## 1 Introduction
Thus, numerous studies on multi-objective optimization (MOO) to balance multiple targets have been carried out. For example, [PERSON] et al. [17] used an ANN and a GA to optimize the material selection of drink containers and achieved multi-objective decision making in four aspects, including the material selection, mechanical performance, production cost, and environmental impact. For the CNC machining of cam disks, [PERSON] [18] integrated an LCA and a GA for optimization to obtain the optimal scheme with the smallest environmental impact, lowest cost, and simplest assembly. Similarly, [PERSON] et al. [19] adopted EnergyPlus for windows design and carried out MOO for the energy consumption, as well as the thermal energy and visual performance, based on a GA. Finally, the authors compared the optimal solutions with the help of [PERSON]'s method. [PERSON] et al. [20] employed a second-order RSM and GA for the MOO of the baffle configuration of a heat exchanger. [PERSON] et al. [21] took eddy current separators for recycling waste as an example to improve the separation efficiency of the machine through optimization that combined the finite element method, the RSM, a GA, and [PERSON]'s method. In addition, [PERSON] et al. [22] investigated the water reuse systems in factories and proposed optimization strategies that considered the eco-efficiency, production efficiency, and production cost at the same time. [PERSON] et al. [23] focused on diesel engines and acquired an optimal design based on multi-objective methods, LCA, and LCC. Furthermore, [PERSON] [24] obtained an energy sustainability index (IESUS) through an all-in-one optimization module and input the data into the DMU system to acquire the optimal decision considering both eco-efficiency and investment. In the meantime, [PERSON] et al. [25] introduced the Lean Design-for-X approach to optimize structures and eco-designs by disassembling a machine tool (press-brake) into modules. [PERSON] and [PERSON] [26] suggested the use of back propagation neural networks (BPNNs), LCAs of components, and a multi-objective genetic algorithm (MOGA) to attain the solution with the shortest design time and lowest carbon emission for an MP3 player. Moreover,Taghdisian et al. [27] performed a multi-objective design based on CO\({}_{2}\) efficiency and realized the production of environmentally friendly methanol through an optimization model (GA + Pareto set). Last, but not least, [PERSON] and [PERSON] [28] took different additive manufacturing, i.e., stereolithography (SL), inkjet (IJ), and fused deposition modeling (FDM), and conducted MOO with the help of an LCA parameter model. In this way, the cheapest and most environmentally friendly component assembly method could be found. From a life-cycle perspective, the design stage is the key to controlling the environmental impacts of a product. At this stage, all the parameters can be optimized to realize the required functions while ensuring that the product is environmentally friendly. This paper proposes an assessment method to achieve an eco-design during the product concept design stage so that both the associated environmental impacts and mechanical properties are considered. In this study, experimental data for these two design goals were obtained via an LCA and a von Mises stress analysis, respectively. After that, the RSM was applied to attain the approximation functions. Finally, a GA was introduced as a multi-disciplinary and MOO approach to realize the eco-design of the product. This paper is organized as follows. The next section, Material and Methodology, illustrates the LCA, RSM, GA, and MOO methods. The third section explains the experimental setup and analyzes the results. It shows how the proposed multi-disciplinary and MOO method were validated based on the design of an LCD screen frame. The fourth section discusses the experimental results to explore the significance and application of the proposed method in eco-design.