WITHDRAWN: Development of a Novel Hybrid Salp Swarm-Kepler Algorithm for Engineering Problems: Optimizing Microgrid Sizing with Integration of Photovoltaic, Wind, Battery, and Supercapacitor Systems

Abstract

Economic growth accelerates, leading to an increasingly important need for efficient resource use in engineering design due to the resulting supply and demand imbalance. This study introduces an integrated hybrid application of the Salp Swarm Algorithm (SSA) and the Kepler Optimization Algorithm (KOA) to optimize engineering design problems. The integration of SSA’s mathematical modeling of salp movement and leader-follower dynamics, along with KOA's optimization mechanisms based on Kepler’s laws, provides significant advancements in avoiding local optimum traps and achieving balance in the search space. The hybrid SSAKOA algorithm is capable of quickly reaching optimal or near-optimal solutions to optimization problems while efficiently working across parameters. Experimental results show that SSAKOA outperforms other algorithms in terms of optimum performance, solution stability, and applicability, effectively reducing resource wastage in engineering designs. The optimization capability of the SSAKOA has been verified for 23 different function problems, revealing that SSAKOA offers higher convergence speed, precision, and robustness than other algorithms. Moreover, this algorithm has yielded the most optimal results compared to 12 different algorithms in sizing a microgrid consisting of grid-connected batteries, supercapacitors, wind turbines, and photovoltaic panel components, which poses a significant engineering challenge. This study demonstrates the effectiveness of the proposed algorithm by applying it to a hybrid renewable energy system on a Turkish university campus. The application reveals an annual cost of $572,369.93 and an energy cost of $0.23996/kWh, achieving a renewable energy fraction of 78.54%. This indicates that the system not only offers a cost-effective alternative to Turkey's conventional grid rate of $0.35/kWh but also underscores the algorithm’s potential in enhancing the economic and environmental sustainability of renewable energy projects. Such findings lay a foundational framework for future advancements in renewable energy applications.