Improving the search pattern of Rooted Tree Optimisation algorithm to solve complex problems

Abstract

Rooted Tree Optimisation (RTO) is a metaheuristic method for solving complex problems. Roots in RTO move to new search space without evaluating such move for better fitness values. Best root in RTO which acts similar to the global best in Particle Swarm Optimisation, is used to influence the movement of the rest of the roots to a promising region. This influence may lead the algorithm to premature convergence.The Lateral Growth Rooted Tree Optimisation (LGRTO) that is proposed in this work eliminates the influence of the best root to direct the search pattern of other roots. This is achieved by introducing hydrotropism and lateral growth equations. In both equations, the influence of the best root is eliminated, and every exploitation or exploration is evaluated before the roots move to new points in the search space.Three types of experiments were done. Two of these experiments are benchmark functions for continuous optimisation problems. The third type is a fourth order Butterworth filter design problem.The result of the nonparametric test of experiments on continuous optimisation problem indicated that LGRTO obtained better performance over Rooted Tree Optimisation and Real Coded Genetic Algorithm. The performance of LGRTO is competitive with the result of Teaching and Learning Based Optimisation (TLBO) and LSHADE with Semi-Parameter Adaptation Hybrid with CMA-ES (LSHADE-SPACMA) methods. For the result of Butterworth design problem, LGRTO obtained a design error that is lower than the value obtained by RTO, Particle Swarm Optimisation (PSO), Differential Evolution (DE), Tabu Search (TS), and Artificial Bee Colony (ABC) methods.

Keywords

• Metaheuristics optimisation
• Rooted Tree Optimisation
• Lateral Growth Rooted Tree Optimisation
• Complex problem
• Numerical optimisation