SOLVING THE PELL EQUATION, DIOPHANTINE EXPONENTIAL EQUATIONS AND SYSTEM OF DIOPHANTINE EQUATIONS USING SPIRAL OPTIMIZATION ALGORITHM WITH CLUSTERING TECHNIQUE - SHOFI EDRIANI (NIM: 20116018), TIARA
The Spiral Optimization Method developed by Kenichi Tamura and Keiichiro Yasuda in 2011 is one of the metaheuristic methods used to solve optimization problems. This method can approach the global optimum solution and is not easily trapped in a local solution. The parameters used in the spiral optimization algorithm, r, θ, k_max, m, affect the performance of the method and are usually determined by trial and error. Therefore, effective setting method for r parameter is determined using stability analysis of the spiral optimization model, so that it can reduce the parameter determination by trial and error. Spiral optimization methods can also be used to solve nonlinear equation systems, by turning them into optimization problems. This thesis proposes the numerical solution of Pell equation, Diophantine exponential equations and system of Diophantine equations which has an integer solution, by modifying the spiral optimization algorithm. The use of the Clustering technique and the Sobol sequence will be added to the spiral optimization algorithm to get all the solution problems in one execution.