Subdividing Labeling Genetic Algorithm: A new method for solving continuous nonlinear optimization problems

Abstract

In most global optimization problems, finding a global optimum point in the whole multi-dimensional search space implies a high computational burden. We present a new approach called subdividing labeling genetic algorithm (SLGA) for continuous nonlinear optimization problems. SLGA applies mutation and crossover operators on a subdivided search space where an integer label is defined on a polytope built on a n-dimensional space. After calculating the fitness of each point composing the polytope, SLGA implements a mutation operator to generate offspring and computes an integer label for the population of the polytope. Then, after completely labeling the polytope, a crossover operator is implemented so as to approach the optimum point by reducing the search space. In this regard, new population is generated by subdividing the search space and further implementing the mutation operator. SLGA has been used to optimize the De Jong functions, as well as nonlinear constrained and unconstrained problems with discrete, continuous and mixed variables. It has also been compared with other well-known algorithms. Experimental results show that the SLGA method has good performance and reduces the number of generations within the solution space, which enhances its convergence capability.