광역 최적해를 위한 Multi-Basin 기반 동적 이웃 탐색 방법

Abstract

We focus on the global optimal solution and approach three phases to find the global optimal solution. In the first phase, we simply find the local minimum of all domain with random points as initial points. In order to improve this local minimum, we use phase 2 algorithms. In this phase, we can find the sup-local minimum using neighbor search, which search the parallel directions of all axes. For comparing this sup-local minimum, we also get other solutions from Direct search, Genetic Algorithm, and Particle swarm optimization. Next, we can get improved sup-local minimum to use Genetic Algorithm and Direct Search with the sup-local minimum point as an initial point. Also, using Multi start algorithm, we find the local minimum from several initial points and get the sup-local minimum from several initial points, and compare all solutions. Finally, we apply proposed algorithm to Heston's model for obtaining an option price.