A New Approach for Finding the Global Optimal Point Using Subdividing Labeling Method (SLM)

TL;DR

This paper introduces a subdividing labeling method (SLM) that efficiently finds the global optimal point in large, multidimensional search spaces with reduced computation and steps, outperforming existing techniques.

Contribution

The paper presents a novel subdividing labeling method (SLM) that reduces computational effort and improves reliability in global optimization tasks across high-dimensional spaces.

Findings

SLM achieves faster convergence than traditional methods.

SLM demonstrates lower computational complexity, O(log n).

SLM outperforms random search, walk, and simulated annealing in tests.

Abstract

In most global optimization problems, finding global optimal point inthe multidimensional and great search space needs high computations. In this paper, we present a new approach to find global optimal point with the low computation and few steps using subdividing labeling method (SLM) which can also be used in the multi-dimensional and great search space. In this approach, in each step, crossing points will be labeled and complete label polytope search space of selected polytope will be subdivided after being selected. SLM algorithm finds the global point until h (subdivision function) turns into zero. SLM will be implemented on five applications and compared with the latest techniques such as random search, random search-walk and simulated annealing method. The results of the proposed method demonstrate that our new approach is faster and more reliable and presents an optimal time complexity O (logn).