon the LR problem on each algorithm. Moreover, a synthetic dataset is used to ensure that the quality of the solution obtained is acceptable to everyone, to prove an optimal solution easily. By utilizing the suggested spatial-based crossover and mutation operators, finding the ideal solution is aimed using the synthetic dataset. In addition, five different modifications on TSA (Tree-Seed Algorithm) are performed and used to solve LR problems. All the modified versions of TSA are carried out only by changing the mechanism of seed reproduction. The novel TSA approaches are respectively named as tcTSA (tournament current), tbTSA (tournament best), pbTSA (personal-best based), t2TSA (double tournament), and elTSA (elitism based). In the experimental studies, the hybrid approach, which includes the crossover and mutation operators, is successfully applied in all of the algorithms under equal conditions for a fair comparison. According to experimental results performed using the dataset, it can be clearly stated that especially t2TSA outperforms all the algorithms in terms of performance and time. [ABSTRACT FROM AUTHOR]

The performance of photovoltaic (PV) cell is affected by the model structure and corresponding parameters. However, these parameters are adjustable and variable, which play an available role in regarding to the efficiency and effectiveness of PV generation. Due to strong non-linear characteristics, existing PV model parameters identification methods cannot easily obtain accurate solutions. To tackle this, this paper proposes an adaptive differential evolution algorithm with the dynamic opposite learning strategy (DOL), named DOLADE. In DOLADE, the opposite learning method expands the current elite population and the population of poor performance, improving the particles' exploration capability. In the process of particles work, the searching area of particles is adjusting dynamically so that the particles' exploitation capability is enhanced. The experimental data of different types of PV are tested, respectively. Three PV models are used to verify the new strategy's accuracy and effectiveness. The proposed DOLADE is compared with several general advanced algorithms, and comprehensive experimental results are demonstrated. The results illustrate that DOLADE well extracts optimal parameters for each PV cell model and brought great competition in terms of accuracy, reliability, and computational efficiency in solving the problem. • Differential evolution variant is proposed to estimate the photovoltaic models' parameter. • Dynamic opposite learning strategy aims to improve exploration and exploitation abilities. • The proposed method is tested under various experimental data and cases. • A series of experimental results indicate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The extremely sensitive and highly non-linear search space of interplanetary transfer trajectory design brings about big challenges on global optimization. As a representative, the current known best solution (fuel consumption) of the global trajectory optimization problem designed by the European space agency is very hard to be found. To deal with this difficulty, a powerful differential evolution with the guided movement for population, named G_DE is proposed in this paper. G_DE employs a two-stage evolutionary process, which concentrates on learning global structure in the earlier process, and tends to self-adaptively probe the structures of numerous local spaces at a later stage. During these two stages, four guidance strategies related to the learning from the population distribution are proposed. The experimental test results show that G_DE can find the current known best solutions of Cassini1 and Sagas directly. For the newly proposed GTOP-X problem, G_DE has found state-of-the-art solutions for four encounter sequences, and using five gravity assists, G_DE found encounter sequences with fuel consumption as low as 1.5676 km/s. The experimental test on 10D CEC2017 problems proves G_DE has a comparable performance with recently proposed differential evolution variant. [ABSTRACT FROM AUTHOR]