# Differential Evolution with Linear Bias Reduction in Parameter Adaptation
## 1 Introduction  
The Computational Intelligence (CI) methods include a variety of approaches, such as Evolutionary Computation (EC), Fuzzy Logic (FL), and Neural Networks (NN). Despite the differences among these directions, one of the most important research areas that connects the parts if CI is the classical numerical optimization, and thus, the development of modern optimization techniques is one of the most important directions. The new heuristic optimization methods, including Evolutionary Algorithms (EA) and Swarm Intelligence (SI), are usually developed by introducing new algorithmic schemes [1] or parameter control or adaptation techniques [2]. Among the numerical optimization techniques, the Differential Evolution (DE) algorithm [3] has attracted the attention of a large number of researchers due to its simplicity and high performance [4]. The results of the annual competitions on numerical optimization, conducted within the IEEE Congress on Evolutionary Computation, show [5] that in the last few years, the winners have been mostly DE-based frameworks, which include hybridization or novel parameter tuning techniques.  
Currently, one of the main directions of studies on differential evolution is the development of parameter adaptation techniques. The parameter tuning mechanism should rely on the search process quality, usually fitness values and their improvement, and for a tuning scheme to be efficient, it should be designed with respect to the algorithm properties, which leads to many different adaptation schemes developed for specific algorithms. The final goal of every tuning scheme is similar: provide the algorithm with the ability to tune parameters to suboptimal values at every stage of the search so that the best possible solution is reached at the end. Several recent surveys considered the existing variants of DE and their properties [6, 7].  
The parameter tuning techniques include parameter adaptation and parameter control methods: the former change parameter values based on feedback, while the latter follow a predeterminedcontrol strategy. Some of the recent advances in parameter adaptation include the success-history adaptation-based SHADE algorithm [8] and the distance-based DISH modification [9], while parameter control includes the linear population size reduction method in the L-SHADE approach [10], as well as rules for parameter control in the jSO algorithm [11]. All these modifications have shown that the potential of DE improvements is far from being exhausted, and thus, new investigations in this area are important.  
In this study, the linear bias reduction technique is proposed, which changed the success-history-based parameter adaptation scheme by introducing the generalized Lehmer mean proposed in [12] and a rule for changing the coefficient in the Lehmer mean depending on the stage of the search. The experiments are performed on the benchmark functions of the CEC 2017 and CEC 2020 competitions, and the results are compared to the state-of-the-art approaches.  
The paper is organized as follows: the second section contains the description of the modern DE variants and, then, proposes the linear bias reduction approach; the third section contains the experimental results and comparison; the fourth section contains the discussion; and the last section concludes the paper, providing the directions for further research.