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Random Lines: A New Population Set-based Global Optimization Algorithm Based on Quadratic Models



Ismet Sahin


In this technical note, we propose a new population set-based evolutionary global optimization algorithm for minimizing cost functions. We select pairs of points, pass a line through these two parent-points, choose another point on this line, and determine a unique quadratic function having same function values at these three points in the mutation operation. Extrema of these quadratic functions become descendant points under certain conditions. Some entries from both parent-points replace corresponding entries of their descendant point based on a crossover constant in the crossover operation. The proposed algorithm achieves a more robust and faster convergence with these mutation and crossover operations since the mutation operation tries to learn cost surface by quadratic models and therefore finds regions of search space with smaller function values and since the crossover operation perturbs the extrema of these models by using two parents and therefore increases diversity in search directions. We compare this algorithm with the Differential Evolution algorithm and demonstrate its high efficiency and robustness over a wide range of cost functions.
Genetic Programming
Publisher Info
Springer Berlin Heidelberg, London, New York


Global Optimization, Continuous Optimization, Stochastic Optimization, Random Lines, Differential Evolution


Sahin, I. (2011), Random Lines: A New Population Set-based Global Optimization Algorithm Based on Quadratic Models, Springer Berlin Heidelberg, London, New York, [online], (Accessed April 24, 2024)
Created April 27, 2011, Updated February 19, 2017