Adaptive Differential Evolution Research Articles

An adaptive differential evolution algorithm based on relaxation strategy to realize the Nash equilibrium of multi-oligopoly game

. Inspired by the idea of game learning, this paper studies the Cournot game model of the multi-oligopoly market and studies the realization of the Nash equilibrium by using adaptive differential evolution algorithm based on relaxation strategies. The realization path of Nash equilibrium is attained through an adaptive differential evolution based on a relaxation strategy procedure applied to an objective function with best response dynamics. Among them, the objective function is derived from the sum of the payoff changes of each oligopoly under best response decisions. And theoretically proved that the Nash equilibrium is the optimal solution of the objective function.

An adaptive differential evolution algorithm with multi-strategy for solving complex optimization problem

In this paper, an adaptive differential evolution algorithm with multi-strategy, namely ESADE is proposed to solve the premature convergence and high time complexity for complex optimization problem. In the ESADE, the population is divided into several sub-populations after the fitness value of each individual is sorted. Then different mutation strategies are proposed for different populations to balance the global exploration and local optimization. Next, a new self-adaptive strategy is designed adjust parameters to avoid falling into local optimum while the convergence accuracy has reached its maximum value. And a complex airport gate allocation multi-objective optimization model with the maximum flight allocation rate, the maximum near gate allocation rate, and the maximum passenger rate at near gate is constructed, which is divided into several single-objective optimization model. Finally, the ESADE is applied solve airport gate allocation optimization model. The experiment results show that the proposed ESADE algorithm can effectively solve the complex airport gate allocation problem and achieve ideal airport gate allocation results by comparing with the current common heuristic optimization algorithms.

Interpretable short-term carbon dioxide emissions forecasting based on flexible two-stage decomposition and temporal fusion transformers

Carbon emissions play a pivotal role in exacerbating the global warming crisis and driving climate change. Accurate and consistent projections of carbon emissions are of utmost importance for nations worldwide, as they shape emission reduction strategies and expedite the pursuit of carbon peaking and carbon neutrality goals. While previous studies have focused on hybrid methodologies for carbon emission forecasting, yielding commendable predictive performance, these approaches often overlook the significance of internal interpretability within the forecasting models. In light of this gap, this study introduces a groundbreaking and elucidating hybrid carbon emission forecasting model that amalgamates the two-stage layer decomposition method, adaptive differential evolution with optional external archive (JADE), and temporal fusion transformers (TFT). To begin with, a series of sub-sequences is derived by employing a flexible two-stage decomposition strategy, which leverages a linear-nonlinear decomposition criterion to thoroughly extract the fluctuating characteristics inherent in the carbon emission series. Subsequently, the JADE algorithm intelligently and efficiently optimizes the parameter combinations within the TFT model, ensuring both stability and reliability of the prediction framework. Empirical investigations conclusively demonstrate the remarkable applicability and efficacy of the proposed model in short-term carbon emission forecasting. By delving into the interpretability of the model's results, the study enhances the capacity of policymakers to devise well-informed strategies based on comprehensive insights gleaned from the forecasting process.

Advanced forecasting of COVID-19 epidemic: Leveraging ensemble models, advanced optimization, and decomposition techniques

In the global effort to address the outbreak of the new coronavirus pneumonia (COVID-19) pandemic, accurate forecasting of epidemic patterns has become crucial for implementing successful interventions aimed at preventing and controlling the spread of the disease. The correct prediction of the course of COVID-19 outbreaks is a complex and challenging task, mainly because of the significant volatility in the data series related to COVID-19. Previous studies have been limited by the exclusive use of individual forecasting techniques in epidemic modeling, disregarding the integration of diverse prediction procedures. The lack of attention to detail in this situation can yield worse-than-ideal results. Consequently, this study introduces a novel ensemble framework that integrates three machine learning methods (kernel ridge regression (KRidge), Deep random vector functional link (dRVFL), and ridge regression) within a linear relationship (L-KRidge-dRVFL-Ridge). The optimization of this framework is accomplished through a distinctive approach, specifically adaptive differential evolution and particle swarm optimization (A-DEPSO). Moreover, an effective decomposition method, known as time-varying filter empirical mode decomposition (TVF-EMD), is employed to decompose the input variables. A feature selection technique, specifically using the light gradient boosting machine (LGBM), is also implemented to extract the most influential input variables. The daily datasets of COVID-19 collected from two countries, namely Italy and Poland, were used as the experimental examples. Additionally, all models are implemented to forecast COVID-19 at two-time horizons: 10- and 14-day ahead (t+10 and t+14). According to the results, the proposed model can yield higher correlation coefficient (R) for both case studies: Italy (t+10 = 0.965, t+14 = 0.961) and Poland (t+10 = 0.952, t+14 = 0.940) than the other models. The experimental results demonstrate that the model suggested in this paper has outstanding results in various kinds of complex epidemic prediction situations. The proposed ensemble model demonstrates exceptional accuracy and resilience, outperforming all similar models in terms of efficacy.

Research on Dynamic Optimization Algorithm of Warehousing Location Layout Based on Nonlinear Optimization

The paper aims to improve the turnover rate and operation efficiency of goods that are shipped out and replenished in the warehouses of electric power enterprises through big data analysis and optimization algorithms.The data is distributed in diverse locations and data nonlinear optimization algorithms certainly helps to understand the patterns for effective management of warehouses.This article focuses on reducing the delay in the operational processes.A multi-objective optimization (MOO) has been proposed which is aiming at improving the efficiency of transition process of commodities, storage, and overall warehouse operations.The study helps in the optimization of the allocation of cargo spaces with the aid of big data analysis optimization technology which collects and manages data in a distributed environment. A multi-objective cargo space optimization algorithm is proposed along with consideration of dynamic constraints.The algorithm is based on the coefficient of variation adaptive differential evolution algorithm.Individual decoding is performed according to the real-time cargo space availability.The simulation results show that the convergence speed of the algorithm is greatly improved.Meanwhile, the efficiency of warehouse transition process, shelf stability and the classification of commodities are remarkably improved.In nutshell, the multi-objective decision-making with the integration of big data analysis optimization technology assists in the effective organization of warehouse allocation system by considering multiple factors and constraints.

Capacity optimization allocation method for off-grid RES-H2 microgrid system considering the load-follow-source mechanism

Based on the uncertainty of the output of renewable energy such as wind and photovoltaic (PV), a capacity optimization allocation method considering the load-follow-source mechanism is proposed to solve the shortages of traditional methods, which is low in utilization rate of energy and low in economy. Firstly, considering the fluctuations of renewable energy sources (RES) and the operating characteristics of the electrolyzer, this paper proposes a capacity optimization method for off-grid hydrogen(H2) production system of renewable energy sources considering the load-follow-source operation mechanism. Then, combined with this mechanism, a capacity optimization allocation model is established, the objectives contain minimizing the levelized cost of hydrogen (LCOH), minimizing the capacity of energy storage, and optimizing the efficiency of power supply. Finally, an adaptive non-dominated sorting differential evolution algorithm (ANSDE) with external archiving is proposed to solve the established model. The calculation results show that the load-follow-source mechanism is effective for improving the economy of the system, and the proposed algorithm is high in efficiency and good in convergence comparing with traditional algorithms.

Calculation on maximum output power of wave energy-PTO system

The energy conversion efficiency of wave energy device is one of the key problems in the large-scale utilization of wave energy. The study of the maximum output POWER of PTO (Power-Take-Off) system provides a theoretical reference for the efficient utilization of energy. In this paper, genetic algorithm and adaptive differential evolution algorithm based on neighborhood search are used to optimize the two-objective multi-order differential equations for the maximum output power of PTO system, and the global optimal solution is obtained. Compared with the traversal algorithm, the algorithm involved in this paper is efficient and the optimal output power obtained can provide a scientific basis for the structural optimization design and material selection of the wave energy device.

Wireless sensor networks-based adaptive differential evolution for multimodal optimization problems

In wireless sensor networks (WSN), we often detect the monitoring areas among different sensors so that the sensors can be switched on and off adaptively to save energy and extend their lifetime. Inspired by the principle of WSN, a WSN-based adaptive differential evolution (WSNADE) algorithm is proposed in this paper, together with a WSN-based adaptive niching technique (WANT) and two novel strategies called protection-based dual-scale mutation (PDM) strategy and multi-level reset (MLR) strategy, for solving multimodal optimization problems (MMOPs). In WANT, each individual is considered as a sensor with its monitoring area. If the monitoring areas of two individuals intersect, which means these two individuals monitor the similar area and should be partitioned into the same niche. In this way, WANT can adaptively form a niche for each individual, avoiding the sensitivity of niching parameters. Based on WANT, the PDM strategy is designed to select the appropriate mutation strategy for each individual. Besides, to save fitness evaluations (FEs) for exploring more promising areas, the MLR strategy is developed to store the promising individuals and reset the stagnant individuals. The experimental results on 20 multimodal benchmark test functions in CEC2015 multimodal competition show that the proposed WSNADE algorithm generally performs better than or at least comparable with other state-of-the-art multimodal algorithms, including the winner of the CEC2015 competition. Finally, WSNADE is applied to a real-world multimodal application in multiple competitive facilities location design (MCFLD) problem to illustrate its practical applicability.

A Constraint Adaptive Multi-Tasking Differential Evolution Algorithm: Designed for Dispatch of Integrated Energy System in Coal Mine

A Constraint Adaptive Multi-Tasking Differential Evolution Algorithm: Designed for Dispatch of Integrated Energy System in Coal Mine

An adaptive differential evolution algorithm based on archive reuse

In recent years, differential evolution algorithms based on archives have achieved significant success because archives can increase population diversity and balance the exploration and exploitation of algorithms. However, insufficient utilisation of archives has led to an imbalance between exploration and exploitation. Herein, a new archive-reuse-based adaptive differential evolution (AR-aDE) algorithm framework is proposed that can be applied to (L)SHADE and its variants. It comprises three main strategies. First, a new external archive update method based on a cache mechanism is proposed, in which the archive size is the same as the population size, eliminating the need to adjust its size. Second, influenced by knowledge transfer in multitasking optimisation, we designed a new method of reusing the archive to better utilise the information in it. Finally, the classic parameter adaptation method was improved. The experimental results for the CEC2020 and CEC2021 competition problem sets show that the KR-aDE has a strong competitive advantage.

Energy-efficient indoor hybrid deployment strategy for 5G mobile small-cell base stations using JAFR Algorithm

In the context of 5th-generation (5G) mobile communication technology, deploying indoor small-cell base stations (SBS) to serve visitors has become common. However, indoor SBS is constrained by factors such as service capacity, signal interference, and structural layout. Merchants within large buildings frequently host diverse activities to attract visitors, significantly increasing indoor traffic and crowd-gathering phenomenon. Consequently, SBS faces challenges of excessive energy consumption, compromised communication quality, and an inability to provide service to all visitors. Merchants aim to deploy SBS that can effectively curtail energy consumption costs while fulfilling visitor needs. However, due to the intermittent nature of high footfall situations, employing additional fixed SBS is not economically viable. Therefore, we address the challenge of maintaining service quality and mitigating energy consumption of SBS during footfall fluctuations by proposing an SBS model with a dynamic sleep mechanism. We simulate the internal structure of a three-dimensional (3D) building and the footfall over time. Within this model, we leverage the flexibility of mobile small-cell base stations (MSBS) to seamlessly traverse service regions. We compute the transmission power and location of SBS and MSBS based on energy efficiency (EE), combining their strengths to tackle the challenge. This approach maintains SBS communication quality while curbing energy consumption. We attain the optimal hybrid deployment strategy by enhancing the adaptive differential evolution with optional external archive (JADE) algorithm and incorporating the final fitness formula, the adaptive ranking mutation operator strategy, and the disorder replacement strategy (DRS) in it to form the proposed joint adaptive fusion with ranking (JAFR) algorithm. Our comparative simulation experiments demonstrate the effectiveness of JAFR in addressing the challenges against conventional methods, recent differential evolution algorithms, and mobile base station (MBS) deployment approaches posed by this model. The results indicate that the JAFR algorithm yields superior SBS deployment strategies in most cases.

Thermal resistance optimization of ultra-thin vapor chamber based on data-driven model and metaheuristic algorithm

The ultra-thin vapor chamber(UTVC) is extensively utilized across various fields due to its excellent heat dissipation performance and good temperature uniformity. The data-driven modeling approach is well suited to predict the thermal resistance of the UTVC due to its great flexibility and accuracy. In this paper, a novel approach is proposed to optimize the UTVC thermal resistance, which combines the radial basis function neural network(RBFNN) model with an improved adaptive differential fish swarm evolution algorithm(ADFEA). The mean square error of the RBFNN model was 0.00016 on the training set and 0.00027 on the test sets, which indicates that the model is able to accurately predict the thermal resistance of the UTVC. The data are obtained from experiments on a mesh wick UTVC with dimensions of 124 × 14 × 1 mm. A novel optimization algorithm, ADFEA, has been designed to enhance optimization capability and convergence accuracy. This algorithm combines differential algorithm and artificial fish swarm algorithm, incorporating a parameter adaptation mechanism. The optimal operating parameters of the UTVC are obtained by ADFEA optimization and the accuracy of the optimized results is verified by experiment. The proposed optimization method provides new insights for the design and optimization of UTVC.

An adaptive population size based Differential Evolution by mining historical population similarity for path planning of unmanned aerial vehicles

Various variants have been proposed to improve the search ability and efficiency of Differential Evolution (DE). However, the variants ignore the impact caused by the use of accumulated historical information, resulting in unpromising performance of the search. Furthermore, the global exploration and local exploitation ability of population is affected by the population number (NP), which commonly adapts with little adaptive control or with linear descendent only. To utilize more historical population information, we propose in this paper a novel adaptive population size-based DE (APSDE) by mining historical population information, to balance global exploration and local exploitation ability. APSDE uses historical population information to mine population distribution and extract information to assign parameters to the current population. Moreover, an archive is utilized to store the historical population information, where historical successful parameter information consists of scaling factor (F), crossover rate (CR) and NP for better balancing the search ability of population. To evaluate the performance of APSDE, we conduct experiments both on the 28 benchmark functions of CEC2017, the 10 benchmark functions of CEC2020, and a real-world application - the path planning of unmanned aerial vehicles (UAVs). The experimental results have demonstrated that APSDE achieves the promising performance in both convergence accuracy and convergence speed.

A novel multi-hybrid differential evolution algorithm for optimization of frame structures

Differential evolution (DE) is a robust optimizer designed for solving complex domain research problems in the computational intelligence community. In the present work, a multi-hybrid DE (MHDE) is proposed for improving the overall working capability of the algorithm without compromising the solution quality. Adaptive parameters, enhanced mutation, enhanced crossover, reducing population, iterative division and Gaussian random sampling are some of the major characteristics of the proposed MHDE algorithm. Firstly, an iterative division for improved exploration and exploitation is used, then an adaptive proportional population size reduction mechanism is followed for reducing the computational complexity. It also incorporated Weibull distribution and Gaussian random sampling to mitigate premature convergence. The proposed framework is validated by using IEEE CEC benchmark suites (CEC 2005, CEC 2014 and CEC 2017). The algorithm is applied to four engineering design problems and for the weight minimization of three frame design problems. Experimental results are analysed and compared with recent hybrid algorithms such as laplacian biogeography based optimization, adaptive differential evolution with archive (JADE), success history based DE, self adaptive DE, LSHADE, MVMO, fractional-order calculus-based flower pollination algorithm, sine cosine crow search algorithm and others. Statistically, the Friedman and Wilcoxon rank sum tests prove that the proposed algorithm fares better than others.

Interpretable wind speed forecasting with meteorological feature exploring and two-stage decomposition

Wind speed plays a pivotal role in ensuring the stability of power grid operations. However, the inherent high volatility and non-stationarity of wind patterns pose significant challenges to achieving accurate predictions. To tackle this issue and enhance the interpretability of existing wind speed prediction models, this study proposes an innovative short-term wind speed prediction model that combines two-stage decomposition, meteorological data feature engineering, adaptive differential evolution with optional external archive (JADE) algorithm, and temporal fusion transformers (TFT). To begin, the wind speed data is subjected to decomposition using improved complete ensemble empirical mode decomposition with adaptive noise (IEEMD), yielding multiple eigenmode functions. Subsequently, the nonlinear decomposition subsequence undergoes further decomposition into multiple submodes via empirical wavelet transform (EWT), followed by the careful screening of nonlinear quadratic decomposition submodes. Additionally, meteorological features are ingeniously reconstructed into combined and statistical meteorological features, enhancing the effectiveness of input features. Next, the hyperparameters of the TFT are meticulously optimized using the powerful JADE algorithm. Empirical results unequivocally demonstrate that the IEEMD-EWT-JADE-TFT model achieves remarkably high prediction accuracy. Meanwhile, this interpretative experimental process and its results chart a novel path for decision-makers seeking reliable wind speed forecasting processes and outcomes.

Interpretable corn future price forecasting with multivariate time series

AbstractEfforts in corn future price forecasting and early warning play a vital role in guiding the high‐quality development of the agricultural economy. However, recent years have witnessed significant fluctuations in global corn future prices due to the impact of COVID‐19 and the escalating risks associated with geopolitical conflicts. Therefore, there is an urgent need for accurate and efficient methods to forecast corn future prices. To address this challenge, a novel and comprehensive framework for explainable corn future price forecasting is designed. This framework takes into account multiple factors contributing to corn price volatility, including supply and demand dynamics, policy adjustments, international market shocks, global geopolitical risks, and investor concerns within the corn market. During the data processing stage, complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) is utilized to thoroughly explore the volatility characteristics of historical corn future prices. Additionally, a convolutional neural network (CNN) is employed to extract essential forecasting information from corn news data. To enhance interpretability, a novel JADE–TFT interpretable corn future price prediction model is proposed. This model combines adaptive differential evolution with optional external archiving (JADE) to intelligently and efficiently optimize the parameters of the temporal fusion transformers (TFTs). Furthermore, in the empirical study, the introduction of a global geopolitical risk coefficient, Baidu indices such as “corn” and “corn price,” and quantized corn news text features is shown to improve the accuracy of corn future price predictions. The proposed corn future price prediction framework contributes to the healthy development of the global grain futures market, thereby fostering the growth and well‐being of enterprises involved in the grain industry.

Emulation-based adaptive differential evolution: fast and auto-tunable approach for moderately expensive optimization problems

AbstractIn the field of expensive optimization, numerous papers have proposed surrogate-assisted evolutionary algorithms (SAEAs) for a few thousand or even hundreds of function evaluations. However, in reality, low-cost simulations suffice for a lot of real-world problems, in which the number of function evaluations is moderately restricted, e.g., to several thousands. In such moderately restricted scenario, SAEAs become unnecessarily time-consuming and tend to struggle with premature convergence. In addition, tuning the SAEA parameters becomes impractical under the restricted budgets of function evaluations—in some cases, inadequate configuration may degrade performance instead. In this context, this paper presents a fast and auto-tunable evolutionary algorithm for solving moderately restricted expensive optimization problems. The presented algorithm is a variant of adaptive differential evolution (DE) algorithms, and is called emulation-based adaptive DE or EBADE. The primary aim of EBADE is to emulate the principle of sample-efficient optimization, such as that in SAEAs, by adaptively tuning the DE parameter configurations. Specifically, similar to Expected Improvement-based sampling, EBADE identifies parameter configurations that may produce expected-to-improve solutions, without using function evaluations. Further, EBADE incepts a multi-population mechanism and assigns a parameter configuration to each subpopulation to estimate the effectiveness of parameter configurations with multiple samples carefully. This subpopulation-based adaptation can help improve the selection accuracy of promising parameter configurations, even when using an expected-to-improve indicator with high uncertainty, by validating with respect to multiple samples. The experimental results demonstrate that EBADE outperforms modern adaptive DEs and is highly competitive compared to SAEAs with a much shorter runtime.

Multi-day tourism recommendations for urban tourists considering hotel selection: A heuristic optimization approach

With the development of tourism, digital technology is increasingly being applied in the design of tourist routes. This study takes into account that tourists are experience-driven in tourism activities and hotel selections. In this study, the tourist trip design problem with hotel selection is formulated based on bi-objective optimization with total utility of the points of interest maximization and the average utility of the hotels maximization, and a three-step hybrid algorithm combined with discrete particle swarm optimization, an adaptive differential evolution with an optional external archive, and a local search is designed to identify the optimal route. To examine the performance of the designed algorithm, a numerical experiment was conducted. The results of Wilcoxon rank sum tests verified that the proposed algorithm performed distinctly better than extant approaches. Moreover, the results also indicate that the two main innovative mechanisms about initialization and hybrid evolution play a critical role in improving the algorithm's efficiency for the tourist trip design problem with hotel selection.

An enhanced adaptive differential evolution algorithm with dual performance evaluation metrics for numerical optimization

In this paper, we present a novel adaptive differential evolution algorithm for global optimization problems by introducing an enhanced mutation operator and a new mixed control parameter setting based on dual performance evaluation metrics. To further strengthen the search efficiency of algorithm and availably balance its exploration and exploitation, a dual performance metrics-based mutation operator is first proposed to implement the search of population by organically integrating the fitness value and history update of individual to find the potential promising areas and allocate the suitable search resources for them. Meanwhile, a dual performance metrics-based mixed parameter setting is developed to yield appropriate associated parameters for each individual by comprehensively measuring its search characteristic and requirement based on both its fitness value and history update. In addition, a new restart strategy is further put forward to boost the search performance of algorithm by reasonably replacing the meaningless individuals measured by both their fitness values and history updates with the randomly generated individuals based on Gaussian walk. In contrast to the existing DE versions, the new algorithm organically takes advantage of the fitness value and history update of individual to assign the proper computational resources for each potential promising region, create the suitable parameters for different individuals, and eliminate the valueless individuals from population. Thereby, it is capable of heightening the search efficiency of algorithm and maintaining a good balance between exploration and exploitation effectively. At last, the performance of the proposed algorithm is evaluated by comparing with 19 typical or up-to-date algorithms on 42 benchmark functions from both IEEE CEC2017 and CEC2022 test suites. Compared to these opponents, the proposed algorithm achieves significantly better performance on 60 out of 77 cases based on the multiproblem Wilcoxon signed-rank test at a significant level of 0.05, and thus is a more promising optimizer.

An adaptive differential evolution algorithm to solve the multi-compartment vehicle routing problem: A case of cold chain transportation problem

This research paper introduces an adaptive differential evolution algorithm (ADE algorithm) designed to address the multi-compartment vehicle routing problem (MCVRP) for cold chain transportation of a case study of twentyeight customers in northeastern Thailand. The ADE algorithm aims to minimize the total cost, which includes both the expenses for traveling and using the vehicles. In general, this algorithm consists of four steps: (1) The first step is to generate the initial solution. (2) The second step is the mutation process. (3) The third step is the recombination process, and the final step is the selection process. To improve the original DE algorithm, the proposed algorithm increases the number of mutation equations from one to four. Comparing the outcomes of the proposed ADE algorithm with those of LINGO software and the original DE based on the numerical examples In the case of small-sized problems, both the proposed ADE algorithm and other methods produce identical results that align with the global optimal solution. Conversely, for larger-sized problems, it is demonstrated that the proposed ADE algorithm effectively solves the MCVRP in this case. The proposed ADE algorithm is more efficient than Lingo software and the original DE, respectively, in terms of total cost. The proposed ADE algorithm, adapted from the original, proves advantageous for solving MCVRPs with large datasets due to its simplicity and effectiveness. This research contributes to advancing cold chain logistics with a practical solution for optimizing routing in multi-compartment vehicles.