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A Systematic Method for Generating Discrete Multidimensional Thomae-like Functions
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DOI：10.3390/electronics15153284.png)
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Abstract
En 中文
Generating multidimensional rugged landscapes is very important for testing and benchmarking, considering the increasing number of multi-objective optimization problems and the pervasive use of computational systems. The diverse nature of such problems has led to a variety of algorithmic solutions, designed to create more scalable and problem-independent algorithms. This paper introduces a method for constructing a class of discrete multidimensional Thomae-like functions, generalizing the classical Thomae function. While the original function is continuous at irrational points and discontinuous at rational ones, we extend this approach to higher-dimensional discrete spaces. We present the properties of three known analytic generalizations and analyze five proposed discrete cases according to the relationship between the numbers of input and output values. The most important properties of such functions are discussed, including their periodicity, number of local maxima, autocorrelation, and output variations under small input changes. The last property has significant importance for simulating and testing in various application areas. This work unifies and extends existing concepts into a systematic method for generating discrete multidimensional functions, opening new directions for both theoretical investigations and practical applications of algorithms in engineering.
Keywords:
Thomae
function
discrete
multidimensional
engineering