# Levy flight-assisted hybrid Sine-Cosine Aquila optimizer for solving chemical equilibrium problems through the Gibbs free energy minimization technique

## TL;DR

This paper introduces a new hybrid optimization algorithm combining Aquila and Sine-Cosine methods to solve chemical equilibrium problems by minimizing Gibbs free energy.

## Contribution

A novel hybrid metaheuristic algorithm is proposed to enhance the performance of solving chemical equilibrium problems.

## Key findings

- The hybrid algorithm outperforms other optimization methods in solving multidimensional benchmark cases.
- It achieves higher solution consistency and finds minimum objective function values in chemical equilibrium scenarios.
- The algorithm effectively handles highly nonlinear and non-convex free energy surfaces.

## Abstract

This research proposes a novel hybrid metaheuristic optimization framework that combines the Aquila Optimization algorithm with the Sine-Cosine Optimizer to find equilibrium points of reacting components under specified operational reaction conditions. The method aims to address the exploitative limitations of the standard Aquila algorithm by incorporating oscillatory sine-cosine movements into the hybrid optimizer, which is one of the significant drawbacks of the base Aquila algorithm that should be addressed. The effectiveness of the hybrid approach is thoroughly tested on a suite of 100 multidimensional unimodal and multimodal benchmark cases, with results compared to those from well-known literature optimizers. Additionally, twenty-eight 30-dimensional benchmark functions from the 2013 Congress on Evolutionary Computation competition are used to evaluate the prediction performance. Three multidimensional constrained engineering design problems are also solved, and their results are compared with those from other literature optimizers. The findings show that the hybrid algorithm produces the best estimates and ranks first among competing algorithms based on average ranking results. To further verify its robustness and accuracy, three more complex chemical equilibrium problems are solved using the Gibbs Free Energy minimization method. The predictions are benchmarked against recent metaheuristic algorithms for each case, demonstrating that the proposed hybrid effectively overcomes the challenges of highly nonlinear and non-convex free energy surfaces, achieving higher solution consistency while finding minimum objective function values across different chemical equilibrium scenarios.