Analysis of dependence of grey wolf optimizer to shift-transformations and its shift-invariant improved methods adaptively controlling the search areas

Abstract

As a metaheuristic method for the continuous optimization problem, the grey wolf optimizer (GWO) has attracted much attention from researchers because the method is reported to be superior to other methods. However, some works show that the GWO is too specialized only to problems having the zero-optimal solution, which can lead to a significant deterioration of the efficiency for other problems. In this paper, we, first, theoretically prove the shift-dependence of the GWO, which is the underlying cause of the over-specialization of the GWO, and we experimentally analyze the property by using a larger number of problems. Secondly, we propose am shift-invariant GWO, GWO-SR, and, modify the GWO-SR by adding two methods: an adjustment technique the size of the search area and a mutation process to enhance the diversity of the search (GWO-AS) Finally, we show advantages of two proposed GWOs by comparing them with other metaheuristic methods.

Keywords

• grey wolf optimizer
• global optimization
• shift-invariance
• reference point
• control of the sizes of search areas
• metaheuristics