An enhanced POSTA based on Nelder-Mead simplex search and quadratic interpolation

TL;DR

This paper addresses the slow convergence and limited accuracy of the parameter-optimal state transition algorithm (POSTA) by leveraging richer historical information through two techniques: Nelder-Mead (NM) simplex search and quadratic interpolation (QI). The authors introduce NM-POSTA, which stores historical solutions in an NM simplex of capacity $D+1$ vertices and uses NM transformations to exploit history, augmented by a collection strategy governed by an update rate $UR$; QI is reserved for the later search stages to refine solutions using three historical points. Building on this, NMQI-POSTA combines NM-driven exploration with QI-driven exploitation in an eagle-strategy framework, while QI-POSTA serves as a baseline that uses QI without NM. Empirical results on 14 benchmark functions across $D=20,30,50$ demonstrate faster convergence and improved robustness compared with other metaheuristics such as ABC, SaDE, GWO, and CLPSO, validating the effectiveness of integrating NM simplex search and QI into POSTA. The work suggests a practical approach to leveraging historical information in metaheuristics and outlines directions for refining history collection and extending the method to other algorithms.

Abstract

State transition algorithm (STA) is a metaheuristic method for global optimization. Recently, a modified STA named parameter optimal state transition algorithm (POSTA) is proposed. In POSTA, the performance of expansion operator, rotation operator and axesion operator is optimized through a parameter selection mechanism. But due to the insufficient utilization of historical information, POSTA still suffers from slow convergence speed and low solution accuracy on specific problems. To make better use of the historical information, Nelder-Mead (NM) simplex search and quadratic interpolation (QI) are integrated into POSTA. The enhanced POSTA is tested against 14 benchmark functions with 20-D, 30-D and 50-D space. An experimental comparison with several competitive metaheuristic methods demonstrates the effectiveness of the proposed method.

Figures (7)

• Figure 1: The geometric transformations in NM simplex search.
• Figure 2: Comparison in utilizing history information.
• Figure 3: Comparison in collecting and utilizing historical information.
• Figure 4: Solution paths of POSTA and NM-POSTA on Rosenbrock function.
• Figure 5: Flow chart of the enhanced POSTA.