# Multiobjective starfish optimization algorithm for engineering design and optimal power flow problems

## TL;DR

This paper introduces MOSFOA, a new multi-objective optimization algorithm inspired by starfish behaviors, which performs well in solving engineering and power flow problems.

## Contribution

The novel MOSFOA algorithm extends the starfish optimization algorithm with elitist non-dominated sorting and crowding distance for multi-objective optimization.

## Key findings

- MOSFOA outperforms ten state-of-the-art algorithms in convergence and diversity metrics like IGD and HV.
- The algorithm demonstrates robustness and scalability in solving real-world engineering and power system problems.
- MOSFOA achieves superior performance in constrained optimization tasks and maintains solution diversity.

## Abstract

This paper presents a robust multi-objective optimization approach—the multi-objective starfish optimization algorithm (MOSFOA)—designed to address complex challenges in engineering design and optimal power flow analysis. As an advanced extension of the starfish optimization algorithm (SFOA), MOSFOA leverages biological inspiration from starfish behaviors such as exploration, predation, and regeneration to balance global exploration and local exploitation. The proposed MOSFOA employs elitist non-dominated sorting (NDS) and crowding distance (CD) mechanisms to preserve solution diversity and guide convergence toward the Pareto-optimal front. The effectiveness of MOSFOA is validated on standard ZDT and DTLZ benchmark suites and further demonstrated on real-world applications, including engineering design tasks and the IEEE 30-bus power system. Performance comparisons with ten state-of-the-art multi-objective algorithms, using metrics such as inverted generational distance (IGD) and hypervolume (HV), confirm the strength of MOSFOA in achieving a well-balanced trade-off between convergence and diversity. Additionally, the KKT proximity metric (KKTPM) is employed to assess convergence. The results demonstrate that MOSFOA significantly outperforms its counterparts in terms of both IGD and HV, achieving superior convergence and diversity performance. These findings underscore MOSFOA’s robustness, scalability, and stability across runs. Moreover, its strong performance in handling constrained engineering problems highlights its practical potential for real-world decision-making and optimization tasks in power systems and complex design optimization, making MOSFOA a promising tool for both theoretical research and industrial applications. Source code of MOSFOA are publicly available at https://www.mathworks.com/matlabcentral/fileexchange/183090-mosfoa-multi-objective-starfish-optimization-algorithm.