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Title (Arabic)

طريقة مقترحة لانشاء تصاميم القطاعات غير الكاملة المتزنة BIBD بتوظيف الخوارزمية الجينية الوراثية

DOI

10.33095/jeas.v13i46.1282

Abstract

Balanced Incomplete Block Designs (BIBD) are specialized experimental designs characterized by specific parameters: t (number of treatments), b (number of blocks), k (number of experimental units per block), r (number of replicates per treatment), and Lambda (the number of times any two treatments appear together in the same block). In a BIBD, because t > k, each block does not contain all treatments, and since b > r, each treatment does not appear in every block. These designs were originally developed for plant breeding and selection to ensure that all comparisons between treatment pairs are made with equal precision. This paper proposes a method for constructing these designs by employing Genetic Algorithms (GA). Genetic Algorithms are search heuristics inspired by the process of natural evolution, used here to optimize the arrangement of treatments within blocks to satisfy the rigorous mathematical requirements of a BIBD. The study details how the GA can be structured to handle the combinatorial complexity of block designs, ensuring that the resulting configuration meets the criteria for balance and incompleteness. This approach provides a flexible and efficient alternative to traditional algebraic or cyclic construction methods, particularly for parameters where standard construction recipes may be complex or unknown.

Abstract (Arabic)

طريقة مقترحة لانشاء تصاميم القطاعات غير الكاملة المتزنة BIBD بتوظيف الخوارزمية الجينية الوراثية

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