Minimization over randomly selected lines

Abstract

This paper presents a population-based evolutionary optimization method for minimizinga given cost function. The mutation operator of this method selects randomly oriented lines in thecost function domain, constructs quadratic functions interpolating the cost function at three differentpoints over each line, and uses extrema of the quadratics as mutated points. The crossover operatormodiŞes each mutated point based on components of two points in population, instead of one point asis usually performed in other evolutionary algorithms. The stopping criterion of this method dependson the number of almost degenerate quadratics. We demonstrate that the proposed method with thesemutation and crossover operations achieves faster and more robust convergence than the well-knownDifferential Evolution and Particle Swarm algorithms.