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This document is a special issue of the journal Algorithms, featuring selected papers from the journal's editorial board members from 2022 and 2023. The issue includes 16 research papers covering a range of topics such as game theory, fault detection in cellular networks, optimization algorithms, machine learning, cryptocurrency trading, and more. Each paper presents its own unique research findings and methodologies. The issue aims to showcase the diverse research interests and expertise of the journal's editorial board members. [Extracted from the article]

In this paper we present the Markovian Multiagent Monte-Carlo Second Order Self-Consistent Field Algorithm (M3-SOSCF). This algorithm provides a highly reliable methodology for converging SCF calculations in single-reference methods using a modified differential evolution approach. Additionally, M3 is embarrassingly parallel and modular in regards to Newton–Raphson subroutines. We show that M3 is able to surpass contemporary SOSCFs in reliability, which is illustrated by a benchmark employing poor initial guesses and a second benchmark with SCF calculations which face difficulties using standard SCF algorithms. Furthermore, we analyse inherent properties of M3 and show that in addition to its robustness and efficiency, it is more user-friendly than current SOSCFs. [ABSTRACT FROM AUTHOR]

Differential Evolution (DE) is widely recognized as a highly effective evolutionary algorithm for global optimization. It has proven its efficacy in tackling diverse problems across various fields and real-world applications. DE boasts several advantages, such as ease of implementation, reliability, speed, and adaptability. However, DE does have certain limitations, such as suboptimal solution exploitation and challenging parameter tuning. To address these challenges, this research paper introduces a novel algorithm called Enhanced Binary JADE (EBJADE), which combines differential evolution with multi-population and elites regeneration. The primary innovation of this paper lies in the introduction of strategy with enhanced exploitation capabilities. This strategy is based on utilizing the sorting of three vectors from the current generation to perturb the target vector. By introducing directional differences, guiding the search towards improved solutions. Additionally, this study adopts a multi-population method with a rewarding subpopulation to dynamically adjust the allocation of two different mutation strategies. Finally, the paper incorporates the sampling concept of elite individuals from the Estimation of Distribution Algorithm (EDA) to regenerate new solutions through the selection process in DE. Experimental results, using the CEC2014 benchmark tests, demonstrate the strong competitiveness and superior performance of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In the era of e-commerce, accurately predicting user purchase intentions has become a crucial factor for enhancing sales efficiency and optimizing the customer experience. Addressing the limitations of traditional ensemble strategies, which often suffer from subjective biases during the model design phase, this paper introduced an adaptive evolutionary ensemble learning model to predict user purchase intentions. This model adaptively selected the optimal base learners and meta-learners, incorporating both the predictive information from the base learners and the differential information between features to expand the feature dimensions, enhancing prediction accuracy. Moreover, to further refine the predictive capabilities of the model, this paper designed a binary adaptive differential evolution algorithm for feature selection, aiming to identify features that significantly influence the prediction outcome. Research results show that the binary adaptive differential evolution algorithm outperforms traditional optimization algorithms in global searches and feature selection. Compared to six common ensemble models and the DeepForest model, the proposed evolutionary ensemble model achieves a 2.76% and 2.72% increase in AUC value, respectively, and effectively mitigates the impacts of data imbalance [ABSTRACT FROM AUTHOR]

This paper proposes a novel multi-hybrid algorithm named DHPN, using the best-known properties of dwarf mongoose algorithm (DMA), honey badger algorithm (HBA), prairie dog optimizer (PDO), cuckoo search (CS), grey wolf optimizer (GWO) and naked mole rat algorithm (NMRA). It follows an iterative division for extensive exploration and incorporates major parametric enhancements for improved exploitation operation. To counter the local optima problems, a stagnation phase using CS and GWO is added. Six new inertia weight operators have been analyzed to adapt algorithmic parameters, and the best combination of these parameters has been found. An analysis of the suitability of DHPN towards population variations and higher dimensions has been performed. For performance evaluation, the CEC 2005 and CEC 2019 benchmark data sets have been used. A comparison has been performed with differential evolution with active archive (JADE), self-adaptive DE (SaDE), success history based DE (SHADE), LSHADE-SPACMA, extended GWO (GWO-E), jDE100, and others. The DHPN algorithm is also used to solve the image fusion problem for four fusion quality metrics, namely, edge-based similarity index ( Q A B / F ), sum of correlation difference (SCD), structural similarity index measure (SSIM), and artifact measure ( N A B / F ). The average Q A B / F = 0.765508 , S C D = 1.63185 , S S I M = 0.726317 , and N A B / F = 0.006617 shows the best combination of results obtained by DHPN with respect to the existing algorithms such as DCH, CBF, GTF, JSR and others. Experimental and statistical Wilcoxon's and Friedman's tests show that the proposed DHPN algorithm performs significantly better in comparison to the other algorithms under test. [ABSTRACT FROM AUTHOR]

This paper proposes the Love Evolution Algorithm (LEA), a novel evolutionary algorithm inspired by the stimulus–value–role theory. The optimization process of the LEA includes three phases: stimulus, value, and role. Both partners evolve through these phases and benefit from them regardless of the outcome of the relationship. This inspiration is abstracted into mathematical models for global optimization. The efficiency of the LEA is validated through numerical experiments with CEC2017 benchmark functions, outperforming seven metaheuristic algorithms as evidenced by the Wilcoxon signed-rank test and the Friedman test. Further tests using the CEC2022 benchmark functions confirm the competitiveness of the LEA compared to seven state-of-the-art metaheuristics. Lastly, the study extends to real-world problems, demonstrating the performance of the LEA across eight diverse engineering problems. Source codes of the LEA are publicly available at https://ww2.mathworks.cn/matlabcentral/fileexchange/159101-love-evolution-algorithm. [ABSTRACT FROM AUTHOR]

Community structure is a very interesting attribute and feature in complex networks, which has attracted scholars' attention and research on community detection. Many single-objective optimization algorithms have been migrated and modified to serve community detection problems. Due to the limitation of resolution, the final algorithm implementation effect is not ideal. In this paper, a multi-objective community detection method based on a pigeon-inspired optimization algorithm, MOPIO-Net, is proposed. Firstly, the PIO algorithm is discretized in terms of the solution space representation, position, and velocity-updating strategies to adapt to discrete community detection scenarios. Secondly, by minimizing the two objective functions of community score and community fitness at the same time, the community structure with a tight interior and sparse exterior is obtained. Finally, for the misclassification caused by boundary nodes, a mutation strategy is added to improve the accuracy of the final community recognition. Experiments on synthetic and real networks verify that the proposed algorithm is more accurate in community recognition compared to 11 benchmark algorithms, confirming the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The optimal operation of reservoir groups is a strongly constrained, multi-stage, and high-dimensional optimization problem. In response to this issue, this article couples the standard Pelican optimization algorithm with adaptive ε constraint methods, and further improves the optimization performance of the algorithm by initializing the population with a good point set, reverse differential evolution, and optimal individual t-distribution perturbation strategy. Based on this, an improved Pelican algorithm coupled with adaptive ε constraint method is proposed (ε-IPOA). The performance of the algorithm was tested through 24 constraint testing functions to find the optimal ability and solve constraint optimization problems. The results showed that the algorithm has strong optimization ability and stable performance. In this paper, we select Sanmenxia and Xiaolangdi reservoirs as the research objects, establish the maximum peak-cutting model of terrace reservoirs, apply the ε-IPOA algorithm to solve the model, and compare it with the ε-POA (Pelican algorithm coupled with adaptive ε constraint method) and ε-DE (Differential Evolution Algorithm) algorithms, the results indicate that ε. The peak flow rate of the Huayuankou control point solved by the IPOA algorithm is 12,319 m3/s, which is much lower than the safe overflow flow rate of 22,000 m3/s at the Huayuankou control point, with a peak shaving rate of 44%, and other algorithms do not find effective solutions meeting the constraint conditions. This paper provides a new idea for solving the problem of flood control optimal operation of cascade reservoirs. [ABSTRACT FROM AUTHOR]

In response to the low efficiency and poor quality of current seed optimization algorithms for multi-threshold image segmentation, this paper proposes the utilization of the normal distribution in the cluster distribution mathematical model, the Levy flight mechanism, and the differential evolution algorithm to address the deficiencies of the seed optimization algorithm. The main innovation lies in applying the BBO algorithm to image multi threshold segmentation, providing a new perspective and method for image segmentation tasks. The second significant progress is the combination of Levy flight dynamics and differential evolution algorithm (DEA) to improve the BBO algorithm, thereby enhancing its performance and image segmentation quality. Therefore, a multi-threshold image segmentation model based on the optimized seed optimization algorithm is developed. The experimental results showed that on the function f1, the iteration of the improved seed optimization algorithm was 53, the Generational Distance value was 0.0020, the Inverted Generational Distance value was 0.098, and the Spacing value was 0.051. Compared with the other two algorithms, the improved seed optimization algorithm has better image segmentation performance and clearer image segmentation details. In summary, compared with existing multi-threshold image segmentation methods, the proposed multi-threshold image segmentation model based on the improved seed optimization algorithm has a better image segmentation effect and higher efficiency, can significantly improve the quality of image segmentation, has positive significance for the development of image processing technology, and also provides references for the improvement and application of optimization algorithms. [ABSTRACT FROM AUTHOR]

Metaheuristics are commonly employed as a means of solving many distinct kinds of optimization problems. Several natural-process-inspired metaheuristic optimizers have been introduced in the recent years. The convergence, computational burden and statistical relevance of metaheuristics should be studied and compared for their potential use in future algorithm design and implementation. In this paper, eight different variants of dragonfly algorithm, i.e. classical dragonfly algorithm (DA), hybrid memory-based dragonfly algorithm with differential evolution (DADE), quantum-behaved and Gaussian mutational dragonfly algorithm (QGDA), memory-based hybrid dragonfly algorithm (MHDA), chaotic dragonfly algorithm (CDA), biogeography-based Mexican hat wavelet dragonfly algorithm (BMDA), hybrid Nelder-Mead algorithm and dragonfly algorithm (INMDA), and hybridization of dragonfly algorithm and artificial bee colony (HDA) are applied to solve four industrial chemical process optimization problems. A fuzzy multi-criteria decision making tool in the form of fuzzy-measurement alternatives and ranking according to compromise solution (MARCOS) is adopted to ascertain the relative rankings of the DA variants with respect to computational time, Friedman's rank based on optimal solutions and convergence rate. Based on the comprehensive testing of the algorithms, it is revealed that DADE, QGDA and classical DA are the top three DA variants in solving the industrial chemical process optimization problems under consideration. [ABSTRACT FROM AUTHOR]

This paper extends our previous algorithm, termed as Particle Swarm Optimization with Distributed Acceleration Constants (PSODAC), which has been introduced for mitigating congestion based on rescheduling in a deregulated environment. The proposed variant adopts a sequential hybridization of the PSODAC principle with Differential Evolution, which is a well-known evolutionary algorithm. The variant in this paper is termed as Sequentially Hybridized Differential Evolution with Particle Swarm Optimization (SH-DEPSO). The experimental investigations are carried out in the IEEE 14 bus system in two scenarios namely, single point congestion and multipoint congestion. Firstly, the performance investigation is carried out on mitigating the congestion using cost analysis, stability analysis, complexity analysis, and strategy analysis. Secondly, the characteristics of the algorithm are observed by performing convergence analysis and investigating the quality of the solution dynamics. The studies demonstrate the competing performance of SH-DEPSO over PSODAC and the traditional PSO. [ABSTRACT FROM AUTHOR]

The optimal operation of reservoir groups is a strongly constrained, multi-stage, and high-dimensional optimization problem. In response to this issue, this article couples the standard Pelican optimization algorithm with adaptive ε constraint methods, and further improves the optimization performance of the algorithm by initializing the population with a good point set, reverse differential evolution, and optimal individual t-distribution perturbation strategy. Based on this, an improved Pelican algorithm coupled with adaptive ε constraint method is proposed (ε-IPOA). The performance of the algorithm was tested through 24 constraint testing functions to find the optimal ability and solve constraint optimization problems. The results showed that the algorithm has strong optimization ability and stable performance. In this paper, we select Sanmenxia and Xiaolangdi reservoirs as the research objects, establish the maximum peak-cutting model of terrace reservoirs, apply the ε-IPOA algorithm to solve the model, and compare it with the ε-POA (Pelican algorithm coupled with adaptive ε constraint method) and ε-DE (Differential Evolution Algorithm) algorithms, the results indicate that ε. The peak flow rate of the Huayuankou control point solved by the IPOA algorithm is 12,319 m3/s, which is much lower than the safe overflow flow rate of 22,000 m3/s at the Huayuankou control point, with a peak shaving rate of 44%, and other algorithms do not find effective solutions meeting the constraint conditions. This paper provides a new idea for solving the problem of flood control optimal operation of cascade reservoirs. [ABSTRACT FROM AUTHOR]

With the rapid development of the geometric modeling industry and computer technology, the design and shape optimization of complex curve shapes have now become a very important research topic in CAGD. In this paper, the Hybrid Artificial Hummingbird Algorithm (HAHA) is used to optimize complex composite shape-adjustable generalized cubic Ball (CSGC–Ball, for short) curves. Firstly, the Artificial Hummingbird algorithm (AHA), as a newly proposed meta-heuristic algorithm, has the advantages of simple structure and easy implementation and can quickly find the global optimal solution. However, there are still limitations, such as low convergence accuracy and the tendency to fall into local optimization. Therefore, this paper proposes the HAHA based on the original AHA, combined with the elite opposition-based learning strategy, PSO, and Cauchy mutation, to increase the population diversity of the original algorithm, avoid falling into local optimization, and thus improve the accuracy and rate of convergence of the original AHA. Twenty-five benchmark test functions and the CEC 2022 test suite are used to evaluate the overall performance of HAHA, and the experimental results are statistically analyzed using Friedman and Wilkerson rank sum tests. The experimental results show that, compared with other advanced algorithms, HAHA has good competitiveness and practicality. Secondly, in order to better realize the modeling of complex curves in engineering, the CSGC–Ball curves with global and local shape parameters are constructed based on SGC–Ball basis functions. By changing the shape parameters, the whole or local shape of the curves can be adjusted more flexibly. Finally, in order to make the constructed curve have a more ideal shape, the CSGC–Ball curve-shape optimization model is established based on the minimum curve energy value, and the proposed HAHA is used to solve the established shape optimization model. Two representative numerical examples comprehensively verify the effectiveness and superiority of HAHA in solving CSGC–Ball curve-shape optimization problems. [ABSTRACT FROM AUTHOR]

The multiple knapsack problem（MKP） is a special knapsack problem with great difficulty. In order to solve MKP by differential evolution（DE）, this paper first established the integer programming model of MKP. Based on a simple and efficient new transfer function based on modulo operation, it proposed a novel discrete differential evolution algorithm MODDE. Then, the method used an efficient algorithm GROA to eliminate the unfeasible solution of MKP by greedy strategy. Therefrom, this paper proposed a new method for solving MKP based on MODDE. Finally, it used MODDE to solve 30 international instances of MKP. Comparing with 4 representative evolution algorithms shows that MODDE not only has better calculation results; but also has stronger stability. It is indeed an efficient algorithm for solving MKP [ABSTRACT FROM AUTHOR]

The traditional differential evolution（DE） algorithm balanced global exploration and local exploitation inadequately, and had problems with easily falling into local optimal solutions, low solution accuracy and slow convergence speed. Therefore, this paper proposed a differential evolution algorithm based on random neighborhood mutation and optimal opposition-based learning（RNODE） and analyzed for its complexity. Firstly, the algorithm generated a random neighborhood for each individual in the current population, and used the global best individual to guide the neighborhood best individual to generate a composite basis vector, combined with an adaptive update mechanism of the control parameters to constitute a random neighborhood mutation strategy, which enabled the algorithm maintained its exploration ability and guided the population towards the optimal direction. Secondly, to further help the algorithm jump out of the local optimum, the algorithm performed the optimal opposition-based learning strategy on the poorer individuals to expand the search area. Finally, this paper compared RNODE with 9 algorithms to verify the effectiveness and advancement of RNODE. The experimental results on 23 benchmark functions and 2 real-world engineering optimization problems show that the RNODE algorithm has a higher convergence accuracy, faster speed and a greater stability. [ABSTRACT FROM AUTHOR]

Among the indoor localization algorithms, the algorithm based on traditional Back Propagation Neural Network (BPNN) has the problems of slow convergence and easy to fall into local optimum. It is difficult to apply the algorithm in noisy environments. Therefore, in this paper, we propose a novel indoor localization algorithm where the whole localization process is divided into two parts: data preprocessing and localization output. Data preprocessing means using filtering algorithm to process the Received Signal Strength Indication (RSSI) sequence. It is considered that the initial value of the received sequence has a significant impact on the performance of Kalman Filter (KF). An improved Kalman Filtering algorithm (DBSCAN-KF) is proposed based on the Density-Based Spatial Clustering of Applications with Noise (DBSCAN) algorithm. First, the RSSI values that are seriously disturbed by noise in the sequence are removed using the DBSCAN algorithm, and then the RSSI sequences are processed using KF so that the RSSI values can be closer to the theoretical values. The localization output part is to reduce the localization error caused by the BPNN. In this paper, the Differential Evolution (DE) algorithm and Particle Swarm Optimization (PSO) algorithm are combined, and the Differential Evolution Particle Swarm Optimization (DE-PSO) algorithm is proposed. The BPNN weights and thresholds are optimized in parallel, which improves the speed and ability of global optimization search and further avoids the shortcomings of traditional BPNNs that are prone to fall into local optimization in the training process. Experimental results show that the BPNN localization algorithm based on DBSCAN-KF improves the average localization accuracy by 0.26m compared with the BPNN localization algorithm without filtering. After filtering, the localization algorithm based on DE-PSO improved BPNN (DE-PSO-BP) improves the average localization accuracy by about 24% compared with the localization algorithm based on DE-PSO-BP. The localization algorithm based on DE-PSO-BP improves the average localization accuracy by about 61% compared with the traditional BPNN. [ABSTRACT FROM AUTHOR]

Automatic generation control is extensively used to regulate power plants in a modern area of the power system network. In this paper, automatic generation and frequency control in interconnected power system is presented. A multisource such as thermal, hydro, and gas-based power plant is considered in this study, which is carried out by incorporating nonlinearity like generation rate constants, HVDC link, and the conventional PID controller design. Further, an optimal setting of the PID controller is performed by employing evolutionary, and metaheuristic algorithm-based approaches such as differential evolution and firefly algorithm, respectively. With these algorithms, the proposed model has been tested with their performance evaluation and comparison characteristics are discoursed. The robustness of the proposed controllers is assessed based on comparative analyses to regulate the interconnected power network's frequency profile under different loading conditions. The stability analysis is performed using the Eigen and Nyquist plots to assess the proposed controllers' efficacy. Besides, the frequency control study is summarized with comparative assessment through various performance indices such as settling time, peak overshoot and undershoots under different operating conditions. Finally, the proposed control scheme, in the interconnected power system, is validated through a real-time digital simulation platform, i.e., OPAL-RT 5142. The comparison of simulation and real-time results demonstrates the effectiveness of the FA-optimized PID controller in comparison with that of the DE-optimized PID controller. [ABSTRACT FROM AUTHOR]

In practical applications, the optimal solutions of multi-objective optimization are not unique. Some problems exist different Pareto Sets (PSs) in the decision space mapped to the same Pareto Front (PF) in the objective space, which are called multimodal multi-objective problems (MMOPs). To tackle this issue, this paper proposes a multimodal multi-objective optimization based on a local optimal neighborhood crowding distance differential evolution algorithm. First, an adaptive partitioning strategy in the initialization phase is proposed by using the characteristics of the heuristic stochastic search. That ensures the local optimal solution is quickly found among multiple PSs. Second, opposition-based learning is combined with differential mutation to generate vectors, which accelerate the convergence of the population to the optimal solution. Finally, a method for neighborhood crowding distances on different Pareto ranks is designed. The distance is computed by a weighted sum of Euclidean distances for the nearest neighbors. While reducing computational complexity, this strategy reflects realistic crowding degree. With these methods, balances the diversity performance of the decision and the objective space, while improving the search capability. Multiple PSs reveal the problem's potential characteristics and meet the needs of the decision-maker. The practical significance is verified by the application of actual distance minimization problem. According to experimental results, the proposed method can achieve a high level of comprehensive performance. [ABSTRACT FROM AUTHOR]

This paper focuses on achieving the low-cost coexistence of the networks in an unlicensed spectrum by making them operate on non-overlapping channels. For achieving this goal, we first give a universal convergence analysis framework for the unlicensed spectrum allocation algorithm. Then, a one-timescale iteration-adjustable unlicensed spectrum allocation algorithm is developed, where the step size and timescale parameter can be jointly adjusted based on the system performance requirement and signal overhead concern. After that, we derive the sufficient condition for the one-timescale algorithm. Furthermore, the upper bound of convergence error of the one-timescale spectrum allocation algorithm is obtained. Due to the multi-timescale evolution of the network states in the wireless network, we further propose a two-timescale iteration-adjustable joint frequency selection and frequency allocation algorithm, where the frequency selection iteration timescale is set according to the slow-changing statistical channel state information (CSI), whereas the frequency allocation iteration timescale is set according to the fast-changing local CSI. Then, we derive the convergence condition of two-timescale algorithms and the upper bound of the corresponding convergence error. The experimentalresults show that the small timescale adjustment parameter and large step size can help decrease the convergence error. Moreover, compared with traditional algorithms, the two-timescale policy can achieve throughput similar to traditional algorithms with very low iteration overhead. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) algorithms tend to be limited to local optimization when solving complex optimization problems. Different iteration schemes lead to different convergence speeds. In this paper, we mainly use the dynamic mutation parameter FS to improve the DE algorithm. Based on two ideas, a total of seven DE schemes are proposed to optimize the DE algorithm. We test the performance of the improved DE scheme on 56 test functions. Experiments show that the improved DE algorithm is better than the baseline DE algorithm in terms of accuracy, convergence and8 convergence speed. [ABSTRACT FROM AUTHOR]

Multi-objective problems have gained much attention during the last decade. To balance the diversity and the convergence of the multi-objective differential evolution algorithm (MODE), an improved MODE is proposed based on the affinity propagation clustering (APC) and the non-dominated count approach in this paper. The proposed algorithm is referred to as AP-MODE, which improves the search efficiency by utilizing the affinity propagation approach to find out the population distribution structure for guiding search. In addition, mating restriction probability is used to select parent individuals for recombination from the neighborhoods or the whole population. Meanwhile, the mating restriction probability is updated according to the non-dominated count approach at each generation. This proposed algorithm is verified by comparing it with some state-of-the-art multi-objective evolutionary algorithms, and the simulation results on DTLZ test problems indicate that AP-MODE can efficiently achieve two goals of multi-objective optimization, i.e., the convergence to actual Pareto front and uniform spread of individuals along Pareto front. [ABSTRACT FROM AUTHOR]

Variational Quantum Algorithms (VQAs) are among the most promising NISQ-era algorithms for harnessing quantum computing in diverse fields. However, the underlying optimization processes within these algorithms usually deal with local minima and barren plateau problems, preventing them from scaling efficiently. Our goal in this paper is to study alternative optimization methods that can avoid or reduce the effect of these problems. To this end, we propose to apply the Differential Evolution (DE) algorithm to VQAs optimizations. Our hypothesis is that DE is resilient to vanishing gradients and local minima for two main reasons: (1) it does not depend on gradients, and (2) its mutation and recombination schemes allow DE to continue evolving even in these cases. To demonstrate the performance of our approach, first, we use a robust local minima problem to compare state-of-the-art local optimizers (SLSQP, COBYLA, L-BFGS-B and SPSA) against DE using the Variational Quantum Eigensolver algorithm. Our results show that DE always outperforms local optimizers. In particular, in exact simulations of a 1D Ising chain with 14 qubits, DE achieves the ground state with a 100% success rate, while local optimizers only exhibit around 40%. We also show that combining DE with local optimizers increases the accuracy of the energy estimation once avoiding local minima. Finally, we demonstrate how our results can be extended to more complex problems by studying DE performance in a 1D Hubbard model. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) has been applied to solve various optimization problems due to its simplicity and high search efficiency. However, researchers have confirmed that it still has some shortcomings such as premature convergence and slow convergence, especially when dealing with complex optimization problems. To address these concerning issues, this paper proposes a hybrid particle swarm-differential evolution algorithm (HPSDE). Firstly, to enhance the optimization performance, a modified updating scheme named particle-swarm mutation strategy is designed and an improved control parameters adaption is developed. Then, DE/rand-to-rand/1 mutation strategy is adopted to increase the population diversity and enhance the ability of particles escaping away from local optima. To achieve an improved DE variant with rapid convergence and fine stability, a random mutation framework is designed to combine the two mutation strategies mentioned above. To evaluate the efficiency of HPSDE algorithm, four different experiments have been taken on twenty-nine benchmark functions. The numerical results validate that HPSDE has better overall performance than the other competitors. Additionally, HPSDE is successfully applied to solve five typical engineering optimization problems. [ABSTRACT FROM AUTHOR]

Purpose: The Wiener-Hammerstein nonlinear system is made up of two dynamic linear subsystems in series with a static nonlinear subsystem, and it is widely used in electrical, mechanical, aerospace and other fields. This paper considers the parameter estimation of the Wiener-Hammerstein output error moving average (OEMA) system. Design/methodology/approach: The idea of multi-population and parameter self-adaptive identification is introduced, and a multi-population self-adaptive differential evolution (MPSADE) algorithm is proposed. In order to confirm the feasibility of the above method, the differential evolution (DE), the self-adaptive differential evolution (SADE), the MPSADE and the gradient iterative (GI) algorithms are derived to identify the Wiener-Hammerstein OEMA system, respectively. Findings: From the simulation results, the authors find that the estimation errors under the four algorithms stabilize after 120, 30, 20 and 300 iterations, respectively, and the estimation errors of the four algorithms converge to 5.0%, 3.6%, 2.7% and 7.3%, which show that all four algorithms can identify the Wiener-Hammerstein OEMA system. Originality/value: Compared with DE, SADE and GI algorithm, the MPSADE algorithm not only has higher parameter estimation accuracy but also has a faster convergence speed. Finally, the input–output relationship of laser welding system is described and identified by the MPSADE algorithm. The simulation results show that the MPSADE algorithm can effectively identify parameters of the laser welding system. [ABSTRACT FROM AUTHOR]

Differential evolutionary (DE) algorithm is one of the most frequently used evolutionary computation method for the solution of non-differentiable, complex and discontinuous real value numerical problems. The analytical structure of the mutation and crossover operators used by DE and the initial values of the parameters of the relevant operators affect the problem-solving ability of DE. Unfortunately, there is no analytical method for selecting and initializing the best artificial genetic operators that DE can use to solve a problem. Therefore, there is a need to develop new evolutionary search methods that are parameter-free and insensitive to the artificial genetic operators they use. In this paper, the Bernstein–Levy differential evolution (BDE) algorithm, which has a unique elitist-mutation operator and a Bernstein polynomials-based stochastic parameter-free crossover operator, is introduced. The numerical problem-solving success of BDE is statistically evaluated by using 30 benchmark problems of CEC2014 in the numerical experiments presented. BDE's success in solving the related benchmark problems is statistically compared with six state-of-the-art comparison algorithms. In this paper, three real-world optimization problems are also solved by using the proposed algorithm, BDE. According to statistics generated from the experimental results, BDE is statistically better than comparison methods in solving the related real-world problems. [ABSTRACT FROM AUTHOR]

With the aim of satisfaction of demand response, this paper proposed an improved polar bear optimization based approach for cost optimization on multi-tenant colocation data centers. This paper used a one-to-many reverse auction model to reveal the relationship between tenants and operator, and encouraged tenants to voluntarily participate in the auction and submit their energy-saving plans and expected rewards. Then, this algorithm adopted the improved polar bear algorithm to solve the optimal tenant combination and minimize the cost. In detail, this method leveraged the sigmoid function to process the discretize problem. Meanwhile, to enhance the ability of jumping out of the local optimum, it integrated a mutation strategy into the algorithm. To further improve the searching ability in a global view, the method designed an adaptive field of view strategy instead of fixed field of view to dynamically adjust the scope of the local search, and reduced the probability of the algorithm trapping into the local optimal solution. Finally, the paper compared the proposed algorithm with several classical algorithms. The experimental results show that the proposed algorithm not only gains the least cost alone, but also improves the efficiency. [ABSTRACT FROM AUTHOR]

Since the past few years, several metaheuristic algorithms, inspired by the natural processes, have been introduced to solve different complex optimization problems. Studying and comparing the convergence, computational burden and statistical significance of those metaheuristics are helpful for future algorithmic development and their applications. This paper focuses on comparing the optimization performance of classical dragonfly algorithm (DA) and its seven different variants, i.e., hybrid memory-based dragonfly algorithm with differential evolution (DADE), quantum-behaved and Gaussian mutational dragonfly algorithm (QGDA), memory-based hybrid dragonfly algorithm (MHDA), chaotic dragonfly algorithm (CDA), biogeography-based Mexican hat wavelet dragonfly algorithm (BMDA), hybrid Nelder–Mead algorithm and dragonfly algorithm (INMDA) and hybridization of dragonfly algorithm and artificial bee colony (HDA) while solving 80 CEC-2021 benchmark problems. It is observed that the convergence rates of different variants of DA algorithm vary, and the corresponding computational times for such variations are also evaluated. This paper finally ranks DA and its variants according to their convergence efficiency and Friedman test. The DADE, QGDA, BMDA and DA evolve out as the most efficient algorithms for solving the considered CEC-2021 benchmark problems. [ABSTRACT FROM AUTHOR]

Real-parameter single objective optimization has been studied for decades. In recent, a new setting is applied in this field based on the consideration that solving difficulty scales exponentially with the increase in dimensionality. Under the new setting, differential evolution (DE) still outstands in performance as before. Meanwhile, a new type of population-based metaheuristic—gaining–sharing knowledge-based algorithm, becomes a dark horse. Furthermore, ensemble of the above two types of algorithm is proposed in the literature. Although such ensemble shows good performance, provided that a more reasonable scheme is used for the communication between the constituent algorithms, better ensemble can be obtained. We believe that the new scheme should be with adaptiveness. In this paper, we propose an adaptive scheme for the communication. According to the scheme, individuals chosen based on fitness and lifetime are exchanged. In fact, in the field of DE, it is rare to consider lifetime of individual. However, lifetime is no less important than fitness in our scheme. In our experiment, our ensemble is compared with seven state-of-the-art algorithms. According to experimental results, our ensemble is comparable to one of the peers and better than the other ones. [ABSTRACT FROM AUTHOR]

Data clustering is a machine learning method for unsupervised learning that is popular in the two areas of data analysis and data mining. The objective is to partition a given dataset into distinct clusters, aiming to maximize the similarity among data objects within the same cluster. In this paper, an improved honey badger algorithm called DELHBA is proposed to solve the clustering problem. In DELHBA, to boost the population's diversity and the performance of global search, the differential evolution method is incorporated into algorithm's initial step. Secondly, the equilibrium pooling technique is included to assist the standard honey badger algorithm (HBA) break free of the local optimum. Finally, the updated honey badger population individuals are updated with Levy flight strategy to produce more potential solutions. Ten famous benchmark test datasets are utilized to evaluate the efficiency of the DELHBA algorithm and to contrast it with twelve of the current most used swarm intelligence algorithms and k-means. Additionally, DELHBA algorithm's performance is assessed using the Wilcoxon rank sum test and Friedman's test. The experimental results show that DELHBA has better clustering accuracy, convergence speed and stability compared with other algorithms, demonstrating its superiority in solving clustering problems. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is a proficient optimizer and has been broadly implemented in real life applications of various fields. Several mutation based adaptive approaches have been suggested to improve the algorithm efficiency in recent years. In this paper, a novel self-adaptive method called SaMDE has been designed and implemented on the mutation-based modified DE variants such as modified randomized localization-based DE (MRLDE), donor mutation based DE (DNDE), and sequential parabolic interpolation based DE (SPIDE), which were proposed by the authors in previous research. Using the proposed adaptive technique, an appropriate mutation strategy from DNDE and SPIDE can be selected automatically for the MRLDE algorithm. The experimental results on 50 benchmark problems taken of various test suits and a real-world application of minimization of the potential molecular energy problem validate the superiority of SaMDE over other DE variations. [ABSTRACT FROM AUTHOR]

Variational Quantum Algorithms (VQAs) are among the most promising NISQ-era algorithms for harnessing quantum computing in diverse fields. However, the underlying optimization processes within these algorithms usually deal with local minima and barren plateau problems, preventing them from scaling efficiently. Our goal in this paper is to study alternative optimization methods that can avoid or reduce the effect of these problems. To this end, we propose to apply the Differential Evolution (DE) algorithm to VQAs optimizations. Our hypothesis is that DE is resilient to vanishing gradients and local minima for two main reasons: (1) it does not depend on gradients, and (2) its mutation and recombination schemes allow DE to continue evolving even in these cases. To demonstrate the performance of our approach, first, we use a robust local minima problem to compare state-of-the-art local optimizers (SLSQP, COBYLA, L-BFGS-B and SPSA) against DE using the Variational Quantum Eigensolver algorithm. Our results show that DE always outperforms local optimizers. In particular, in exact simulations of a 1D Ising chain with 14 qubits, DE achieves the ground state with a 100% success rate, while local optimizers only exhibit around 40%. We also show that combining DE with local optimizers increases the accuracy of the energy estimation once avoiding local minima. Finally, we demonstrate how our results can be extended to more complex problems by studying DE performance in a 1D Hubbard model. [ABSTRACT FROM AUTHOR]

This paper presents the minimization of total harmonic distortion in a seven-level cascaded H-bridge multilevel inverter with resistive load using the teaching–learning-based optimization algorithm. The minimization of Total Harmonic Distortion (THD)is a challenging optimization problem due to the fact that nonlinear equations are involved. Recently, bio-inspired algorithms have become very popular approaches to solving various optimization problems in different areas of engineering. For this reason, the results obtained with the Teaching–Learning-Based Optimization (TLBO)algorithm were compared with three other popular bio-inspired algorithms, the genetic algorithm, differential evolution, and particle swarm optimization. The comparative analysis, conducted by sweeping the modulation index, made it possible to obtain graphs and data on the behavior of the four analyzed algorithms. Finally, it was concluded that the TLBO algorithm is very effective and is able to solve the THD-minimization problem. Its main advantage over the other algorithms is the fact that it does not require control parameters for its correct operation in the solution of the problem. [ABSTRACT FROM AUTHOR]

The differential evolution (DE) algorithm is a simple and efficient population-based evolutionary algorithm. In DE, the mutation strategy and the control parameter play important roles in performance enhancement. However, single strategy and fixed parameter are not universally applicable to problems and evolution stages with diverse characteristics; besides, the weakness of the advanced DE optimization framework, called selective-candidate framework with similarity selection rule (SCSS), is found by focusing on its single strategy and fixed parameter greedy degree (GD) setting. To address these problems, we mainly combine the multiple candidates generation with multi-strategy (MCG-MS) and the adaptive similarity selection (ASS) rule. On the one hand, in MCG-MS, two symmetrical mutation strategies, "DE/current-to-pbest-w/1" and designed "DE/current-to-cbest-w/1", are utilized to build the multi-strategy to produce two candidate individuals, which prevents the over-approximation of the candidate in SCSS. On the other hand, the ASS rule provides the individual selection mechanism for multi-strategy to determine the offspring from two candidates, where parameter GD is designed to increase linearly with evolution to maintain diversity at the early evolution stage and accelerate convergence at the later evolution stage. Based on the advanced algorithm jSO, replacing its offspring generation strategy with the combination of MCG-MS and ASS rule, this paper proposes multi-strategy differential evolution algorithm with adaptive similarity selection rule (MSDE-ASS). It combines the advantages of two symmetric strategies and has an efficient individual selection mechanism without parameter adjustment. MSDE-ASS is verified under the Congress on Evolutionary Computation (CEC) 2017 competition test suite on real-parameter single-objective numerical optimization, and the results indicate that, of the 174 cases in total, it wins in 81 cases and loses in 30 cases, and it has the smallest performance ranking value, of 3.05. Therefore, MSDE-ASS stands out compared to the other state-of-the-art DEs. [ABSTRACT FROM AUTHOR]

This paper deals with the optimal design of different VLSI circuits, namely, the CMOS voltage reference circuit and the CMOS ring oscillator (RO). The optimization technique used here is the multiobjective differential evolution algorithm (MDEA). All the circuits are designed for 90 nm technology. The main objective of the CMOS voltage reference circuit is to minimize the voltage variation at the output. The targeted value of the reference voltage is 550 mV. A CMOS ring oscillator (RO) is designed depending on the performance parameters such as power consumption and phase noise. The optimal transistor sizing of each circuit is obtained from MDEA. Each circuit is implemented in SPICE by taking the optimal dimensions of the transistors, and the performance parameters are achieved. The designed voltage reference circuit achieves a reference voltage of 550 mV with 600 nW power dissipation. The reference voltage variation of 8.18% is observed due to temperature variation from −40°C to + 125°C. The MDEA-based optimal design of RO oscillates at 2.001 GHz frequency, has a phase noise of −87 dBc/Hz at 1 MHz offset frequency, and consumes 71 μW power. This work mainly aims to optimize the MOS transistors' sizes using MDEA for better circuit performance parameters. SPICE simulation has been carried out by using the optimal values of MOS transistor sizes to exhibit the performance parameters of the circuit. Simulation results establish that design specifications are closely met. SPICE results show that MDEA is a better technique for the optimal design of the above-mentioned VLSI circuits. [ABSTRACT FROM AUTHOR]

Reducing the dimensions of the original data set while preserving the information as much as possible is conducive to improving the accuracy and efficiency of the model. To achieve this, this paper presents a multi-strategy African vulture optimization algorithm that is the chaotic and elite opposition-based African vulture optimization with the simplex method and differential evolution strategy(CESDAVO). Three main improvements are introduced into African vultures optimization(AVO) to improve its capabilities in this study. Firstly, the chaotic elite opposition-based learning strategy is used to initialize and diversify individual positions of vultures. Secondly, the simplex method is used to optimize those poor individuals so as to further improve the local exploitation ability of the algorithm. Thirdly, the differential evolution strategy is used to make the algorithm escape from the local optimum and improve the global optimization capability of the algorithm. The results of the ablation experiments show that mixing the three strategies greatly improves the optimization performance of the algorithm. In addition, Nine algorithms are compared with CESDAVO on 15 benchmark functions, and this experimental result shows that its optimization capability is superior to the others. Then, the proposed CESDAVO is employed for feature selection, and 12 standard datasets are used for experiments. According to the experimental results, CESDAVO obtained the highest average classification accuracy on 11 datasets and the highest feature selection rate on 8 datasets, which is significantly better than other algorithms. Finally, CESDAVO is also applied to feature reduction for essays, removing 24 features and significantly improving the classification accuracy on multiple classifiers. [ABSTRACT FROM AUTHOR]

Accurate and reliable prediction of PM2.5 concentrations is the basis for appropriate warning measures, and a single prediction model is often ineffective. In this paper, we propose a novel decomposition-and-ensemble model to predict the concentration of PM2.5. The model utilizes Ensemble Empirical Mode Decomposition (EEMD) to decompose PM2.5 series, Support Vector Regression (SVR) to predict each Intrinsic Mode Function (IMF), and a hybrid algorithm based on Differential Evolution (DE) and Grey Wolf Optimizer (GWO) to optimize SVR parameters. The proposed prediction model EEMD-SVR-DEGWO is employed to forecast the concentration of PM2.5 in Guangzhou, Wuhan, and Chongqing of China. Compared with six prediction models, the proposed EEMD-SVR-DEGWO is a reliable predictor and has achieved competitive results. [ABSTRACT FROM AUTHOR]

In order to solve the problems of uneven resource utilization and long task completion time in complex task group scheduling, this paper constructed a complex task group resource scheduling model to minimize the mean square error of resource load and the task group completion time, and proposed a multi-objective optimization algorithm based on boundary range local search and NSGA-Ⅱ, called BRLSN. The algorithm used an effective coding method and cross mutation operator for iterative optimization, and constructed an elite retention strategy based on local search in boundary region to expand the search scope of the algorithm and preserved good individuals in the population. Experimental results show that compared with other multi-objective algorithms, the convergence and diversity of BRLSN are significantly improved. At the same time, the algorithm convergence speed is faster, the population quality is higher, and the result value of the final objective function is obviously optimized. [ABSTRACT FROM AUTHOR]

Differential evolution (DE) is one of the most popular and widely used optimizers among the community of evolutionary computation. Despite numerous works having been conducted on the improvement of DE performance, there are still some defects, such as premature convergence and stagnation. In order to alleviate them, this paper presents a novel DE variant by designing a new mutation operator (named "DE/current-to-pbest_id/1") and a new control parameter setting. In the new operator, the fitness value of the individual is adopted to determine the chosen scope of its guider among the population. Meanwhile, a group-based competitive control parameter setting is presented to ensure the various search potentials of the population and the adaptivity of the algorithm. In this setting, the whole population is randomly divided into multiple equivalent groups, the control parameters for each group are independently generated based on its location information, and the worst location information among all groups is competitively updated with the current successful parameters. Moreover, a piecewise population size reduction mechanism is further devised to enhance the exploration and exploitation of the algorithm at the early and later evolution stages, respectively. Differing from the previous DE versions, the proposed method adaptively adjusts the search capability of each individual, simultaneously utilizes multiple pieces of successful parameter information to generate the control parameters, and has different speeds to reduce the population size at different search stages. Then it could achieve the well trade-off of exploration and exploitation. Finally, the performance of the proposed algorithm is measured by comparing with five well-known DE variants and five typical non-DE algorithms on the IEEE CEC 2017 test suite. Numerical results show that the proposed method is a more promising optimizer. [ABSTRACT FROM AUTHOR]

The success-history based adaptive differential evolution (SHADE) algorithm is an efficient modified version of the differential evolution (DE) algorithm, and it has been successfully applied to solve some real-world optimization problems. However, to the best of our knowledge, it has been rarely applied in the field of structural optimization. The optimal design of structures with frequency constraints is well known as a highly nonlinear and non-convex optimization problem with many local optima. In this paper, the SHADE algorithm is examined in the context of size optimization of large-scale truss structures with multiple frequency constraints. In SHADE, a historical memory of successful control parameter settings is used to guide the generation of new control parameters. In order to demonstrate the effectiveness and efficiency of SHADE, three truss optimization problems with multiple frequency constraints are presented. The three examples considered in this paper include a 600-bar single-layer dome-shaped truss, a 1180-bar single-layer dome-shaped truss, and a 1410-bar double-layer dome-shaped truss. The results obtained by the SHADE algorithm are presented and compared with the best-known results reported in the literature. Numerical results indicate the effectiveness and superior performance of SHADE over other algorithms in terms of solution accuracy and robustness. It is worth mentioning that in all the three cases considered, the optimal designs obtained by SHADE are the best ones reported in the literature so far. However, SHADE often requires fewer structural analyses than those required by the other algorithms. [ABSTRACT FROM AUTHOR]

Two goals of multi-objective evolutionary algorithms are effectively improving their convergence and diversity and making the Pareto set evenly distributed and close to the real Pareto front. At present, the challenges to be solved by the multi-objective evolutionary algorithm are to improve the convergence and diversity of the algorithm, and how to better solve functions with complex PF and/or PS shapes. Therefore, this paper proposes a gray wolf optimization-based self-organizing fuzzy multi-objective evolutionary algorithm. Gray wolf optimization algorithm is used to optimize the initial weights of the self-organizing map network. New neighborhood relationships for individuals are built by self-organizing map, which can maintain the invariance of feature distribution and map the structural information of the current population into Pareto sets. Based on this neighborhood relationship, this paper uses the fuzzy differential evolution operator, which constructs a fuzzy inference system to dynamically adjust the weighting parameter in the differential operator, to generate a new initial solution, and the polynomial mutation operator to refine them. Boundary processing is then conducted. Experiments on 15 problems of GLT1-6 and WFG1-9 and the algorithm proposed in this paper achieve the best on 18 values. And the result shows that the convergence and diversity of the proposed algorithm are better than several state-of-the-art multi-objective evolutionary algorithms. [ABSTRACT FROM AUTHOR]

This paper presents a multi-unmanned aerial vehicle (UAV)-assisted mobile edge computing system, where multiple UAVs are used to serve mobile users. We aim to minimize the overall energy consumption of the system by planning the trajectories of UAVs. To plan the trajectories of UAVs, we need to consider the deployment of hovering points (HPs) of UAVs, their association with UAVs, and their order for each UAV. Therefore, the problem is very complicated, as it is non-convex, nonlinear, NP-hard, and mixed-integer. To solve the problem, this paper proposed an evolutionary trajectory planning algorithm (ETPA), which comprises four phases. In the first phase, a variable-length GA is adopted to update the deployments of HPs for UAVs. Accordingly, redundant HPs are removed by the remove operator. Subsequently, a differential evolution clustering algorithm is adopted to cluster HPs into different clusters without knowing the number of HPs in advance. Finally, a GA is proposed to construct the order of HPs for UAVs. The experimental results on a set of eight instances show that the proposed ETPA outperforms other compared algorithms in terms of the energy consumption of the system. [ABSTRACT FROM AUTHOR]

Aiming at the shortcoming of salp swarm optimization algorithm such as low accuracy, slow convergence speed and easy to fall into local optimum, this paper proposed an adaptive t-distribution and dynamic weight salp swarm optimization algorithm. Firstly, the leader position update introduced the global search stage formula of butterfly optimization algorithm to enhance the global exploration ability. Secondly, the follower location update introduced an adaptive dynamic weighting factor to strengthen the guiding role of elite individuals, so as to enhance the local development ability. Finally, the adaptive t-distribution mutation strategy mutated the optimal individual in order to avoid the algorithm falling into local optimum. By solving 12 benchmark test functions, and according to comparison results of the mean value, standard deviation, solving success rate, Wilcoxon test and convergence curve, the proposed algorithm was superior to standard salp swarm algorithm, the compared other improved salp swarm algorithm and the compared other swarm intelligence algorithms. The results also show that it has a significant improvement in the optimization accuracy and convergence speed, and has the ability to jump out of local optimum. The experimental results verify the effectiveness of the proposed algorithm by applying it to find the lowest point of denitrification inlet concentration. [ABSTRACT FROM AUTHOR]

In order to fix the integer ambiguity quickly and accurately, this paper proposed a new ambiguity search algorithm based on measurement accuracy constraints to solve the problems of the LAMBDA algorithm, such as the wide search range of the integer ambiguity and the low search efficiency. When the least squares problem got optimally weighted, the algorithm took the carrier phase measurement accuracy as the constraint condition to test the fixed ambiguity solution on the basis of the stan-dard differential evolution （DE） algorithm. This algorithm solved the influence of different satellite altitude angles, and could achieve 99% success rate when solving 3D integer ambiguity. Compared with the MLAMBDA algorithm, the standard DE algorithm and the adaptive weighted differential evolution （AWDE） algorithm, the proposed algorithm further improves the efficiency and success rate of ambiguity resolution. [ABSTRACT FROM AUTHOR]

Complex systems provide an opportunity to analyze the essence of phenomena by studying their intricate connections. The networks formed by these connections, known as complex networks, embody the underlying principles governing the system's behavior. While complex networks have been previously applied in the field of evolutionary computation, prior studies have been limited in their ability to reach conclusive conclusions. Based on our investigations, we are against the notion that there is a direct link between the complex network structure of an algorithm and its performance, and we demonstrate this experimentally. In this paper, we address these limitations by analyzing the dynamic complex network structures of five algorithms across three different problems. By incorporating mathematical distributions utilized in prior research, we not only generate novel insights but also refine and challenge previous conclusions. Specifically, we introduce the biased Poisson distribution to describe the algorithm's exploration capability and the biased power-law distribution to represent its exploitation potential during the convergence process. Our aim is to redirect research on the interplay between complex networks and evolutionary computation towards dynamic network structures, elucidating the essence of exploitation and exploration in the black-box optimization process of evolutionary algorithms via dynamic complex networks. [ABSTRACT FROM AUTHOR]

The knapsack problem (KP) is a discrete combinatorial optimization problem that has different utilities in many fields. It is described as a non-polynomial time (NP) problem and has several applications in many fields. The differential evolution (DE) algorithm has been successful in solving continuous optimization problems, but it needs further work to solve discrete and binary optimization problems and avoid local optima. According to the literature, no DE search operator or algorithm is optimal for all optimization tasks. As a result, using more than one search operator in a single algorithm architecture, called multi-operator-based algorithms, is a solution to address this problem. These methods outperformed single-based methods for continuous optimization problems. Thus, in this paper, a binary multi-operator differential evolution (BMODE) approach is presented to tackle the 0–1 KP. The presented methodology utilizes multiple differential evolution (DE) mutation strategies with complementary characteristics, with the best mutation operator being asserted utilizing the produced solutions' quality and the population's diversity. In BMODE, two types of transfer functions (TFs) (S-shaped and V-shaped) are used to transfer the continuous solutions to binary ones to be able to calculate the fitness function value. To handle the capacity constraints, a feasibility rule is utilized and some of the infeasible solutions are repaired. The performance of BMODE is tested by solving 40 instances with multiple dimensions, i.e., low, medium, and high. Experimental results of the proposed BMODE are compared with well-known state-of-the-art 0–1 knapsack algorithms. Based on Wilcoxon's nonparametric statistical test ( α = 0.05 ), the proposed BMODE can obtain the best results against the rival algorithms in most cases, and can work well on stability and computational accuracy. [ABSTRACT FROM AUTHOR]

The discounted {0-1} knapsack problem (DKP) is an NP-hard problem that is more challenging than the classical knapsack problem. In this paper, an enhanced version of the sine-cosine algorithm (SCA) called TMHSCA is proposed to solve the DKP. The SCA is a novel metaheuristic algorithm based on sine-cosine theory. Three effective improvements are proposed for the SCA to enhance the convergence speed and exploitation capability of the algorithm. First, by dividing the initial population into three subpopulations using random, greedy and opposition-based learning (OBL) strategies, the diversity of the population can be effectively enhanced. Furthermore, a forward-inverse sine-cosine search that expands the search space by utilizing the worst solution as another target is proposed. The proposed forward-inverse sine-cosine search strategy facilitates the algorithm to explore the easily ignored solution space. The last improvement includes the use of an OBL mutation and the mutation operator of differential evolution at a two-stage mutation, which increases the algorithm's convergence speed and fitness. In our proposed two-stage mutation, the number of mutations can be adaptively adjusted based on the optimization capabilities of the optimal individual. Additionally, a reshuffling repair strategy for repairing infeasible solutions by sorting items into groups to obtain the weight-to-value ratio is proposed. Extensive experiments are conducted on 40 publicly available datasets and are compared to the greedy algorithm, 3 SCAs and 8 competitive baseline methods. The experimental results demonstrate that our method achieves a state-of-the-art performance. [ABSTRACT FROM AUTHOR]

In this paper, we consider an optimal control problem of nonlinear systems with mixed control variables and probability constraints. To obtain a numerical solution of this optimal control problem, our target is to formulate this problem as a constrained nonlinear parameter optimization problem (CNPOP), which can be solved by using any gradient-based numerical computation method. Firstly, some binary functions are introduced for each value of the discrete-valued control variable (DCV). Following that, we relax these binary functions and impose a penalty term on the relaxation such that the solution of the resulting relaxed problem (RP) can converge to the solution of the original problem as the penalty parameter increases. Secondly, we introduce a simple initial transformation for the probability constraints. Following that, an adaptive sample approximation method (ASAM) and a novel smooth approximation technique (NSAT) are adopted to formulate the probability constraints as some deterministic constraints. Thirdly, a control parameterization approach (CPA) is used to transform the deterministic problem (i.e., an infinite dimensional problem) into a finite dimensional CNPOP. Fourthly, in order to combine the advantages of limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithms and differential evolution (DE) algorithms, a L-BFGS-based DE (L-BFGS-DE) algorithm is proposed for solving the resulting approximation problem based on an improvied L-BFGS (IL-BFGS) method and an improved DE (IDE) algorithm. Following that, we establish the convergence result of the L-BFGS-DE algorithm. The L-BFGS-DE algorithm consists of two stages. The objectives of the first and second stages are to obtain a probable position of the global solution and to accelerate the convergence rate, respectively. In the IL-BFGS method, we propose a novel updating rule (NUR), which uses not only the gradient information of the objective function but also the value of the objective function. This will improved the performance of the IL-BFGS method. In the IDE algorithm, a novel adaptive parameter adjustment (NAPA) method, a novel population size decrease (NPSD) strategy, and an improved mutation (IM) scheme are proposed to improve its performance. Finally, an anti-cancer drug therapy problem (ADTP) is further extended to illustrate the effectiveness of the L-BFGS-DE algorithm by taking into account some probability constraints. Numerical results show that the L-BFGS-DE algorithm has good performance and can obtain a stable and robust performance when considering the small noise perturbations in initial state. [ABSTRACT FROM AUTHOR]

As one of the three basic control parameters of the differential evolution algorithm (DE), the population size (PS) has attracted extensive attention. In general, the most appropriate population size varies for different types of problems and problems with different dimensions. As a result, the performance of an algorithm with a fixed population size is limited to some extent. In this paper, a new enhanced algorithm with a population entropy based population adaptation strategy has been proposed under the framework of SHADE (PE-SHADE). Firstly, a method to calculate the entropy of the population is introduced, through which the distribution state of the population is also characterized. Secondly, the population size is adapted according to the distribution state with a population increasing strategy and a population reduction strategy. In order to evaluate the performance of the proposed algorithm, experiments on the standard benchmark CEC2014 have been conducted, as well as the sensitivity experiments for the extra parameters. The performance comparisons with SHADE, L-SHADE, and some other well-known DE variants are analyzed, which statistically supports the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper uses a fuzzy set scheme to present an adaptive fractional differential algorithm for image edge enhancement and texture preservation. In the proposed algorithm, an image's membership function and area feature are used to calculate the fuzzy set of images. The function of adaptive fractional differential order (FAFDO) can be constructed by making the linear transformation of the fuzzy set. Then, the fuzzy adaptive fractional differential mask (FAFDM) is obtained by substituting the FAFDO into the fractional differential mask. Finally, the image edge and texture are enhanced and preserved by applying airspace filtering of the FAFDM convolution. The experimental results show that, compared to fractional differential or fuzzy set‐based image enhancement algorithms, the proposed algorithm can adaptively enhance the image edge and preserve the image texture by analysing the fuzziness of the image itself. [ABSTRACT FROM AUTHOR]