# Advanced Parameter-Setting-Free Harmony Search Algorithm
## 1 Introduction  
A metaheuristic is a heuristic technique that can be applied to various problems irrespective of the type and information of the problem. Various such methods have been proposed, including the representative genetic algorithm. This metaheuristic method is a technique that can be optimized not only in engineering but also in various other fields, such as natural science, business administration, and social science, because of the simplicity of its concept and theory.  
The harmony search (HS) algorithm [1] is one of the metaheuristic algorithms and was inspired by the musical idea of finding each instrument's notes by modifying each one a little bit, to create harmony among the instrument's notes. Similarly, the HS algorithm has the characteristic that the variable data that gives the best result in the memory called harmony memory (HM) can be stored and updated during the execution of the algorithm, and the value stored in the HM can be used for the next iteration. The HS algorithm has been used in various fields because it is easy to apply in any field and has the advantage of fast convergence and proper results [2; 3].  
It is common to use random values for each variable when performing HS but to use the values in HM as they are or change them slightly depending on the probability. The performance of the HS algorithm depends on the parameters that determine this probability. When the HS algorithm is used, the parameters of the harmony memory consideration rate (HMCR) and pitch adjustment rate (PAR) are determined according to the type of problem and the number of variables required for the problem. It is important. In general, these two parameters are set manually by a human and fixed during HS operation, but this does not apply to the change of HM according to the progress of the operation. Therefore, many executions are needed overall. To solve this problem, a parameter-setting-free (PSF)method [4; 5; 6] has been proposed. In this method, if the result is stored in HM, the variables used to derive the value are stored separately, and the result is put in HM to determine the value of HMCR and PAR for each variable. However, this method can make the value of HMCR and PAR 0 or 1 before the maximum iterations are reached. If the value of HMCR or PAR becomes 0 or 1, even if HS is performed, it is difficult to produce good results because new random values are not used in certain variables or only some variables are changed.  
[PERSON] et al. [7] proposed a method that modifies the values of HMCR and PAR with predefined values near 0 or 1 when they result in 1 or 0 during the execution of HS. However, the problem with such a method is that the values of HMCR and PAR are fixed at the predefined values after a certain number of iterations. We propose a novel PSF scheme that the HMCR and PAR values are automatically adjusted to converge into a certain value in the range of 1 and 0 following the optimization problem during the optimization process of HS.  
In this paper, we explain and interpret the meaning of the HMCR and PAR values in the HS algorithm and present an advanced PSF scheme for these parameters. Section 2 will look at the basic parameters of the HS algorithm and how the HS algorithm works, and it describes the conventional PSF scheme and the problems that occur when using it. Section 3 proposes our advanced PSF scheme and explains why it is good to use the advanced PSF scheme. Section 4 compares the results between the HS algorithm using fixed HMCR and PAR, the existing PSF HS algorithm, and the new PSF HS algorithm.