۱- Introduction

۲- Related work

۳- ARM-based parameter adaptive strategy

۴- Experimental results on benchmark functions

۵- Experimental results on real-world problems

۶- Conclusions and future work

References

Abstract

It is a very challenging and important task to adaptively adjust the scale factor F and the crossover rate Cr for Differential Evolutionary (DE) algorithms. Most recent adaptive techniques were designed to generate parameters randomly based on successful trial values during the previous evolving process, lacking explicit guidelines to generate appropriate values. This paper proposes a novel parameter adaption strategy, which could incorporate promising F and Cr pairs extracted by using Association Rule Mining (ARM) into DE algorithms. First, all successful F and Cr values generated by their original methods are recorded during the whole evolution, resulting in an increasing dataset. Second, we discretize the dataset and extract the most frequent itemset of parameters by using a modified version of the widely used Apriori algorithm. Third, a greedy operator is developed to generate new parameters in the next generation by comparing the presented ARM-based and original-method-based fitness values. The presented technique provides an additional pair of F and Cr values to be evaluated, without replacing existing strategies for the control parameters. The main contribution of this paper is that we propose a novel way, which utilizes information generated during the evolutionary process, to enhance exploration capabilities by adjusting control parameters. Experimental results demonstrate that the proposed ARM-based parameter adaptive strategy is able to enhance performances of some state-of-the-art DE variants. Further, this methodology might be helpful for other control parameters of Evolutionary Algorithms (EA).

Introduction

Since 1995, Differential Evolution (DE) algorithm and its variants have become very popular in evolutionary computing community (Storn and Price, 1997). DE family also has been successfully and widely used to solve many real-world engineering problems on diverse domains (Arce, et al., 2018; Baig, et al., 2017; Buba and Lee, 2018; Cui, et al., 2018; Das, et al., 2016; Das and Suganthan, 2011; Hu, et al., 2018; Mlakar, et al., 2017; Muangkote, et al., 2017; Neri and Tirronen, 2010; Tsakiridis, et al., 2017). The performance of DE algorithm mainly depends on the evolutionary operators and the control parameters which are usually the scaling factor F and the crossover rate Cr (Cui, et al., 2016). Selecting the most appropriate parameter values is a task, which requires adjusting processes by trial-and-error. Therefore, it is also a time-consuming task. Meanwhile, it also depends on given optimization problems. This approach is not suitable when pre-knowledge is needed, nor the problem would be optimized in an automated environment (Mallipeddi, et al., 2011). Thus, it is very important to adaptively and automatically tune F and Cr by using potential helpful information during the whole evolution process. Since the last decade, a good number of articles which have focused on adapting two main control parameters, usually the scale factor F and the crossover rate Cr, have emerged. A DE variant with an adaptive parameter control was proposed in (Elsayed, et al., 2013). The authors designed two candidates sets, which store F and Cr values selected from the top10-40% individuals. First, a counter is used and initialized to zero for each of the combinations of F and Cr. A trial vector is generated by randomly selecting a pair of the F and Cr from the sets. If the trial vector has better fitness value, the counter automatically is incremented by 1. After some generations the top 50% of valuable combinations of F and Cr are selected, their counters are reset to zero and the rest are discarded. Later, this work has been improved (Sarker, et al., 2014).