Adaptive memetic differential evolution with multi-niche sampling and neighborhood crossover strategies for global optimization
Introduction
Differential evolution (DE), proposed by Storn and Price [25], has received much attention due to its good convergence property and easy implementation. DE, which aims for identifying global optima of optimization problems, is a population-based stochastic search technique that uses mutation, crossover and selection operators to evolve the population [33]. DE has been successfully applied to various fields, such as power system optimization [5], [36], feature selection [1] and time series prediction [9].
Nevertheless, DE suffers from premature convergence [20]. Premature convergence refers to the situation, where the population converges to a local optimum, due to the loss of diversity. It is widely believed that an appropriate degree of population diversity is crucial for the success of DE [6], [19]. To address this issue, many approaches have been developed [8], [37] to maintain the population diversity during the run of DE. For example, the first approach tends to adjust the values of mutation rate F and crossover rate CR to enhance the diversity of population. The adaptive DE algorithms such as L-SHADE [27], SaDE [23], jDE [4] and JADE [40] belong to this approach. The second approach tries to perturb the population by reinitializing part of its individuals [30], [16] during evolution to maintain the population diversity. The third approach tends to adopt structured or multiple populations with controlled migration to maintain the population diversity [10], [3]. While, the fourth approach, which is perhaps the most popular approach, tries to preserve the population diversity during evolution by introducing the niching technique into DE [13], [31]. The above approaches are able to improve the population diversity during evolution, thus enhancing the performance of DE. However, they generally ignore that, to properly search the solution space, DE may require different population diversities at different stages of evolution, thus limiting their performance.
Another critical issue of traditional DE is that, although it is good at global search, it is not good at local search. This could greatly reduce its efficiency of identifying the optimum in the solution space. To alleviate this issue, incorporating local search operations into DE, resulting hybrid DEs (also termed as memetic algorithms), have been widely proposed [7], [29]. For instance, in [29], three local search algorithms were incorporated into a DE to speed up the convergence of population. In [7], Chen et al. tried to employ a chaotic local search to ensure efficient convergence of DE and applied the resulting algorithm to address complex high dimensional optimization tasks. In [21], Pei et al. proposed a hybrid DE, in which a bat-inspired algorithm was incorporated into a DE to enhance the search efficiency.
To address the above issues, this paper proposes four strategies and incorporates them into a DE algorithm, resulting a method called adaptive memetic DE with multi-niche sampling and neighborhood crossover strategies, to deal with global optimization problems. The primary contribution is fourfold:
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A multi-niche sampling strategy, which can dynamically sample an appropriate subpopulation at each generation for evolution, is devised to support a diverse search at the early stage of evolution while an intensive search towards the end of evolution.
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A neighborhood crossover operation, which tends to encourage high potential solutions for exploitation while low potential solutions for exploration, is designed for facilitating the DE to appropriately search the solution space.
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An adaptive local search strategy, which considers the stage of evolution as well as the problem instance to implement the local search, is developed and employed to appropriately fine-tune promising solutions in the sampled subpopulation during evolution.
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An adaptive elimination operation, which tends to dynamically determine an appropriate number of individuals to be removed from the population, is devised and employed to eliminate unpromising individuals during evolution.
Extensive experiments on 15 widely used benchmark functions have been carried out to assess the effectiveness of devised strategies and to compare our proposed algorithm with related methods. The results demonstrate the significance of the devised strategies as well as the superiority and flexibility of the proposed algorithm.
The rest of this paper proceeds as follows. Section 2 briefly describes the basic DE. Section 3 reviews related works. Section 4 presents the details of our algorithm. This is followed by experimental evaluation and comparison in Section 5. Finally, Section 6 concludes the paper with a summary.
Section snippets
Differential evolution
DE starts with an initial population of NP candidate solutions and each solution is encoded using a D-dimensional decision vector, i.e., . The initial population is randomly generated within the search space constrained by the prescribed decision variable’s bounds by:where and are the lower and upper bounds of the dimension, rand(0,1) denotes a uniformly distributed random variable in the range of [0,1]. After
Related works
Population diversity plays a critical role for the performance of DE. Many methods have been proposed to maintain the population diversity of DE. The first kind of approach involves in schemes, which try to increase the variance of population by dynamically changing the values of scale factor F and crossover rate CR during DE evolution. For example, Zhang et al. [40] introduced a scheme, which tends to dynamically update the parameters F and CR based on their historical records of success.
Proposed algorithm
In this section, we propose an adaptive memetic DE with multi-niche sampling and neighborhood crossover strategies for global optimization. The proposed algorithm starts with a population randomly generated in the solution space and an initial DE parameter setting. At each generation, the population is first divided into niches by employing the speciation cluster niching scheme [12], [24]. A subpopulation is then dynamically sampled from the resulting niches to support a well-balanced
Experiments
In this section, we first describe the data sets used in experiments and parameter settings of the proposed algorithm. Then, a series of experiments are carried out to access the significance of devised strategies as well as to verify the proposed algorithm by comparing it with related work. All algorithms are implemented on a workstation with an Intel Core i7-8700 CPU at 3.20 GHz and 8 GB RAM. Unless otherwise stated, we run each Algorithm 50 times on each test problem, and report the mean
Conclusion
In this paper, we propose and implement an adaptive memetic DE with multi-niche sampling and neighborhood crossover for global optimization. The multi-niche sampling strategy is designed to sample an appropriate subpopulation for supporting a well-balanced evolutionary search of DE. Further, a neighborhood crossover strategy is developed to encourage high potential solutions for exploitation while low potential solutions for exploration, thus appropriately searching the solution space.
CRediT authorship contribution statement
Zuling Wang: Methodology, Investigation, Software, Writing - original draft. Ze Chen: Methodology, Writing - original draft, Validation. Zidong Wang: Conceptualization, Writing - review & editing, Supervision. Jing Wei: Software, Investigation. Xin Chen: Software, Investigation. Qi Li: Investigation, Writing - review & editing. Yujun Zheng: Validation, Writing - review & editing. Weiguo Sheng: Conceptualization, Methodology, Validation, Supervision, Writing - original draft.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work was supported in part by the National Natural Science Foundation of China under Grant No. 61873082, Grant No. 62003121 and Grant No. 61872123, the Zhejiang Provincial Natural Science Foundation of China under Grant No. LQ20F030014, and the Royal Society of the U.K.
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These authors contributed equally.