Hippopotamus algorithm for optimal sizing of hybrid renewable energy system

• Developing a new met-heuristic approach for giving the optimal sizing of hybrid PV Wind system. • Several terms of reliability are used such as loss of power supply probability, energy not supplied, reliability of power supply. • Two configurations: PV-battery system and PV-Wind-battery system have been investigated. • HO algorithm is compared with that of the Particle swarm optimization algorithm (PSO), Bat algorithm (BA), Firefly technique (FA) and Teaching Learning based optimization algorithm (TLBO). • HO algorithm generally emerges as the best-performing one across all optimization approach for the different changes. In recent years, meta-heuristic optimization algorithms have attracted increasing global attention due to their remarkable capability in solving complex, nonlinear, and multi-objective engineering problems. Among various applications, the optimal design of hybrid renewable energy systems remains one of the most challenging tasks, as it involves minimizing system cost while ensuring a high level of reliability under uncertain environmental and operational conditions. In this context, the present paper proposes a novel meta-heuristic optimization technique, termed the Hippopotamus Optimization (HO) algorithm, developed to determine the optimal sizing and configuration of hybrid photovoltaic (PV)/wind energy systems. The principal objective of the HO algorithm is to simultaneously minimize the total system cost and maximize the power supply reliability, taking into account realistic operational and technical constraints. To achieve this, several reliability metrics are incorporated, including the Loss of Power Supply Probability (LPSP), Energy Not Supplied (ENS), and Reliability of Power Supply (RPS). These indicators ensure that the designed system can provide continuous and stable energy even under fluctuating solar radiation, wind speed, and load demand conditions. Two hybrid configurations are investigated in this study: a PV–battery system and a PV/Wind–battery system. The proposed HO algorithm searches for the most cost-effective configuration, avoiding both over-sizing and under-sizing, by exploring the solution space efficiently and adaptively according to different climatic and system scenarios. To assess its effectiveness and robustness, the performance of the HO algorithm is compared against several well-established meta-heuristic techniques, namely the Particle Swarm Optimization (PSO) algorithm, the Bat Algorithm (BA), the Firefly Algorithm (FA), and the Teaching–Learning-Based Optimization (TLBO) method. Comparative simulations are carried out under multiple environmental conditions and load profiles to evaluate convergence speed, solution accuracy, and stability. The results reveal that the proposed Hippopotamus Optimization (HO) algorithm outperforms PSO, BAT, FA, and TLBO in all evaluated scenarios. For the PV–battery configuration, HO achieved the lowest annual system cost of 9912 €, with LPSP = 0.008, ENS = 0.09, and RPS = 0.91, compared with PSO which yielded 12001 €, LPSP = 0.040, and RPS = 0.68. In the PV–wind–battery configuration, HO further improved performance with ACsys = 20292 €, LPSP = 0.008, ENS = 0.07, and RPS = 0.93, confirming its superior capability in minimizing cost while maximizing reliability. Overall, the findings confirm that the Hippopotamus Optimization algorithm is a highly efficient and robust optimization tool for renewable hybrid energy system design. Its strong performance across various test cases demonstrates its potential as a promising alternative to existing meta-heuristic algorithms for future optimization challenges in energy management and other multidisciplinary engineering applications.