Cauchy distribution with Cuckoo search algorithms for solving job shop scheduling Problem

Abstract

This research applies the Cuckoo Search Algorithm, specifically the Original Cuckoo Search(CS), Improved Cuckoo Search(ICS), and Global Feedback cuckoo search(GFCS) with different values of parameters instead of using a fixed value of probability a banda (Pa) which equal to 0.25 by another researcher to solve the problem of Job Shop Scheduling. The goal is to modify the method to improve its effectiveness and total completion time (Makespan) using benchmark datasets for basic scheduling problems, and suggest using the Cauchy distribution, with its ability to generate random numbers from distant points, and the stronger perturbation ability of Cauchy variation compared to Gaussian variation, along with Levy flight, effectively prevent the cuckoo algorithm from falling into local optima. Notably, when the step size is 0.1 and Pa is 0.1, with a population of 10 and 100 iterations, GFCS obtains the ideal Makespan of 140 when applied to the (20x20) set. Also, the Cauchy distribution for the CS produces the best results compared levy distribution that increases the variety of the nests, enabling escape from regional extreme values and fostering global search.