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Now, we have entered the "internet plus" era, and all industries are making use of information technology to seek a longer-term development. For vegetable distribution, we must rely on the power of information technology. Faced with complex global optimization problems, traditional optimization algorithms have many performance limitations, such as complex solution process and easy to fall into local optimization, which can't meet the needs of practical applications. This paper studies the design and application of optimization algorithm for vegetable planting and distribution based on adaptive differential evolution algorithm. The method adopted in this paper is adaptive differential evolution algorithm. In the original differential evolution algorithm, there are three undetermined parameters: population size (NP), variation factor (F) and crossover probability (CR). In the process of evolution, NP takes a fixed value, while the key control parameters F and CR, which affect the performance of the algorithm, will adaptively take different values on [0,1], and the values of F and CR will be recalculated for each individual in each generation. Let F and CR automatically adjust and change in the process of evolution. The research in this paper shows that the algorithm in this paper is effective and suitable for application. [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]

Multimodal multi-objective optimization (MMO) can offer more elegant solutions and provide diverse decisions to decision-makers in real world optimization problems. Many multimodal evolutionary mechanisms have been proposed to explore and exploit two solution spaces (i.e. decision space and objective space) in recent years. However, most existing methods only use single evolutionary operator to generate offsprings and ignore the advantage of using hybrid evolutionary algorithm. Moreover, it is still a great challenge to balance the effectiveness and efficiency simultaneously in the evolutionary process of MMO. In view of this, an efficient Two-Archive model based multimodal evolutionary algorithm is proposed in this paper. Two parallel offspring generation mechanisms based on competitive particle swarm optimizer and differential evolution are applied to expand two solution spaces with different evolutionary requirements. Moreover, niching local search scheme and reverse vector mutation strategy play roles in achieving better convergence and diversity. Finally, 22 MMO test problems are used to validate the superiority of the proposed method by comparing it with 5 state-of-the-art MMO algorithms. The proposed method is also expanded to solve 9 feature selection problems for validating the effectiveness of the proposed method on real world applications. • Two offspring generation mechanisms based on competitive PSO and DE are proposed. • Two diversity maintenance strategies named niching local search scheme and reverse vector mutation strategy are designed. • This paper proposes a novel multimodal multi-objective optimization algorithm with a new Two-Archive model. • Experiments validate that the proposed method can solve MMOPs effectively and efficiently with a relatively smaller population size. • The proposed algorithm is expanded to deal with 9 real world feature selection problems. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents combination of differential evolution (DE) and biogeography-based optimization (BBO) algorithm to solve complex economic emission load dispatch (EELD) problems of thermal generators of power systems. Emission substances like NO X , SO X , COX, Power demand equality constraint and operating limit constraint are considered here. Differential evolution (DE) is one of the very fast and robust, accurate evolutionary algorithms for global optimization and solution of EELD problems. Biogeography-based optimization (BBO) is another new biogeography inspired algorithm. Biogeography deals with the geographical distribution of different biological species. This algorithm searches for the global optimum mainly through two steps: migration and mutation. In this paper combination of DE and BBO (DE/BBO) is proposed to accelerate the convergence speed of both the algorithm and to improve solution quality. To show the advantages of the proposed algorithm, it has been applied for solving multi-objective EELD problems in a 3-generator system with NO X and SO X emission, in a 6-generators system considering NO X emission, in a 6-generator system addressing both valve-point loading and NO X emission. The current proposal is found better in terms of quality of the compromising and individual solution obtained. [Copyright &y& Elsevier]

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]

Intelligent optimization algorithms are widely utilized to deal with complex optimization problems in various areas. However, a single intelligent optimization algorithm cannot handle well more and more complex optimization problems. The ensemble strategy can integrate several different operators and algorithms by using some appropriate strategies and maybe obtain better optimization performance. In this paper, a new ensemble multi-swarm method based on teaching–learning-based optimization (EMTLBO) was proposed by integrating three different algorithms including the original teaching–learning-based optimization algorithm, its variant with neighborhood search and the variant with differential evolution. In EMTLBO, a new evaluating mechanism based on the fitness-based and diversity-based metrics (FDEM) for each sub-swarm was proposed to evaluate the optimization performance after a continuous generation interval. Moreover, an algorithm matching mechanism based on ranking for sub-swarms (AMM) is adapted to re-divide the population into three sub-swarms and match a suitable algorithm for each sub-swarm so as to increase the whole optimization performance. Furthermore, the experimental results on CEC2014 and CEC2017 test suits verify the feasibility and optimization performance of EMTLBO. Finally, the proposed algorithm is extended to optimize the segmentation thresholds of images and the segmentation performances on different benchmark images show that EMTLBO has good performance in most cases. • A new evaluating mechanism was proposed to evaluate the optimization performance. • Algorithm matching mechanism is adopted to match a suitable algorithm for each sub-swarm. • The experimental results on CEC2014 and CEC2017 test suits verify EMTLBO. • The proposed EMTLBO algorithm is extended to deal with image segmentation problems. [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]

Differential evolution (DE) refers to a class of population based stochastic optimization algorithms. In order to solve practical problems involving constraints, such algorithms are typically coupled with a constraint handling scheme. Such constraints often emerge out of user requirements, physical laws, statutory requirements, resource limitations etc and are routinely evaluated using computationally expensive analysis i.e., solvers relying on finite element methods, computational fluid dynamics, computational electromagnetics etc. In this paper, we introduce a novel scheme of constraint handling, wherein every solution is assigned a random sequence of constraints and the evaluation process is aborted whenever a constraint is violated. The solutions are sorted based on two measures i.e., the number of satisfied constraints and the violation measure. The number of satisfied constraints takes precedence over the amount of violation. We illustrate the performance of the proposed scheme and compare it with other state of the art constraint handling methods using a common framework based on differential evolution. The results are compared using CEC-2006 , CEC-2010 and CEC-2011 test functions with inequality constraints. The results clearly highlight two key aspects (a) the ability to identify feasible solutions earlier than other constraint handling schemes and (b) potential savings in computational cost offered by the proposed strategy. [ABSTRACT FROM AUTHOR]

Cooperative optimization algorithms have been applied with success to solve many optimization problems. However, many of them often lose their effectiveness and advantages when solving large scale and complex problems, e.g., those with interacted variables. A key issue involved in cooperative optimization is the task of problem decomposition. In this paper, a fast search operator is proposed to capture the interdependencies among variables. Problem decomposition is performed based on the obtained interdependencies. Another key issue involved is the optimization of the subproblems. A cross-cluster mutation strategy is proposed to further enhance exploitation and exploration. More specifically, each operator is identified as exploitation-biased or exploration-biased. The population is divided into several clusters. For the individuals within each cluster, the exploitation-biased operators are applied. For the individuals among different clusters, the exploration-biased operators are applied. The proposed operators are incorporated into the original differential evolution algorithm. The experiments were carried out on CEC2008, CEC2010, and CEC2013 benchmarks. For comparison, six algorithms that yield top ranked results in CEC competition are selected. The comparison results demonstrated that the proposed algorithm is robust and comprehensive for large scale optimization problems. [ABSTRACT FROM AUTHOR]

According to the regularity of continuous multi-objective optimization problems (MOPs), an immune multi-objective optimization algorithm with differential evolution inspired recombination (IMADE) is proposed in this paper. In the proposed IMADE, the novel recombination provides two types of candidate searching directions by taking three recombination parents which distribute along the current Pareto set (PS) within a local area. One of the searching direction provides guidance for finding new points along the current PS, and the other redirects the search away from the current PS and moves towards the target PS. Under the background of the SBX (Simulated binary crossover) recombination which performs local search combined with random search near the recombination parents, the new recombination operator utilizes the regularity of continuous MOPs and the distributions of current population, which helps IMADE maintain a more uniformly distributed PF and converge much faster. Experimental results have demonstrated that IMADE outperforms or performs similarly to NSGAII, NNIA, PESAII and OWMOSaDE in terms of solution quality on most of the ten testing MOPs. IMADE converges faster than NSGAII and OWMOSaDE. The efficiency of the proposed DE recombination and the contributions of DE and SBX recombination to IMADE have also been experimentally investigated in this work. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, a comparison is made between the Coupled Local Minimizers (CLM) method and the Differential Evolution (DE) algorithm to perform FE model updating for the damage detection in a cracked beam. CLM method is a gradient-based method with multiple local optimization runs. DE algorithm is a direct search approach which uses a population of solution vectors collecting the design parameters. Two benchmark examples of damage assessment are considered, i.e., beams under flexural vibrations with one crack and two cracks, with unknown position and depth. The effectiveness of the two methods to obtain the set of unknown parameters has been verified by performing a number of optimization processes starting from initial values of parameters selected randomly. Both exact and pseudo-experimental input data are used. A statistical analysis of the optimization results is presented. Both methods give results much better than the classical gradient optimization method. Better performances in term of speed rate and precision have been obtained by CLM when the number of identified parameters is limited. On the other hand, DE shows good efficiency when the number of parameters increases or in the case of pseudo-experimental input data. [Copyright &y& Elsevier]

In this paper, a new compact algorithm is proposed. Two sinusoidal formulas are used to automatically adjust the crossover rate and the mutation scaling factor in the compact Differential Evolution (cDE) metaheuristic. The proposed algorithm, called Compound Sinusoidal cDE, CScDE, is compared to seven state-of-the-art compact algorithms on the well-known BBOB test-bed, the CEC-2014 test suite for continuous optimisation, as well as five real-world optimisation problems chosen from the CEC-2011 benchmarks. The CScDE algorithm outperformed its competitors for most problem categories and over most dimensions. It is also compared to some well-established population-based metaheuristics. • A compact compound sinusoidal differential evolution, CScDE, is proposed. • CScDE uses sinusoidal formulas to adjust the parameters of compact DE. • Both binomial and exponential crossover are tested. • CScDE is applied on 89 reference problems with several dimensions. • CScDE outperformed state-of-the-art compact algorithms. [ABSTRACT FROM AUTHOR]

Trajectory optimization is essentially an optimal control problem (OCP) with highly nonlinear dynamic properties and complex constraints, and a critical part of spacecraft design. In this paper, a hybrid algorithm is proposed for automatic reentry trajectory optimization of reusable launch vehicle (RLV) without providing user-specified initial guesses and a priori knowledge about the optimal trajectory. The method combines the strong robustness and global optimization properties of hyper-heuristic whale optimization algorithm (HHWOA) with the efficient and accurate features of the Gauss pseudospectral method (GPM). HHWOA works as the first-stage optimizer aims to obtain an approximate solution to provide a high-quality initial guess for the GPM, while the GPM works as the second-stage optimizer aims to accelerate the search of the optimum neighborhood to obtain an accurate optimal solution. Additionally, to enhance the progress during the evolutionary process, HHWOA is equipped with opposition-based learning, differential evolution operators, chaotic map sequences and smoothing technique strategies. The utilization of such strategies can potentially smooth the flight trajectory and improve the global convergence of the algorithm, while the three OCPs have shown their superiority in HHWOA. In order to evaluate the performance of the hybrid algorithm, complex constrained RLV maximum cross-range reentry problems with three different path constraint scenarios are investigated. Furthermore, more discussion and experiments are likewise conducted to investigate the impact of the parameters on the performance of the algorithm. The results show that the proposed hybrid algorithm can be very effective in addressing RLV reentry trajectory optimization problems. [ABSTRACT FROM AUTHOR]

Moth–Flame Optimization (MFO) algorithm is widely used to solve real parameter global optimization problems. However, the original MFO algorithm has some problems. First, the global search ability of the algorithm is insufficient due to the lack of high-quality flames or the lack of diversity of the population. Moreover, due to the reduction of the number of flames mechanism and the simple transverse orientation flight mode of moths, the algorithm is easy to fall into local optimum. To overcome these difficulties, a new MFO called ODSFMFO is proposed in this paper, which consists of an improved flame generation mechanism based on Opposition-Based Learning (OBL) and Differential Evolution (DE) algorithm, and an enhanced local search mechanism based on Shuffled Frog Leaping Algorithm (SFLA) and death mechanism. The ODSFMFO firstly obtains a high-quality population through opposition-based learning, then enhances the diversity of the population through differential evolution algorithm, to improve the global search ability of the algorithm, and then, employs an improved shuffled frog leaping algorithm as a local search algorithm, and uses the death mechanism to eliminate the individuals with low fitness value, which not only make the algorithm easy to jump out of the local optimum, but also further improve the convergence speed. To demonstrate the effectiveness of the proposed algorithm, the ODSFMFO and other fourteen well-known optimization algorithms are tested and compared on 28 benchmark tasks of CEC 2013 and 30 benchmark tasks of CEC 2017. Simulation results show that the proposed algorithm obtains better results compared with other competitive algorithms. • An improved flame generation mechanism of MFO is proposed. • A new updating mechanism of SFLA is proposed to improve the local search ability. • The SFLA and death mechanism are applied in combination to MFO. • ODSFMFO is better than 14 compared algorithms. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes an optimization-based model for generic document summarization. The model generates a summary by extracting salient sentences from documents. This approach uses the sentence-to-document collection, the summary-to-document collection and the sentence-to-sentence relations to select salient sentences from given document collection and reduce redundancy in the summary. To solve the optimization problem has been created an improved differential evolution algorithm. The algorithm can adjust crossover rate adaptively according to the fitness of individuals. We implemented the proposed model on multi-document summarization task. Experiments have been performed on DUC2002 and DUC2004 data sets. The experimental results provide strong evidence that the proposed optimization-based approach is a viable method for document summarization. [Copyright &y& Elsevier]

Abstract: Several geometries of the hydrocyclones have been proposed in the literature to improve the separation efficiency or reduce the energy costs. In the present paper, a new geometrical configuration of hydrocyclone has been found through the use of response surface technique combined with the Differential Evolution algorithm. The result obtained with these optimization techniques has been validated by experimental data. The optimized configuration of hydrocyclone presented a high efficiency and a small reduced cut size. [Copyright &y& Elsevier]

Abstract: The sale of electric energy generated by photovoltaic (PV) plants has attracted much attention in recent years. The installation of PV plants aims to obtain the maximum benefit of captured solar energy. The current methodologies for planning the design of the different components of a PV plant are not completely efficient. This paper addresses the optimization of the design of PV plants with solar tracking, which consists of the optimization of the variables that make up the PV plant to obtain the minimum electric (Joule) losses possible. These variables are the size and distribution of solar modules in the solar tracker, the distribution of the solar trackers in the field and the choice of inverter. Evolutionary algorithms (EAs) are adaptive methods based on natural evolution that may be used for searching and optimization. Four different EAs have been used for optimizing the design of PV plants: steady-state genetic algorithm, generational genetic algorithm, CHC algorithm and DE algorithm. In order to test the performance of these algorithms we have used different proposed fields to mount PV plants. The results obtained show that EAs, and specifically DE with rand mutation schemes, are promising techniques to optimize design of PV plants. Furthermore, the results are contrasted with nonparametric statistical tests to support our conclusions. [Copyright &y& Elsevier]

Abstract: This paper focuses on the application of an original engineering global optimization algorithm, based on matrixing operators, positive semi-definite transformation and DE algorithm, for the resolution of constrained optimization problem for credit derivative correlation relationships. Results are analyzed confirming their efficiencies from a financial point view. [Copyright &y& Elsevier]

Abstract: This paper proposes a new differential evolution approach named as multiagent based differential evolution (MADE) based on multiagent systems, for solving optimal power flow problem with non-smooth and non-convex generator fuel cost curves. This method integrates multiagent systems (MAS) and differential evolution (DE) algorithm. An agent in MADE represents an individual to DE and a candidate solution to the optimization problem. All agents live in a lattice like environment, with each agent fixed on a lattice point. In order to obtain optimal solution quickly, each agent competes and cooperates with its neighbors and it can also use knowledge. Making use of these agent–agent interaction and DE mechanism, MADE realizes the purpose of minimizing the value of objective function. MADE applied to optimal power flow is evaluated on 6 bus system and IEEE 30 bus system with different generator characteristics. Simulation results show that the proposed method converges to better solutions much faster than earlier reported approaches. [Copyright &y& Elsevier]

Abstract: Differential evolution (DE) is a simple and efficient global optimization algorithm. However, DE has been shown to have certain weaknesses, especially if the global optimum should be located using a limited number of function evaluations (NFEs). Hence hybridization with other methods is a research direction for the improvement of differential evolution. In this paper, a hybrid DE based on the one-step k-means clustering and 2 multi-parent crossovers, called clustering-based differential evolution with 2 multi-parent crossovers (2-MPCs-CDE) is proposed for the unconstrained global optimization problems. In 2-MPCs-CDE, k cluster centers and several new individuals generate two search spaces. These spaces are then searched in turn. This method utilizes the information of the population effectively and improves search efficiency. Hence it can enhance the performance of DE. A comprehensive set of 35 benchmark functions is employed for experimental verification. Experimental results indicate that 2-MPCs-CDE is effective and efficient. Compared with other state-of-the-art evolutionary algorithms, 2-MPCs-CDE performs better, or at least comparably, in terms of the solution accuracy and the convergence rate. [Copyright &y& Elsevier]

Abstract: The performance of an optimization tool is largely determined by the efficiency of the search algorithm used in the process. The fundamental nature of a search algorithm will essentially determine its search efficiency and thus the types of problems it can solve. Modern metaheuristic algorithms are generally more suitable for global optimization. This paper carries out extensive global optimization of unconstrained and constrained problems using the recently developed eagle strategy by Yang and Deb in combination with the efficient differential evolution. After a detailed formulation and explanation of its implementation, the proposed algorithm is first verified using twenty unconstrained optimization problems or benchmarks. For the validation against constrained problems, this algorithm is subsequently applied to thirteen classical benchmarks and three benchmark engineering problems reported in the engineering literature. The performance of the proposed algorithm is further compared with various, state-of-the-art algorithms in the area. The optimal solutions obtained in this study are better than the best solutions obtained by the existing methods. The unique search features used in the proposed algorithm are analyzed, and their implications for future research are also discussed in detail. [Copyright &y& Elsevier]

Abstract: An improved spectral clustering approach based on differential evolution algorithm (DESC) is proposed in this paper. In our algorithm, we replace k-means with differential evolution (DE) as the final step in spectral clustering, thus it overcomes the deficiencies in sensitivity to initialization and local optima. Experimental results over artificial dataset and UCI dataset demonstrate DESC''s superiority in difficult clustering, steady performance and better accuracy. [Copyright &y& Elsevier]

Abstract: This paper presents a constrained Self-adaptive Differential Evolution (SaDE) algorithm for the design of robust optimal fixed structure controllers with uncertainties and disturbance. Almost all real world optimization problems have constraints which should be satisfied along with the best optimal solution for the problem. In evolutionary algorithms (EAs) the presence of constraints reduces the feasible region and complicates the search process. Therefore, a suitable method to handle the constraints must also be executed. In the SaDE algorithm, four mutation strategies and the control parameter CR are self-adapted. Self-adaptive Penalty (SP) method is introduced into the SaDE algorithm for constraint handling. The performance of SaDE algorithm is demonstrated on the design of robust optimal fixed structure controller of three systems, namely the linearized magnetic levitation system, F-8 aircraft linearized model and a SISO plant. For the comparison purpose, reported results of constrained PSO algorithm and five DE algorithms with different strategies and parameter values are taken into account. Statistical performance in 20 independent runs is considered to compare the performance of algorithms. From the obtained results, it is observed that SaDE algorithm is able to self-adapt the mutation strategy and the crossover rate and hence performs better than the other variants of DE and the constrained PSO algorithm. Better performance of SaDE is achieved by sustained maintenance of diversity throughout the evolutionary process thus producing better individuals consistently. This also aids the algorithm to escape from local optima thereby avoiding premature convergence. [Copyright &y& Elsevier]

Abstract: The differential evolution (DE) is a global optimization algorithm to solve numerical optimization problems. Recently the quantum-inquired differential evolution (QDE) has been proposed for binary optimization. This paper proposes DE/QDE to learn the Takagi–Sugeno (T–S) fuzzy model. DE/QDE can simultaneously optimize the structure and the parameters of the model. Moreover a new encoding scheme is given to allow DE/QDE to be easily performed. The two benchmark problems are used to validate the performance of DE/QDE. Compared to some existing methods, DE/QDE shows the competitive performance in terms of accuracy. [Copyright &y& Elsevier]

Abstract: Differential evolution (DE) has attracted much attention recently as an effective approach for solving numerical optimization problems. However, the performance of DE is sensitive to the choice of the mutation strategy and associated control parameters. Thus, to obtain optimal performance, time-consuming parameter tuning is necessary. Different mutation strategies with different parameter settings can be appropriate during different stages of the evolution. In this paper, we propose to employ an ensemble of mutation strategies and control parameters with the DE (EPSDE). In EPSDE, a pool of distinct mutation strategies along with a pool of values for each control parameter coexists throughout the evolution process and competes to produce offspring. The performance of EPSDE is evaluated on a set of bound-constrained problems and is compared with conventional DE and several state-of-the-art parameter adaptive DE variants. [ABSTRACT FROM AUTHOR]

Abstract: This paper proposes new Differential Evolution (DE) algorithm, named as Chaotically Initialized Differential Evolution (CIDE), that uses chaotic maps with certainty, ergodicity, unpredictability, non-periodicity, complex temporal behavior and the stochastic property for initial population generation. This has been done by using of different chaotic number generators each time a random number is needed by the classical DE algorithm in its initial step. Seven chaotic maps have been analyzed in the benchmark functions. It has been detected that coupling emergent results in different areas, like those of DE and complex dynamics, can improve the quality of results in some optimization problems and also that chaos may be a desired process. It has been also shown that, Sinus map and Circle map have somewhat increased the solution quality, that is in some cases they improved the global searching capability by escaping the local solutions. [Copyright &y& Elsevier]

Abstract: Dynamic economic dispatch (DED) plays an important role in power system operation, which is a complicated nonlinear constrained optimization problem. It has non-smooth and non-convex characteristic when generation unit valve-point effects are taken into account. This paper proposes a novel hybrid method to solve DED problem with valve-point effects, by integrating an improved differential evolution(IDE) with the Shor’s r-algorithm. The proposed method is developed in such a way that IDE is applied as a based level search, which can give a good direction to the optimal global region, and a local search Shor’s r-algorithm is used as a fine tuning to determine the optimal solution at the final. A feasibility-based selection comparison technique and a heuristic rule are devised to handle constraints effectively in IDE, which does not require penalty factors or any extra parameters and can guide the population to the feasible region quickly. The feasibility and effectiveness of the proposed hybrid method is demonstrated for an application example and the test results are compared with those of other methods. It is shown that the proposed method is capable of yielding higher quality solutions. [Copyright &y& Elsevier]

Abstract: In many chemical engineering applications, one frequently encounters dynamic optimization problems. The solution of these types of problems is usually very difficult due to their highly nonlinear, multidimensional and multimodal nature. In fact, several deterministic techniques have been proposed to solve these problems but difficulties related to ease of implementation, global convergence, and good computational efficiency have been frequently found. Recently, evolutionary algorithms (EAs) are gaining popularity for solving complex problems encountered in many engineering disciplines. They are found to be robust and more likely to locate global optimum as compared to several deterministic (gradient based) optimization methods. This paper deals with the application and evaluation of one such algorithm called trigonometric differential evolution (TDE) algorithm for solving dynamic optimization problems encountered in chemical engineering. This is a modified version of differential evolution (DE) which provides enhanced convergence speed. Both DE and TDE algorithms have been applied to seven dynamic optimization problems (five optimal control problems and two kinetic parameter estimation problems) taken from recent literature. The obtained numerical simulation results indicate better performance of TDE as compared to that of DE particularly for problems involving large number of control stages. [Copyright &y& Elsevier]

Abstract: In recent years, evolutionary algorithms (EAs) are gaining popularity for finding the optimal solution of non-linear multimodal problems encountered in many engineering disciplines. Differential evolution (DE), one of the evolutionary algorithms, is a novel optimization method capable of handling nondifferentiable, non-linear and multimodal objective functions. Previous studies have shown that differential evolution is an efficient, effective and robust evolutionary optimization method. Still, DE takes large computational time for optimizing the computationally expensive objective functions. And therefore, an attempt to speed up DE is considered necessary. This paper introduces a modification to original DE that enhances the convergence rate without compromising on solution quality. Our modified differential evolution (MDE) algorithm utilizes only one set of population as against two sets in original DE at any given point of time in a generation. Such an improvement reduces the memory and computational efforts. The proposed MDE is applied to benchmark test functions and five non-linear chemical engineering problems. Results obtained are compared with those obtained using DE by considering the convergence history (CPU time and the number of runs converged to global optimum) and the established statistical techniques, taking into account the variability in the results, such as t-test. As compared to DE, MDE is found to perform better in locating the global optimal solution for all the problems considered. [Copyright &y& Elsevier]

Abstract: In this paper, a novel algorithm is proposed for solving multiobjective optimization problems. The proposed algorithm, multiobjective differential evolution (MODE), is applied to optimize industrial adiabatic styrene reactor considering productivity, selectivity and yield as the main objectives. Five combinations of the objectives are considered. Pareto set (a set of equally good solutions) obtained for all the cases is compared with results reported using non-dominated sorting genetic algorithm (NSGA). The results show that all objectives besides profit can be improved compared to those reported using NSGA and current operating conditions. The Pareto optimal front provides wide-ranging optimal operating conditions and an appropriate operating point can be selected based on the requirements of the user. [Copyright &y& Elsevier]

In practical applications, solving multimodal multiobjective optimization problems (MMOPs), which have multiple Pareto optimal sets (PSs) in the decision space mapping to the same Pareto front (PF) in the objective space, has great significance for decision makers. The issue of how to maintain diversity in both decision space and objective space remains a key problem for existing multimodal multiobjective evolutionary algorithms. To address this issue, a novel grey prediction evolution algorithm for multimodal multiobjective optimization, termed MMGPE, is proposed in this paper. This is the first time that the grey prediction evolution algorithm (GPE), which is a recently proposed competitive optimization algorithm with strong exploration capability, is improved for MMOPs. These improvements are conducted in the following four aspects: (1) an initialization operator based on particle swarm optimization, (2) an adaptive parameter setting strategy depending on the domain of decision variables of MMOPs, (3) an accelerating convergence mechanism inspired by the niche principle, and (4) an environmental selection operator based on a nondominated sorting mechanism and a special crowding distance approach. The performance of MMGPE is compared with two state-of-the-art multiobjective evolutionary algorithms and four multimodal multiobjective evolutionary algorithms on 11 multimodal multiobjective test functions. MMGPE is also applied to solve a practical problem. The results show the MMGPE's effectiveness and superiority in achieving the goal of finding multiple PSs while obtaining a well-distributed PF. [ABSTRACT FROM AUTHOR]

• A new multi-objective optimization method used OBL strategy, WOA and DE algorithms • It combines DE and the OBL to improve the performance of the WOA • The MWDEO results outperformed all other algorithms in most of the test problems • 32 multi-objective test problems are used in the experiments and CEC2017 problems The optimization problems are divided into a single objective and multi-objective. Single objective optimization has only one objective function; whereas, multi-objective optimization has multiple objective functions that generate the Pareto set; therefore, solving a multi-objective problem is a challenging problem. This paper presents a new multi-objective optimization method (called MWDEO) based on improved whale optimization algorithm (WOA) by combining the differential evolution (DE) algorithm and the opposition-based learning (OBL). The MWDEO uses the WOA to perform a global exploration, whereas DE is used to exploit the search space; while the OBL is applied to improve the exploration and exploitation by generating the opposite values. The proposed algorithm is evaluated using 32 multi-objective test problems besides a set of benchmark problems of CEC'2017. The experimental results are compared with nine state-of-the-art multi-objective methods. The analysis of the results showed that the proposed MWDEO outperformed all other algorithms in most of the test problems which indicates that the proposed MWDEO is competitive and effective in solving different types of multi-objective problems. [ABSTRACT FROM AUTHOR]

It is imperative to distribution system operators to provide quantitative as well as qualitative power demand and satisfy consumers' satisfaction. So, it is important to address one of the most promising combinatorial optimization problems for the optimal integration of power distribution network reconfiguration (PDNR) with distributed generations (DGs). In this regard, this paper proposes an improved equilibrium optimization algorithm (IEOA) combined with a proposed recycling strategy for configuring the power distribution networks with optimal allocation of multiple distributed generators. The recycling strategy is augmented to explore the solution space more effectively during iterations. The effectiveness of the proposed algorithm is checked on 23 standard benchmark functions. Simultaneous integration of PDNR and DG are carried out considering the 33 and 69-bus distribution test systems at three different load levels and its superiority is established. Verification of the proposed technique on large scale distribution system with a variety of control variables is introduced on a 137-bus large scale distribution system. These simulations lead to enhanced distribution system performance, quality and reliability. While, the integration represents a challenge for complexity and disability to achieve optimal solutions of the considered problem especially for multi-objective framework. To solve this challenge, a multi-objective function is developed considering total active power loss and overall voltage enhancement with respecting the system limitations. The proposed algorithm is contrasted with harmony search, genetic, refined genetic, fireworks, and firefly optimization algorithms. The obtained results confirm the effectiveness and robustness of the proposed technique compared with the competitive algorithms. • A newly proposed meta-heuristic IEOA is introduced in this work. • The proposed IEOA is applied on 23 standard benchmark functions. • The proposed technique verification is compared with other previous techniques. • The suggested IEOA is validated on three distribution systems. • The findings of simultaneous PDNR/DG allocation show the IFOA effectiveness. [ABSTRACT FROM AUTHOR]

The problem of optimally designing an interplanetary trajectory for a space mission is considered in this paper. To tackle the extreme non-linearity of the search space, a case learning-based differential evolution algorithm, named CLDE, is proposed. It stores successful control parameters (scaling factor and crossover possibility) and retrieve the available reference information according to a geographic similarity in each generation. To depart from the basin of attraction of a local optimum, CLDE will give up learning from the successful cases once no better offsprings have been obtained within a certain number of generations and generate new control parameters. Two versions of CLDE have been developed, for global optimization (G-CLDE) and local optimization (L-CLDE), respectively. Their performance has been tested on GTOP benchmarks and real mission design. Experimental results show that G-CLDE performs better than related algorithms, including PYGMO algorithms and recently published L-SHADE variants. L-CLDE can improve upon the best known solution for the Messenger benchmark (full version). By connecting G-CLDE and L-CLDE together, CLDE finds promising results in acceptable computational time on the GTOP benchmark. • A parameter learning method is proposed according to geographic similarity criteria. • Two versions of CLDE are tested for global and local space search respectively. • A new benchmark record solution for Messenger(full) problem is provided. [ABSTRACT FROM AUTHOR]