Evolutionary Algorithm For Global Optimization Research Articles

A novel differential evolution algorithm with multi-population and elites regeneration.

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.

Correction to: Love evolution algorithm: a stimulus–value–role theory-inspired evolutionary algorithm for global optimization

Correction to: Love evolution algorithm: a stimulus–value–role theory-inspired evolutionary algorithm for global optimization

Differential Evolution with exponential crossover can be also competitive on numerical optimization

Differential Evolution (DE) is a powerful population-based evolutionary algorithm for global optimization, and it is widely used in many scientific and engineering applications. There are two commonly used crossover schemes in the literature: one is binomial crossover and the other is exponential crossover. The majority of DE researchers believe that DE variants employing binomial crossover usually obtain superior performance than the ones employing exponential crossover on numerical optimization and DE variants with exponential crossover are good at tackling optimization problems with linkages among neighboring variables. On the contrary, here in this paper, a new perspective is proposed that DE variant with exponential crossover can obtain competitive performance with the ones employing binomial crossover on numerical optimization regardless of whether there are linkages among the variables or not after discovering the proper crossover rate Cr and its corresponding parameter control, and the main contributions of the paper can be summarized as follows: (1) The first powerful DE variant with exponential crossover, namely the DE-EXP algorithm, which is superior to the recent winner DE variants, e.g. LSHADE, iLSHADE and jSO, in Congress on Evolutionary Computation (CEC) competitions, is developed for numerical optimization; (2) A novel parameter control of crossover rate Cr is developed for exponential crossover and the value of Cr can be automatically generated not only in the initialization stage but also during the evolution. (3) A black-box model illustrating the fitness-value-dependency weakness of the recent winner DE variants in CEC competitions is given and a novel fitness-value-independent adaptation scheme for scale factor F is proposed in the DE-EXP algorithm to overcome the fitness-value-dependency weakness. A larger test suite containing 88 benchmarks is used for the validation of our DE-EXP algorithm, and experiment results show its superiority in comparison with several state-of-the-art DE variants.

A proportional, integral and derivative differential evolution algorithm for global optimization

The proportional, integral, and derivative differential evolution algorithm (PID-DE) is proposed as a new type of interdisciplinary metaheuristic evolutionary algorithm in this paper. The inspiration of PID-DE is derived from the classical proportional, integral, and derivative control method in engineering, and it is used in the framework of the differential evolution (DE) algorithm. To begin, the mathematical models of proportional search, integral search, and derivative search are established as the fundamental search operations. Five different types of optimizers that use a combination of these three basic operations and an additional mutation operation are presented. The selection and crossover methods in DE are then modified to maintain population diversity while also improving global search capacity, and a feedback strategy is established to adaptively adjust the subgroup member of each optimizer. Following that, an integrated high-accuracy, rapid-convergence, and stable metaheuristic is invented using the comprehensive information utilization principle and flexible parameter determination method. Five groups of experiments are studied to assess the overall performance of the proposed algorithm. The first test comprises 12 standard benchmark functions with minimum optima. In Tests 2 and 3, the 52 functions of Congress on Evolutionary Computation (CEC) 2014 and CEC 11 are evaluated using PID-DE under standard test conditions. Besides, three classic real-world engineering design problems and the CEC 2020 test suit are studied for the constrained optimization test. The experimental tests validate PID-DE’s higher accuracy and faster convergence speed in numerical optimization when compared with the representative approaches and top algorithms in the CEC competitions.

Reducing N2O emissions while maintaining yield in a wheat–maize rotation system modelled by APSIM

CONTEXTModelling approaches have already been used to quantitatively assess the trade-offs between crop yield and N2O emissions as impacted by management practices. However, the model's performance in terms of predicting N2O emissions was mainly assessed against total emissions per growing season or year, which may reduce accuracy in modelling due to the uncertainties in total emissions estimated using the manual (static) chamber method. OBJECTIVEHere, a comparison between optimizations for Agricultural Production Systems sIMulator (APSIM) with total N2O emissions and daily N2O emissions was conducted. We further used the validated model to develop simple surrogate models for estimating total N2O emissions in different years and target potential opportunities to reduce N2O emissions while still maintaining the grain yield under long-term climatic conditions. METHODSFive parameters relating to denitrification and nitrification were optimized using differential evolution algorithm for global optimization based on two-year field experimental data at Huantai site in North China Plain, and comprehensive simulation experiments were further conducted under long-term climate variability in an irrigated wheat–maize rotation system. The method of Levenberg-Marquardt was implemented to fit simple surrogate models for estimating total N2O emissions in different years, and Analysis of Variance was used for model comparison. RESULTS AND CONCLUSIONSAPSIM model optimized with daily N2O emissions could better simulate soil N2O and nitrate dynamics than that optimized with total N2O emissions. We obtained the posterior distributions of five key parameters to which N2O emissions are sensitive, and demonstrated that original model using default parameters could underestimate the rate of nitrification and denitrification and the subsequent N2O emissions. Total N2O emissions increased exponentially with nitrogen application rate and mean temperature, and IPCC (1% emission factor) could underestimate whole-year N2O emissions when N rate was higher than the optimized nitrogen rate for crop production. We also found that there was potential to optimize nitrogen fertiliser rate to reduce N2O emissions while still maintaining crop yield in the irrigated wheat–maize rotation system. SIGNIFICANCEThis study demonstrated the necessity of optimization with daily N2O emissions in improving model accuracy, and the posterior distributions of five parameters relating to N2O emissions offered reference range for future model improvement and applications.

Predictive modeling in a steelmaking process using optimized relevance vector regression and support vector regression

The existence of contaminants in metal alloys products is the main problem affecting the product quality, which is an important requirement for competitiveness in industries. This paper proposes the application of a relevance vector machine for regression (RVR) and a support vector machine for regression (SVR) optimized by a self-adaptive differential evolution algorithm for regression to model the phosphorus concentration levels in a steelmaking process based on actual data. In general, the appropriate choice of learning hyperparameters is a crucial step in obtaining a well-tuned RVM and SVM. To address this issue, we apply a self-adaptive differential evolution algorithm, which is an evolutionary algorithm for global optimization. We compare the performance of the RVR and SVR models with the ridge regression, multiple linear regression, model trees, artificial neural network, and random vector functional link neural network models. RVR and SVR models have smaller RMSE values and better performance than the other models. Our study indicates that the RVR and SVR models are adequate tools for predicting the phosphorus concentration levels in the steelmaking process.

Hip-DE: Historical population based mutation strategy in differential evolution with parameter adaptive mechanism

Differential Evolution (DE) was a powerful population-based evolutionary algorithm for global optimization, and it achieved great success in both evolutionary computation competitions and engineering applications. Despite the excellent performance of the state-of-the-art DE variants, there are still two main weaknesses existing within them: one is the weakness in a given mutation strategy and the other is the weakness in the corresponding parameter control (of the mutation strategy). By reviewing the existing mutation strategies in the recent state-of-the-art DE variants, it can be seen that all of them have insufficient use of the knowledge obtained during the evolution because the historical information of the population is not taken into consideration, which inevitably leads to a bad perception of the landscapes of the objectives. Moreover, the adaptations of the control parameters including F and CR in these state-of-the-art DE variants are interlaced with one another. A bad F and a good CR may produce a good trial vector candidate, then the bad F is of misuse in the parameter control and vice versa. In this paper, a novel DE variant, called Hip-DE, meaning the latest fashion of DE, with historical population based mutation strategy was proposed to tackle the above mentioned weaknesses. Moreover, novel parameter adaptive mechanisms for control parameters F and CR as well as a platform based step-decrease scheme of population size were proposed to enhance capacity of the mutation strategy. By incorporating these three advancements, the novel Hip-DE algorithm secured an overall better performance on the tested benchmarks in comparison with the recent proposed state-of-the-art DE variants.

Co-Evolutionary Niching Differential Evolution Algorithm for Global Optimization

Preserving an appropriate population diversity is critical for the performance of evolutionary algorithms. In this paper, we present a co-evolutionary niching strategy (CoEN) to dynamically evolve appropriate niching methods and incorporate it into differential evolution (DE) to preserve the population diversity. The proposed CoEN strategy is achieved by optimizing a criterion, which involves both fitness improvement and population diversity resulting from employing the niching methods during evolution of DE. To verify the performance of proposed method, an extensive test on benchmark functions taken from CEC2019 and CEC2014 has been carried out. The results show the significance of proposed CoEN and, by incorporating CoEN, the resulting DE is able to achieve a better or competitive performance than related algorithms.

Differential evolution algorithm with multi-population cooperation and multi-strategy integration

Differential evolution with a multi-population based ensemble of mutation strategies (MPEDE) has been considered among the most efficient Evolutionary Algorithms for global optimization. Our research results reveal that the performance of MPEDE may be improved by adding an information sharing mechanism and modifying the grouping mechanism. In MPEDE, the entire population is divided into four subpopulations, and most computing resources are allocated to the best strategy, but a better strategy has the same computing resources as the worst strategy. In order to rationally distribute computational resources, a differential evolution variant with multi-population cooperation and multi-strategy integration (MPMSDE) is proposed in this paper. MPMSDE develops a new grouping method instead of the grouping method in MPEDE, and the new grouping method utilizes the ranking of strategies to assign computational resources to different strategies. Also, an information sharing mechanism is introduced in the largest sub-population to avoid falling into local optimum. In MPMSDE, a new mutation strategy, “DE/pbad-to-pbest-to-gbest/1”, is used to replace the mutation strategy “DE/rand/1” in MPEDE. The new strategy not only uses personal history optimal solution and the worst solution but also uses the global best solution to update individuals. The new strategy can not only balance exploration and exploitation but also can accelerate the convergence of the algorithm. The performance of MPMSDE is compared with MPEDE and other state-of-the-art evolutionary algorithms on CEC2005 and CEC2014 benchmark functions. The experimental results show that the performance of the MPMSDE algorithm is very competitive in calculation accuracy and convergence speed.

A case learning-based differential evolution algorithm for global optimization of interplanetary trajectory design

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.

An Adaptation Multi-Group Quasi-Affine Transformation Evolutionary Algorithm for Global Optimization and Its Application in Node Localization in Wireless Sensor Networks.

Developing metaheuristic algorithms has been paid more recent attention from researchers and scholars to address the optimization problems in many fields of studies. This paper proposes a novel adaptation of the multi-group quasi-affine transformation evolutionary algorithm for global optimization. Enhanced population diversity for adaptation multi-group quasi-affine transformation evolutionary algorithm is implemented by randomly dividing its population into three groups. Each group adopts a mutation strategy differently for improving the efficiency of the algorithm. The scale factor F of mutations is updated adaptively during the search process with the different policies along with proper parameter to make a better trade-off between exploration and exploitation capability. In the experimental section, the CEC2013 test suite and the node localization in wireless sensor networks were used to verify the performance of the proposed algorithm. The experimental results are compared results with three quasi-affine transformation evolutionary algorithm variants, two different evolution variants, and two particle swarm optimization variants show that the proposed adaptation multi-group quasi-affine transformation evolutionary algorithm outperforms the competition algorithms. Moreover, analyzed results of the applied adaptation multi-group quasi-affine transformation evolutionary for node localization in wireless sensor networks showed that the proposed method produces higher localization accuracy than the other competing algorithms.

A bi-population QUasi-Affine TRansformation Evolution algorithm for global optimization and its application to dynamic deployment in wireless sensor networks

In this paper, we propose a new Bi-Population QUasi-Affine TRansformation Evolution (BP-QUATRE) algorithm for global optimization. The proposed BP-QUATRE algorithm divides the population into two subpopulations with sort strategy, and each subpopulation adopts a different mutation strategy to keep the balance between the fast convergence and population diversity. What is more, the proposed BP-QUATRE algorithm dynamically adjusts scale factor with a linear decrease strategy to make a good balance between exploration and exploitation capability. We compare the proposed algorithm with two QUATRE variants, PSO-IW, and DE algorithms on the CEC2013 test suite. The experimental results demonstrate that the proposed BP-QUATRE algorithm outperforms the competing algorithms. We also apply the proposed algorithm to dynamic deployment in wireless sensor networks. The simulation results show that the proposed BP-QUATRE algorithm has better coverage rate than the other competing algorithms.

Self-adaptive mutation differential evolution algorithm based on particle swarm optimization

Differential evolution (DE) is an effective evolutionary algorithm for global optimization, and widely applied to solve different optimization problems. However, the convergence speed of DE will be slower in the later stage of the evolution and it is more likely to get stuck at a local optimum. Moreover, the performance of DE is sensitive to its mutation strategies and control parameters. Therefore, a self-adaptive mutation differential evolution algorithm based on particle swarm optimization (DEPSO) is proposed to improve the optimization performance of DE. DEPSO can effectively utilize an improved DE/rand/1 mutation strategy with stronger global exploration ability and PSO mutation strategy with higher convergence ability. As a result, the population diversity can be maintained well in the early stage of the evolution, and the faster convergence speed can be obtained in the later stage of the evolution. The performance of the proposed DEPSO is evaluated on 30-dimensional and 100-dimensional functions. The experimental results indicate that DEPSO can significantly improve the global convergence performance of the conventional DE and thus avoid premature convergence, and its average performance is better than those of the conventional DE, PSO and the compared algorithms. Moreover, DEPSO is applied to solve arrival flights scheduling and the optimization results show that it can optimize the sequence and decrease the delay time.

An Insight into Bio-inspired and Evolutionary Algorithms for Global Optimization: Review, Analysis, and Lessons Learnt over a Decade of Competitions

Over the recent years, continuous optimization has significantly evolved to become the mature research field it is nowadays. Through this process, evolutionary algorithms had an important role, as they are able to obtain good results with limited resources. Among them, bio-inspired algorithms, which mimic cooperative and competitive behaviors observed in animals, are a very active field, with more proposals every year. This increment in the number of optimization algorithms is apparent in the many competitions held at corresponding special sessions in the last 10 years. In these competitions, several algorithms or ideas have become points of reference, and used as starting points for more advanced algorithms in following competitions. In this paper, we have obtained, for different real-parameter competitions, their benchmarks, participants, and winners (from the competitions’ website) and we review the most relevant algorithms and techniques, presenting the trajectory they have followed over the last years and how some of these works have deeply influenced the top performing algorithms of today. The aim is to be both a useful reference for researchers new to this interesting research topic and a useful guide for current researchers in the field. We have observed that there are several algorithms, like the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), the Success-History based Adaptive Differential Evolution with Linear Population Size Reduction (L-SHADE), Mean-Variance Mapping Optimization (MVMO), and Multiple Offspring Sampling (MOS), which have obtained a strong influence over other algorithms. We have also suggested several techniques that are being widely adopted among the winning proposals, and that could be used for more competitive algorithms. Global optimization is a mature research field in continuous improvement, and the history of competitions provides useful information about the past that can help us to learn how to go forward in the future.

Differential evolution with Gaussian mutation and dynamic parameter adjustment

Differential evolution (DE) is a remarkable evolutionary algorithm for global optimization over continuous search space, whose performance is significantly influenced by its mutation operator and control parameters (scaling factor and crossover rate). In order to enhance the performance of DE, we adopt a novel Gaussian mutation operator and a modified common mutation operator to collaboratively produce new mutant vectors, and employ a periodic function and a Gaussian function to generate the required values of scaling factor and crossover rate, respectively. In the proposed variant of DE (denoted by GPDE), the two adopted mutation operators are adaptively applied to generate the corresponding mutant vector of each individual based on their own cumulative scores, the periodic scaling factor can provide a better balance between exploration ability and exploitation ability, and the Gaussian function-based crossover rate will possess fluctuant value, which possibly enhance the population diversity. To verify the performance of proposed GPDE, a suite of thirty benchmark functions and four real-world problems are applied to conduct the simulation experiment. The simulation results demonstrate that the proposed GPDE performs significantly better than five state-of-the-art DE variants and other two meta-heuristics algorithms.

Game Theory-Inspired Evolutionary Algorithm for Global Optimization

Many approaches that model specific intelligent behaviors perform excellently in solving complex optimization problems. Game theory is widely recognized as an important tool in many fields. This paper introduces a game theory-inspired evolutionary algorithm for global optimization (GameEA). A formulation to estimate payoff expectations is provided, which is a mechanism to make a player become a rational decision-maker. GameEA has one population (i.e., set of players) and generates new offspring only through an imitation operator and a belief-learning operator. An imitation operator adopts learning strategies and actions from other players to improve its competitiveness and applies these strategies to future games where one player updates its chromosome by strategically copying segments of gene sequences from a competitor. Belief learning refers to models in which a player adjusts his/her strategies, behavior or chromosomes by analyzing the current history information to improve solution quality. Experimental results on various classes of problems show that GameEA outperforms the other four algorithms on stability, robustness, and accuracy.

Differential evolution with individual-dependent and dynamic parameter adjustment

Differential evolution (DE) is a powerful and versatile evolutionary algorithm for global optimization over continuous search space, whose performance is significantly influenced by its mutation operator and control parameters (population size, scaling factor and crossover rate). In order to enhance the performance of DE, we adopt a new variant of classic mutation operator, a gradual decrease rule for population size, an individual-dependent and dynamic strategy to generate the required values of scaling factor and crossover rate during the evolutionary process, respectively. In the proposed variant of DE (denoted by IDDE), the adopted mutation operator merges the superiority of two classic mutation operators (DE/best/2 and DE/rand/2) together, and the adjustment mechanism of control parameters applies the fitness value information of each individual and dynamic fluctuation rule, which can provide a better balance between the exploration ability and exploitation ability. To verify the performance of proposed IDDE, a suite of thirty benchmark functions is applied to conduct the simulation experiment. The simulation results demonstrate that the proposed IDDE performs significantly better than five state-of-the-art DE variants and other two evolutionary algorithms.

Interleaving of particle swarm optimization and differential evolution algorithm for global optimization

Stochastic optimization algorithms have potential to solve optimization problems in various fields of engineering and science. However, increasing non-linearity, non convexity, multi-modality, discontinuity, and even dynamics make the problems more complex and intractable. Classical optimization techniques are not able to determine global solution by analyzing rough non-linear surfaces. Heuristic algorithms have been used for determining global solution for this type of problems. However, heuristic algorithm is knowledge dependent, so finding a unique heuristic optimization algorithm for obtaining optimum solutions for all problems is not feasible. Hybridization is an integrated framework where merits of algorithms are utilized to improve performance of the optimizers. Particle Swarm Optimization (PSO) and Differential Evolution (DE) algorithm are two heuristic algorithms despite certain shortcomings have been applied to solve global optimization problems. In this paper, we propose an integrated framework where improved version of PSO and DE (IPSODE) is executed in interleaved fashion for balancing exploration and exploitation dilemma in the evolution process. In IPSODE algorithm, generation starts with improved PSO and switch to either improved DE or continue with improved PSO based on the fitness value. The algorithm is experimented on 20 benchmark/test functions which are uni modal, multi-modal, shifted, and rotated with 10, 20, and 30 different dimensions. The performance of the proposed method is confirmed by comparing with basic PSO, basic DE, and three hybridization methods of PSO and DE based on evaluation criteria like solution quality, robustness, convergence speed, scalability, and statistical t-test.

Global Optimization Under Uncertainty and Uncertainty Quantification Applied to Tractor-Trailer Base Flaps

Using a global optimization evolutionary algorithm (EA), propagating aleatory and epistemic uncertainty within the optimization loop, and using computational fluid dynamics (CFD), this study determines a design for a 3D tractor-trailer base (back-end) drag reduction device that reduces the wind-averaged drag coefficient by 41% at 57 mph (92 km/h). Because it is optimized under uncertainty, this design is relatively insensitive to uncertain wind speed and direction and uncertain deflection angles due to mounting accuracy and static aeroelastic loading. The model includes five design variables with generous constraints, and this study additionally includes the uncertain effects on drag prediction due to truck speed and elevation, steady Reynolds-averaged Navier–Stokes (RANS) approximation, and numerical approximation. This study uses the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA) optimization and uncertainty quantification (UQ) framework to interface the RANS flow solver, grid generator, and optimization algorithm. The computational model is a simplified full-scale tractor-trailer with flow at highway speed. For the optimized design, the estimate of total predictive uncertainty is +15/−42%; 8–10% of this uncertainty comes from model form (computation versus experiment); 3–7% from model input (wind speed and direction, flap angle, and truck speed); and +0.0/−28.5% from numerical approximation (due to the relatively coarse, 6 × 106 cell grid). Relative comparison of designs to the no-flaps baseline should have considerably less uncertainty because numerical error and input variation are nearly eliminated and model form differences are reduced. The total predictive uncertainty is also presented in the form of a probability box, which may be used to decide how to improve the model and reduce uncertainty.

Adaptive backtracking search optimization algorithm with pattern search for numerical optimization

The backtracking search optimization algorithm (BSA) is one of the most recently proposed population-based evolutionary algorithms for global optimization. Due to its memory ability and simple structure, BSA has powerful capability to find global optimal solutions. However, the algorithm is still insufficient in balancing the exploration and the exploitation. Therefore, an improved adaptive backtracking search optimization algorithm combined with modified Hooke-Jeeves pattern search is proposed for numerical global optimization. It has two main parts: the BSA is used for the exploration phase and the modified pattern search method completes the exploitation phase. In particular, a simple but effective strategy of adapting one of BSA's important control parameters is introduced. The proposed algorithm is compared with standard BSA, three state-of-the-art evolutionary algorithms and three superior algorithms in IEEE Congress on Evolutionary Computation 2014 (IEEE CEC2014) over six widely-used benchmarks and 22 real-parameter single objective numerical optimization benchmarks in IEEE CEC2014. The results of experiment and statistical analysis demonstrate the effectiveness and efficiency of the proposed algorithm.