# A memorized multi-objective Sinh-Cosh optimizer for solving multi-objective engineering design problems

## TL;DR

A new optimization algorithm called MOSCHO is introduced to solve complex engineering design problems with multiple objectives.

## Contribution

MOSCHO integrates a memorized local optimum with global solutions to enhance multi-objective optimization performance.

## Key findings

- MOSCHO achieves high convergence and diversity in solving multi-objective problems.
- MOSCHO outperforms other algorithms on ZDT3, ZDT4, and MMF14 functions.
- Real-world engineering applications show strong performance with MOSCHO.

## Abstract

The Multi-Objective Sinh-Cosh Optimization Algorithm (MOSCHO) is presented in this article based on the memorized technique. MOSCHO is an extension version of the recently proposed Sinh-Cosh optimizer for multiple objective optimizations. The memorized local optimum is integrated with the global optimal solution to bound the search space and update positions of solutions for obtaining non-dominated solutions. The proposed method is tested on mathematical non-constrained functions, SRN constrained function, and three real-world design engineering applications, as a vital challenge to handle the difficulties of real-world engineering applications. The MOSCHO’s performance was evaluated by seven performance metrics compared to some of the most popular multi-objective optimization algorithms. The results demonstrate the ability of MOSCHO to achieve a high convergence and a good diversity. The results clarify that three functions have the best performance for all tested performance metrics: ZDT3, ZDT4, and MMF14. Five functions have the best performance for more than 75% of the performance metrics. Two functions have the best performance for more than 50% of performance metrics. The others have only the best values for more than 25% of performance metrics. However, SRN and real-world problems exhibit the best performance in more than 75% of the tested performance metrics.

The online version contains supplementary material available at 10.1038/s41598-025-33789-8.