## 1 Introduction  
Hydrogen derived from renewable sources has gained recognition as a strategically important energy carrier in the context of global climate change mitigation efforts [1]. As the capacity of wind turbines and solar power plants continues to grow, under the on-grid and stand-alone condition, the technology for producing green hydrogen through water electrolysis using renewable energy sources has advanced significantly and has shown a trend of replacing traditional chemical hydrogen production [2]. Under the stand-alone condition, the direct coupling of photovoltaics or a wind turbine with the electrolysis system has a positive impact on system efficiency [3]. The autonomous operation capability of electrolyzers, coupled with progressively enhanced cost-effectiveness in energy supply, render stand-alone photovoltaic systems as a highly promising solution for sustainable green hydrogen production [4]. Compared with anion exchange membrane electrolyzers (AEMEs) and solid oxide electrolyzers (SOEs), which are still in the laboratory research stage, alkaline electrolyzers (AWEs) and proton exchange membrane electrolyzers (PEMEs) have gained wide application due to their low cost, high efficiency, and loose application condition, respectively [3,5]. Therefore, the investigation of optimal integration strategies for alkaline water electrolysis (AWE) and proton exchange membrane electrolysis (PEME) in stand-alone wind-photovoltaic-battery hybrid systems, in order to leverage their complementary advantages to enhance both economic viability and energy conversion efficiency in green hydrogen production, represents a critical research direction warranting further systematic exploration. Experts and scholars have conducted extensive research on off-grid application [6], optimizing control [7] and capacity allocation [8] to improve the economy and energy efficiency of hydrogen-containing energy systems [9]. A comprehensive evaluation of round-trip efficiency was performed for different electrolyzer types, focusing on hydrogen production energy losses in power-to-power storage applications. The analysis demonstrated peak efficiencies of 29% for solid oxide, 22.2% for AWE, and 21.8% for PEME. The results underscore substantial opportunities for technological advancement, with potential efficiency gains projected to reach 40-42% in the next decade [10]. The optimization of hybrid renewable energy systems was studied in three small communities on the island of Manoka in Douala, Cameroon, under off-grid conditions including solar panels, wind turbines, batteries, fuel cell generators, biogas, and electrolyzers [11]. By designing an integrated photovoltaic-hydrogen renewable energy system, the feasibility of integrating electrolyzers, fuel cells, and hydrogen storage tanks with renewable energy systems was demonstrated in the Saudi Arabia region [12]. A significant body of research has shown some challenges faced by energy management and the optimal allocation of hybrid energy systems. New energy sources, including hydrogen-producing electrolyzers and battery energy storage systems, are applicable in both on-grid and off-grid conditions. However, there are generally varying degrees of complex trade-offs among multiple optimization objective functions [13]. Three distinct approaches can be employed to resolve optimization problems that involve multiple objective functions. The multi-objective optimization challenge can be addressed through scalarization techniques, specifically via weighted linear combination, as proposed in [14]. The methodological framework was successfully demonstrated in reference [15], wherein multiple optimization objectives--encompassing battery discharge power characteristics, charge/discharge cycle parameters, and hydrogen production capacity metrics--were systematically consolidated into an integrated cost function formulation. This optimization process was specifically designed to facilitate enhanced energy management strategies for standalone renewable energy systems.