Comparative Study of Hybridization and Parameter Tuning Improvement Methods for EAs in WFLOP

In recent years, wind farm layout optimization problem (WFLOP) using evolutionary algorithms has become a popular research area. However, there still lack of comparative study of effective improvement strategies for evolutionary algorithm on WFLOP. To fill this blank, this study tries to guide researcher more effectively in identifying the proper algorithm improvement strategies for WFLOP. According to the parameter tuning strategy, an adaptive parameter tuning differential evolution (APDE) is proposed. APDE can adaptively adjust its parameter setting according to the current cases, addressing the complex optimization like WFLOP. The experimental results suggest that parameter tuning strategy is effective on WFLOP. This finding might help researchers more effectively choose the proper methods for improvement.


INTRODUCTION
With the rapid development of artificial intelligence, an increasing number of new technologies are being applied in the field of renewable energy, like wind power.WFLOP is an effective tool to decrease wind power losses caused by the wake effect [20].The wake effect is the interference from the wind turbines positioned upstream [16].As the Fig. 1 shows, the goal of the WFLOP is try to avoid power losses caused by wake effect.
Evolutionary algorithms excel at dealing with complex optimization problems, particularly when the solution space is difficult to compute with mathematical formulas.Because of the complexity of WFLOP, evolutionary algorithms, are more widely used for solving the WFLOP than general analytical optimization.[7], there are a lot of researches of the evolutionary algorithms for WFLOP, these studies focused on testing various candidate evolutionary algorithms to analyze their performance on WFLOP [2,10], but there is still lack of comparative study on the improvement strategies of evolutionary algorithms for WFLOP.Due to this lack, researchers will cost a lot of time on testing different improvement methods until find a proper one.This study is aiming to fill this blank, and try to guide the researches choosing proper improvement strategies of evolutionary algorithms when facing WFLOP.
The improvement strategies can be classified into two categories: algorithm hybridization strategy and parameter tuning strategy [23].The algorithm hybridization strategies is to combine two algorithm's advantages to make algorithm performs better [18], while parameter tuning strategies is to adjust the parameter setting about an algorithm to make it perform better [1].
We conducted experiments using the most classic and popular evolutionary algorithms: Differential Evolution (DE) [15] and Genetic Algorithms (GA) [11].Two improvement strategies are respectively been tested: combining DE with GA and introducing adaptive parameter tuning mechanism into DE, this improved version of DE is called APDE.The hybridization of DE with GA is taking the advantage of GA's randomness, which will introduce more diversity into the progress to help DE get rid of local optimization.And the APDE introduced a adaptive parameter mechanism [19] into DE.This adaptive mechanism will record each scaling factor  parameter (the parameter determing the searching range and The main contributions of this study are summarized as: (1) In this paper, we attempted to improve on classic but popular evolutionary algorithms: DE and GA.And we tried to make improvements to them on two main strategies: algorithm hybridization and algorithm parameter tuning.Through comprehensive experiments and systematic analysis on the WFLOP, we concluded that algorithm parameter tuning is more suitable for this problem than algorithm hybridization.(2) Additionally, our experiments revealed that for different wind-direction conditions in WFLOP, biased exploration algorithms perform more effectively under single-direction conditions, while biased exploitation algorithms perform more effectively under multi-direction conditions.(3) According to the characteristic of WFLOP, we proposed an adaptive parameter differential evolution (APDE), to enable it to adaptively change its parameters during the process.Our experiment results showed that this method of improvement not only outperforms DE's hybridization improvement but also allows the improved algorithm to more effectively address the effects under different wind conditions, achieving better results.
The remaining sections of the article are as follows: Section 2 introduces related work.Section 3 introduces the main current methods for improving the evolutionary algorithms.Section 4 analyzes the experimental results of the hybrid algorithm and the experimental results of the parameter-tuning algorithm.Section 5 contains the conclusion and discussion about future work.

RELATED WORK
Evolutionary algorithms are often used as effective solutions for problems that are difficult or impossible to solve perfectly.There are two primary strategies for evolutionary algorithm improvement: algorithm hybridization and algorithm parameter tuning.HCOEA combines genetic algorithm with local search operators, balancing the algorithm's global and local search capabilities, finally enhancing the overall performance of the algorithm [21].Diveev et al. proposed an effective hybrid evolutionary algorithm to optimize the control problem for a group of interacting robots, which is combined with two popular evolutionary algorithms: particle swarm optimization and gray wolf optimizer [5].In addition, parameter tuning of the evolutionary algorithm has always been considered an effective strategy for improving evolutionary algorithm [6].In parameter tuning strategies, allowing evolutionary algorithms to adaptively adjust their parameters is a popular research focus [1].Li et al. proposed a self-adaptive evolutionary algorithm named HPEA, which can effectively solve various optimization problems [12].
In WFLOP, GAs [14] and DEs [22], along with their improved versions [13], are the most commonly used and dominant algorithms.According to Shakoor et al., [17], GAs and DEs are used in over 75% of WFLOP problems.Within these improved versions, algorithm hybridization and parameter tuning are still two major strategies, for example, Chen et al. proposed a hybrid genetic algorithm [4] and Bai et al. proposed an adaptive evolutionary algorithm [3] to address WFLOP.However, with the ongoing research in evolutionary algorithms, a large of new algorithms have emerged.How to improve algorithms more specifically to effectively address WFLOP has become a key research issue.This study aims to identify appropriate evolutionary algorithm improvement strategies for addressing WFLOP.Through comparative experiments between two primary algorithm improvement strategies, we can determine which strategy better balances exploration and exploitation performance in WFLOP, thus helping researchers avoid less fitful improvement strategies.

METHOD OF ALGORITHM IMPROVEMENT 3.1 A genetic algorithm enhanced differential evolution
The method of improving evolutionary algorithms through algorithm hybridization method involves merging the strengths of two evolutionary algorithms, which usually results in a change in the structure of the algorithm.According to this principle, we utilized the randomness inherent in the mutation operation of the GA [8] to assist the population in generating some individuals with randomness, to ensure the exploration capability of the algorithm.Among these randomly generated individuals, some might guide the DE toward potential directions close to the global optimization solution.
The hybrid algorithm produced by enhancing the DE using the GA can be described as follows: (1) First, the flag is set to 1, and the DE is checked to see if it produces a better solution in one iteration.If a better solution is found, the counter is reset to zero, while if no better solution is found, the counter is incremented by 1. (2) Secondly, when the counter reaches a set threshold  , which the threshold is to judge DE has fallen into local optimization or not, the flag is set to 0, and in the next iteration, the GA algorithm is used to mutate the population and other operations.After that iteration is complete, the flag is reassigned to 1 and switches back to DE for iteration.(3) Lastly, update the iterative population and repeat steps (1), (2), and (3) until the termination criteria are met.

Adaptive parameter differential evolution
For different optimization problems, setting the parameters of the algorithm is essential, by altering the inherent parameters of the algorithms, it can be tailored to achieve better results for a specific optimization problem, and directly adjusting these parameters is the most straightforward method.But it is hard to find a parameter setting suitable for all the cases, the presented simple example in Fig. 2 also illustrates that, as the Differential Evolution (DE) algorithm seeks global optimization in the solution space, varying scenarios demand different magnitudes of the scaling factor  to effectively facilitate a balance between algorithmic exploitation and exploration.However, a fixed parameter value proves inadequate for accommodating all situations.Consequently, for optimization problems akin to WFLOP, which encompass diverse constraints, the algorithm's capacity to dynamically adapt its parameters becomes imperative for achieving superior performance.Since it's impossible to find a suitable parameter setting that adapts to all constraints when facing WFLOP.It's vital for an algorithm to possess the capability to adjust the balance between its exploitation and exploration performance based on current results.In this study, we employed the successful history record mechanism [19] to enhance the DE, enabling it to adaptively adjust the value of scaling factor  of the DE based on the current results during the algorithm's operation.The specific algorithm process is as follows: (1) Create a successful history record memory  .
(2) In each iteration, when the differential evolution algorithm finds a better solution, record the value of the used scaling factor   and the difference in new fitness and old fitness △  to an array   .(3) For each   and △  recorded in the array   , its weight can be calculated according to the following equation: (4) Use values in array   , to calculate the weighted average   as the equation as follows: and record   into the successful history record memory  .(5) When generating new  for the next iteration, the algorithm will select a   () from memory  randomly and generate value of new  according to the Cauchy distribution.
This adaptive parameter differential evolution(APDE) is to use a successful history record mechanism to mediate the size of the parameters.Specifically, it involves recording those parameters that successfully lead the algorithm to a better solution and generating parameters for the next iteration round based on these recorded parameters.There are two main advantages to this adaptive approach: 1) It ensures that the algorithm can adaptively adjust parameters during the iterative process without overly relying on the initial parameter settings.2) It enables the DE to ensure a trend towards finding better solutions not only by updating individuals who have found better solutions but also by updating the parameters that led to these improved results, thereby enhancing the algorithm's overall performance.Since each trial implements the same optimization strategy, good parameters are considered effective for the

Performance evaluation criteria
The following assessment tools are used to evaluate the performance of the evolution algorithms in this study: 1) Wilcoxon rank-sum test: This is a non-parametric statistical test, used to assess the null hypothesis that two samples come from the same population, rather than the competing hypothesis.In this study, the test was used to compare data obtained from the optimization of 51 functions and to identify the differences between the improved algorithm and other algorithms, with results represented as  / /.Specifically,  represents the number of functions where the improved algorithm significantly outperformed other algorithms,  indicates the number of functions where the improved algorithm showed no significant difference compared to other algorithms, while  stands for the number of functions where the improved algorithm was noticeably inferior to other algorithms.The result is indicated by "+" if the improved algorithm performed better, "=" if there was no significant difference, and "−" if the improved algorithm performed worse.
2) Box-and-whisker plot: The box-and-whisker plot is a graphical representation used to depict the distribution of a dataset through its quartiles.The box represents the interquartile range (IQR) and contains 50% of the data.The line inside the box indicates the median, the line above the box represents the upper quartile (75th percentile), and the line below the box indicates the lower quartile (25th percentile).The red "+" symbols represent outliers, while the whiskers extend to the minimum and maximum values, excluding outliers.

Experimental results on 𝐼 𝐸𝐸𝐸 𝐶𝐸𝐶2017
In this section, we tested the GA-enhanced DE based on the hybridization method, this hybrid algorithm is termed the hybrid DE in this section.In terms of parameter settings, we set both the scaling factor  and crossover probability  of the DE to 0.9, and the counter threshold  , used to determine if the DE falls into local optimization, was set to 10.We tested the hybrid DE, DE, and GA algorithms on the   2017 test set.2017 is a benchmark for testing evolutionary algorithms, it can tell whether an evolutionary algorithm good or not to some degree, and from the Table .1, it's evident that the hybrid DE outperforms the other two, this also demonstrates that the algorithm hybridization method effectively enhanced the performance of the DE, and the inclusion of the GA algorithm resulted in an overall improvement in the exploration capacity of the algorithm, thus achieving a better balance between the exploitation and exploration capabilities of the algorithm.

Experimental results on WFLOP
The model for WFLOP generally consists of five sub-models: wind condition model, wind farm land model, wake effect model, wind turbine model, and wind farm cost model.In this study, we utilized the wind farm layout model proposed by Ju et al. [9].
In WFLOP, the direction and speed of the wind are key factors.In this study, four different wind types are selected.Wind speed for  1 ,   2 ,   3 is always 13m/s.In detail,  1 has a single wind direction.While   2 has four wind directions and each direction has an equal chance of occurrence.For  3 has six wind directions and the possibilities of wind from each direction are 20%, 30%, 20%, 10%, 10% and 10% respectively. 4 has 12 wind directions, and for each direction has a 58.33% possibility of wind blowing 13m/s, 16.67% possibility of wind blowing 10m/s, 8.33% possibility of wind blowing 7m/s.
The study by Ju et al. [9] has investigated situations where some parts of a wind farm might not be suitable for placing wind turbines.This case shown in Fig. 3 is an example of a wind farm layout solution, where the shaded areas represent unsuitable locations for placing wind turbines.The light blue blocks indicate potential turbine placement locations, green ones represent already placed turbines.The numbers in Fig. 3 represent the index labels  for each block.Subsequently, these labels are transformed into a twodimensional (2) coordinate system to locate each block in the wind farm.
Fig. 1 illustrates how the wake effect of one wind turbine impacts the wind turbines behind it, leading to a reduction in the wind energy that can be captured by the wind turbines located behind it, eventually resulting in a decrease in wind farm output.The objective of WFLOP is to optimize the placement of wind turbines to minimize the wake effect between them, hence maximizing the energy output of the wind farm.
To test the specific performance of algorithms for WFLOP, we tested each algorithm under 13 different wind farm cases, each wind farm having a varying number of wind turbines, and adopting four different wind direction distributions:  1 ,  2 ,  3 , and  4 .The first set of wind farms,  1 −  6 , offers 120 available blocks, while  7 −  1 2 comprises 132 available blocks.In the basic case  0 , there are no land constraints, offering 144 blocks.In each wind direction distribution, on different wind farm lands, we executed each algorithm a total of 51 times, with a fixed evaluation count 20,000 times.
As an experiment, we applied the improved algorithm and the original algorithm specifically to the WFLOP, which is also the core research objective of this study.Surprisingly, based on the results, the hybrid algorithm is not effective on the WFLOP, and in fact, it performs worse than the DE before the hybridization.We then repeatedly modified the threshold of the hybrid algorithm's counter to achieve a thorough validation.The final results, as shown in the Table .2 and Fig. 4, indicate that regardless of how the threshold parameter T is adjusted, the hybrid algorithm cannot achieve better results than the original algorithm on the WFLOP.Moreover, as the threshold parameter T increases, the results obtained by the hybrid algorithm improve and tend to approach the original algorithm.There are two possible reasons that can explain this outcome: (1) In WFLOP, the DE attempts to identify a direction where a potential optimization solution might exist for exploration and exploitation.However, the improvements in the hybrid algorithm might disrupt the original exploration direction.In this context, the addition of the GA algorithm instead undermines the overall capability of the algorithm to find the optimization solution.
(2) When the counter threshold is set too low, switching algorithms at this setting is not rational.This is because the DE hasn't truly fallen into local optimization, and there might be a good chance that a better solution can be found in the subsequent iterations.In other words, overly frequent algorithm switching can actually hinder the overall performance capability of the algorithm, leading to a significant deterioration in its performance.
In summary, the improved hybrid algorithm has been proven effective on the 2017 problem set, but it yielded the opposite results in the WFLOP.This further highlights the significance of our study: when selecting suitable evolutionary algorithm improvement methods for the WFLOP, comparative experiments revealed that the hybrid algorithm's improvements are not suitable for this particular problem.Furthermore, it's imperative to mention that it's inadequate and irrational to only validate an enhanced algorithm on problem sets like 2017.Only when applied to specific optimization cases can its advantages or limitations be genuinely manifested.

DISCUSSION & CONCLUSIONS
In previous research, researchers broadly categorized evolutionary algorithm improvement methods into two types: those based on algorithm hybridization and those based on parameter tuning.However, although both of these methods can improve the algorithm to some extent, helping it balance between exploration and exploitation, and achieve better results on public benchmarks like 2017, neither guarantees improvement for specific optimization problems.This makes researchers to conduct extensive comparative testing to select an appropriate improvement method.Consequently, algorithm enhancements often heavily rely on the researcher's experience and a lot of trial and error.
To assist researchers in better-selecting improvement methods for EAs when studying WFLOP, we initiated discussions on optimizing WFLOP using the most classic evolutionary algorithms (GA and DE) and widely accepted improvement strategies.The emphasis was on the core tenet of improving evolutionary algorithms, namely balancing their exploration and exploitation capacities.Under four wind directions, three turbine quantities, and thirteen land constraints, the parameter tuning improvement method was shown to be superior to the algorithm hybridization method.Moreover, by adaptively changing parameters, the proposed APDE demonstrated better performance to various constraints in the WFLOP problem than the original algorithm.However, this conclusion still requires further verification.Firstly, although we based our improvements on the most classical evolutionary algorithms, GA and DE, in an attempt to reach a more general conclusion, there are still many other excellent evolutionary algorithms that could serve as a foundation for testing.Additionally, numerous algorithm improvement techniques and details were not deeply analyzed, limiting our ability to draw broader conclusions.
Therefore, we recommend two areas of improvement for future research.Firstly, apply more excellent evolutionary algorithms as the foundation for improvements and conduct further experiments on the WFLOP based on the two primary improvement methods.Secondly, during the algorithm improvement process, apply a broader range of algorithm improvement techniques and details to comprehensively evaluate and compare the most suitable improvement methods for WFLOP.Our research has not yet incorporated the cost and economic indicators of the wind farm itself.However, there are existing studies [20] that have explored this aspect.We plan to reference these studies in our future work to construct a more comprehensive model.This improved model will thoroughly introduce these cost and economic indicators for a more holistic evaluation.Additionally, while the model used in this paper does simulate under different wind speeds and conditions, the simulation is based on probabilistic statistics and represents a discrete scenario.It does not simulate based on the continuity of time.In the real world, wind conditions often change over time and tend to be a continuous issue.Therefore, optimizing the model to address this continuity is also a key area of focus for future research.

Figure 1 :
Figure 1: Wind farm layout optimization to reduce the impact of the wake effect (a) Situation that DE needs big scaling factor  (b) Situation that DE needs small scaling factor

Figure 2 :
Figure 2: An example of DE's scaling factor affecting algorithm's exploration capability

Figure 3 :
Figure 3: An example of a wind farm layout with land restrictions.

Table 1 :
Comparison between evolutionary algorithms on IEEE CEC2017 Figure 4: Boxplot result on  2 where turbine number= 15

Table 3 :
Comparison between APDE and DE with different parameter under wind type  2

Table 4 :
Comparison between APDE and DE with different parameter under wind type  1 ,  3 and  4