An adaptive differential evolution algorithm using fitness distance correlation and neighbourhood-based mutation strategy

A novel trajectory optimization technique has been proposed in this paper to generate reference trajectory for Satellite Launch Vehicle (SLV). For this purpose, a suitable objective function has been formulated subsuming parameters like height, velocity, injection angle and payload mass. The contribution of these parameters in evolving the objective function has been represented by assigning different weighting factors against the different parameters. Moreover, optimal selection of the setting of parameters has also been achieved by proper optimization of the weighting factors associated with the objective function. In the next step, an attempt has been made to optimize the objective function using the existing Differential Evolution (DE) scheme. As an enhancement of this work, a novel Self Adaptive Differential Evolution (SADE) algorithm has been proposed to optimize the trajectory in a more effective manner. Finally, a comparative study has been presented between the proposed SADE based design and the existing DE based design.

JADE is an state-of-the-art adaptive differential evolution algorithm which implements “DE/current-to-pbest” as its mutation strategy, adapts its mutation factor and crossover rate, and uses an optional external archive to keep track of potential removed individuals in previous generations. This paper proposes MPADE, which extends JADE by using a multi-populated approach to solve high dimensional real-parameter optimization problems. This mechanism helps preventing the two well-known problems affecting the differential evolution algorithm performance, which are premature convergence and stagnation. The algorithm was tested using the benchmark functions in IEEE Congress on Evolutionary Computation 2014 test suite. MPADE was compared using Wilcoxon test to JADE algorithm and with other state-of-the-art algorithms that either use a multi-population approach or adapt their parameters. The experimental results show that the proposed new algorithm improves significantly its precursor and it is also suggested that other state-of-the-art algorithms could benefit from the multi-populated based approach.

This paper presents enhanced adaptive differential evolution (EADE) algorithm for solving high-dimensional optimization problems over continuous space. To utilize the information of good and bad vectors in the DE population, the proposed algorithm introduces a new mutation rule. It uses two random chosen vectors of the top and bottom 100p% individuals in the current population of size NP, while the third vector is selected randomly from the middle [NP-2(100p%)] individuals. The mutation rule is combined with the basic mutation strategy DE/rand/1/bin, where the only one of the two mutation rules is applied with the probability of 0.5. This new mutation scheme helps to maintain effectively the balance between the global exploration and local exploitation abilities for searching process of the DE. Furthermore, we propose a novel self-adaptive scheme for gradual change of the values of the crossover rate that can excellently benefit from the past experience of the individuals in the search space during evolution process which, in turn, can considerably balance the common trade-off between the population diversity and convergence speed. The proposed algorithm has been evaluated on the 7 and 20 standard high-dimensional benchmark numerical optimization problems for both the IEEE CEC-2008 and the IEEE CEC-2010 Special Session and Competition on Large-Scale Global Optimization. The comparison results between EADE and its version and the other state-of-art algorithms that were all tested on these test suites indicate that the proposed algorithm and its version are highly competitive algorithms for solving large-scale global optimization problems.

Differential evolution (DE) algorithm is a global optimization algorithm over continuous search space. DE also has been applied in many fields, such as artificial neural networks, chemical engineering, mechanical design, robotics, signal processing, biological information, and economics. At the same time, as a powerful evolutionary algorithm for solving global numerical optimization problems, the DE algorithm has drawn more and more attention. However, how to make a proper balance between the global and local search is a burning question and to limit the optimization performance of DE. In this paper, an improved algorithm η_CODE with a new η_Cauchy operator is proposed to enhance the global and local search ability of a well-known DE variant JADE. In order to guarantee the effective performance of the proposed operator, all the fitness values are ranked through a ranking scheme based on increasing order before a new η_Cauchy operator is conducted. The pNP individuals that have better fitness are selected and carried out Cauchy disturbance operation considering the complexity of the algorithm. The Dynamic parameter mechanism is utilized to select pNP individuals that number is also adjusted dynamically in each generation. The scale factor F and crossover probability CR are obtained with Lehmer mean without using determined parameter c in JADE, which aims to balance the exploration and exploitation of the algorithm during the running time. A total of sixty benchmark functions from CEC2014 and CEC2017 on real parameter optimization are employed to prove the validity of η_CODE for solving complex high-dimensional problems. The experiments indicate that η_CODE is better than or at least comparable with several state-of-the-art DE variants, including JADE, SinDE, TSDE, AGDE, and EFADE in the global numerical optimization problems. In order to further analyze the performance of η_CODE, we also select extra two high-powered modified algorithms called EBLSHADE and LSHADESPACMA based on LSHADE to discuss advantages and disadvantages of the proposed algorithm.

In this paper, we study the multiobjective game in a multiconflict situation. First, the feasible strategy set and synthetic strategy space are constructed in the multiconflict situation. Meanwhile, the value of payoff function under multiobjective is determined, and an integrated multiobjective game model is established in a multiconflict situation. Second, the multiobjective game model is transformed into the single-objective game model by the Entropy Weight Method. Then, in order to solve this multiobjective game, an adaptive differential evolution algorithm based on simulated annealing (ADESA) is proposed to solve this game, which is to improve the mutation factor and crossover operator of the differential evolution (DE) algorithm adaptively, and the Metropolis rule with probability mutation ability of the simulated annealing (SA) algorithm is used. Finally, the practicability and effectiveness of the algorithm are illustrated by a military example.

In this work, a method to control the parameters of Differential Evolution (DE) algorithm is proposed. Here the control parameters of DE are co-evolved by Particle Swarm Optimization (PSO) algorithm. The classical DE algorithm has two main control parameters: Scale Factor (F) and Cross-over Rate (CR). These are selected on trial-and-error basis for solving optimization problems. Several optimization problems lead to optimal or sub-optimal solution by proper selection of control parameters of the DE algorithm. In this proposed method, PSO algorithm is used to tune the scale factor and cross-over rate in DE algorithm. Basically PSO algorithm is used as a meta-optimizer for DE algorithm. The proposed method is termed as mPSO-DE in this paper. The mPSO-DE algorithm is applied on 12 benchmark unconstrained optimization problems. The obtained results are compared with that of classical DE algorithm. From the experimental studies, it has been found that the proposed mPSO-DE algorithm performed better than DE algorithm.

For the differential evolution (DE) algorithms, there are many parameter adaptation methods, which aim at tuning the mutation factor F and the crossover probability CR. When the population diversity is very small and has been converged in a local optimum, even if the evolution goes on, the population will no longer improve. This is also true for the DE algorithms with adaptive F and CR. The enhancement of population diversity is necessary to DE algorithms. In this paper, we test the JADE algorithm with auto-enhanced population diversity (AEPD) on the newest benchmark functions.

Multi-objective robust dynamic pricing and operation strategy optimization for integrated energy system based on stackelberg game

In response to the low accuracy exhibited by the Storm Water Management Model (SWMM), we propose an enhanced Differential Evolution and Bayesian Optimization Algorithm (DE-BOA) . This algorithm integrates the global search capability of the differential evolution algorithm with the local search capability of the Bayesian optimization algorithm, which enables a more comprehensive exploration of the vector solution space. A comparative analysis of various types of rainfall events is conducted. For model calibration and validation, a drainage subzone in Jinshazhou, Guangzhou City, is selected as the research subject. In total, 20 specific rainfall events are selected, and the DE-BOA algorithm outperforms the manual calibration, differential evolution algorithm, and Bayesian optimization algorithm regarding model calibration accuracy. Furthermore, the DE-BOA algorithm exhibits robust adaptability to rainfall events characterized by multiple peaks and higher precipitation levels, with Nash–Sutcliffe Efficiency coefficient values surpassing 0.90. This study’s findings could hold significant reference value for dynamically updating model parameters, thereby enhancing the model simulation performance and improving the accuracy of the urban intelligent water management platform.

Application of a Derivative-Free Method with Projection Skill to Solve an Optimization Problem

In wireless sensor network (WSN) there are many sensors and tiny devices which are used to sense the real-time environmental circumstances. The sensed data will be meaningless if each node in WSN doesn't know its location in the real world. There are many cost-effective techniques for localization used to locate the sensor node. Among those techniques, the range-based localization techniques are known for their accuracy in predicting sensor node location. Differential Evolution Algorithm (DEA) is popular optimization technique as it has good convergence properties but it has few control parameters, which are fixed throughout the entire iteration process and it is not an easy task to tune that control parameters. So, in this paper, we propose Adaptive Differential Evolution Algorithm (ADEA) for obtaining adaptive control over the parameters. In DEA we consider appropriate solutions to have more probability of reproduction compared to inappropriate ones, but there is always a possibility that population elements that look inappropriate in each stage may contain more useful information than appropriate ones. So, we propose Invasive Weed Optimization Algorithm (IWO) which reaches an optimal solution more easily by giving a chance for inappropriate one's to survive and reproduce similar to the mechanism that happens in nature.

A local search enhanced differential evolutionary algorithm for sparse recovery

In this paper, a new adaptive grouping differential evolution (AGDE) algorithm is proposed to improve the optimization performance by implementing a prediction strategy of the constraints for constrained optimization problems. It is unnecessary to calculate the constraint values when dealing with the constraints in this method. The constraints are handled after a simple prediction according to the Lipschitz condition. When the constraints are very complex, the load arisen from the calculation of the constraint values is reduced dramatically and the feasibility of the solutions remains with great probability. In AGDE algorithm, the population is dynamically grouped to three subpopulations with respective newly-designed mutation strategy. Meanwhile, the mutation factor and crossover probability are adopted associated with the evolutionary process according to the information of the entire population. Both of the above improvements not only increase the diversity of population and speed up the convergence, but also reduce the complexity of the parameter selection. Four sets of comparative experiments are carried out to evaluate the feasibility and effectiveness of the proposed method that deals with the constraints.

In this paper, a novel Adaptive Parameter Strategy Differential Evolution (APSDE) algorithm is proposed to overcome the parameters dependence and avoid local optima. The Parameter Update Mechanism (PUM), which has three different strategies, is used to reduce the dependence on parameters of DE. The Adaptive Proportion Adjustment Mechanism (APAM) is used to balance the proportion of PUM strategies in different development terms of exploitation and exploration, and the Random Restart Mechanism (RRM) is used to improve population diversity when exploitation is in stagnation. The proposed algorithm is verified in the CEC2018 test functions and the results show that APSDE has good abilities of exploitation, exploration, convergence, and stability. Secondly, Midcourse Guidance Maneuver Decision-making (MGMD) in Beyond Visual Range (BVR) air combat is studied and transformed into a single objective variational optimization problem, a MGMD system based on APSDE is established. Finally, the simulation of MGMD is carried out. The APSDE ranks first in the typical MGMD scenario experiment. In the adaptive Midcourse guidance confrontation, the winning rate of APSDE is 54%, and the statistical results show that the APSDE has an excellent MGMD ability.

In recent years, Differential Evolution (DE) algorithm that is one of the most important delegate of the evolutionary algorithms have been successfully used for solving different optimization problems with its both serial and parallel variants. In this study, the performance of DE algorithm powered with cooperative emigrant creation strategy was investigated over the different types of numerical problems and obtained results were compared with the results of the serial DE and parallel DE algorithm supported with conventional emigrant creation strategy. Experimental studies showed that the convergence speed of the parallel DE algorithm is significantly improved with the cooperative emigrant creation strategy and the proposed parallel DE algorithm produces better results compared to the serial DE algorithm and parallel DE algorithm with the conventional emigrant creation strategy.