Experimental Comparison of GA/NSGA-II Operator and Encoding Choices in MATLAB: A Reproducible Two-Variable Non-Convex Benchmark

This paper presents an instructional and reproducible assessment of how operator choice and encoding affect GA/NSGA-II performance on a non-convex, oscillatory two-variable benchmark over 𝑥,𝑦∈[−۱۰,۱۰]. A real-coded GA (MATLAB ga) was tested under six crossover–mutation pairings (single-point, two-point, arithmetic) × (uniform, Gaussian), with ۲۰ independent runs per pairing; best objective value, associated (𝑥,𝑦), and runtime were recorded. A binary GA with a ۳۲-bit chromosome (۱۶ bits per variable) and linear decoding to [−۱۰,۱۰] was then compared against the best real-coded setting (arithmetic + Gaussian), reaching the same reported best minimum 𝑓(𝑥,𝑦)≈−۲۱.۰۵۶۹۰۵. Finally, a multiobjective variant was solved using MATLAB gamultiobj (NSGA-II) by defining the second objective as the inverse of the first; nine operator combinations (۳ crossovers × ۳ mutations) were evaluated and Pareto fronts were analyzed in terms of coverage and diversity.

کلیدواژه ها:

Genetic Algorithm ، NSGA-II ، operator comparison ، binary encoding ، MATLAB