# An Enhanced Educational Competition Optimizer Integrating Multiple Mechanisms for Global Optimization Problems

## TL;DR

This paper introduces EECO, an improved optimization algorithm that outperforms existing methods in solving complex global optimization problems.

## Contribution

EECO introduces three novel mechanisms to enhance diversity, exploitation, and exploration–exploitation balance in optimization.

## Key findings

- EECO achieved higher solution accuracy and smaller standard deviations than eight recent algorithms on CEC-2017 benchmarks.
- EECO consistently ranked first in the Friedman hierarchy across multiple dimensions and real-world engineering problems.
- Statistical tests confirm the improvements in EECO's performance are significant.

## Abstract

The Educational Competition Optimizer (ECO) formulates search as a three-stage didactic process—primary, secondary and tertiary learning—but the original framework suffers from scarce information exchange, sluggish late-stage convergence and an unstable exploration–exploitation ratio. We present EECO, which introduces three synergistic mechanisms: a regenerative population strategy that uses the covariance matrix of elite solutions to maintain diversity, a Powell mechanism that accelerates exploitation within promising regions, and a trend-driven update that adaptively balances exploration and exploitation. EECO was evaluated on the 29 benchmark functions of CEC-2017 and nine real-world constrained engineering problems. Results show that EECO delivers higher solution accuracy and markedly smaller standard deviations than eight recent algorithms, including EDECO, ISGTOA, APSM-jSO, LSHADE-SPACMA, EOSMA, GLSRIME, EPSCA, and ESLPSO. Across the entire experimental battery, EECO consistently occupied the first place in the Friedman hierarchy: it attained average ranks of 2.138 in 10-D, 1.438 in 30-D, 1.207 in 50-D, and 1.345 in 100-D CEC-2017 benchmarks, together with 1.722 on the nine real-world engineering problems, corroborating its superior and dimension-scalable performance. The Wilcoxon rank sum test confirms the statistical significance of these improvements. With its remarkable convergence accuracy and reliable stability, EECO emerges as a promising variant of the ECO algorithm.