## 5 Conclusions  
To take advantage of the low cost of AWE and high efficiency of PEME, a hydrogen production hybrid electrolyzer combining both AWE and PEME was implemented in a stand-alone wind-photovoltaic-battery system. Subsequently, a multi-objective optimization model was developed, focusing on the economy and efficiency of hydrogen production. The main conclusions are as follows. 1. An adjustable parameter was introduced to transform a multi-objective problem into a single-objective optimization problem with specific parameter constraints. This allowed for the effective and controllable drawing of the Pareto front associated with the multi-objective optimization problem. The adjustable parameter can be quantitatively modified by stepping; the non-dominated solution that exhibits the most significant change in slope is recommended as the optimal solution. This has provided a new approach for selecting recommended solutions for multi-objective optimization problems. Figure 10: The optimization results with changes in the permissible abandonment rate of new energy and the permissible cut-off rate of the load. 2. A hybrid electrolyzer that combines AWE and PEME can effectively balance the costs and losses of hydrogen production. This approach takes advantage of AWE's lower production costs and PEME's higher efficiency. In terms of the composition of hydrogen production, a hybrid electrolyzer based on AWE and PEME can better balance the economy and losses of hydrogen production. As a result, the complementary advantages of the hydrogen production cost of AWE and the hydrogen production efficiency of PEME can be fully leveraged. With the changing efficiency and costs of hydrogen production methods, particularly AWE and PEME, if AWE's efficiency improves or if PEME's costs decrease, the design of hydrogen production electrolyzers is likely to transition to a unified structure. 3. Under the structure of a hybrid electrolyzer compared with a single optimization objective function focused solely on minimizing the cost of hydrogen production, the proposed method achieved notable improvements. Specifically, this approach resulted in a 1.00% decrease in production costs while increasing hydrogen utilization by 21.71%. Additionally, compared with the single optimization objective function minimizing the loss of hydrogen production, the utilization and economy of hydrogen production were reduced by 5.22% and increased by 6.46%, respectively. 4. In a stand-alone wind-photovoltaic-battery system with a hybrid electrolyzer, when the hydrogen production efficiency of AWE falls below 72%, the proportion of PEME will significantly increase. In terms of per unit hydrogen production and investment construction cost, the relative value between AWE and PEME is crucial in determining the composition of the hydrogen production electrolyzer. Furthermore, under stand-alone conditions, the relationship between the new energy source and load electricity consumption is a key factor influencing the hybrid electrolyzer's total rated power and composition ratio. The physical processes and operational parameters governing hydrogen production, storage, and the levelized cost of the system constitute critical determinants of electrolyzer capacity. The refinement of the system's mathematical model represents a central focus for subsequent research efforts. Furthermore, the variability in renewable energy generation capacity and the fluctuations in end-user electricity demand under extreme weather conditions are pivotal factors that significantly influence the operational performance and cost viability of hydrogen production units within a stand-alone system. These critical aspects necessitate comprehensive and in-depth investigation. Conceptualization, S.M. ; Methodology, S.M. and M.C. ; Validation, Z.M. and Y.M. ; Formal analysis, Y.M. and Y.J. ; Writing--original draft, S.M. and Z.M. ; Writing--review and editing, Y.M. and M.C. ; Visualization, Y.J. ; Funding acquisition, S.M.