# Shape Design Optimization of a Robot Arm Using a Surrogate-Based Evolutionary Approach
## 1 Introduction
The response surface method (RSM), also known as the surrogate model or approximation model, can be used to improve the design efficiency. In RSM, a set of sample data (obtained by running the computer code/simulation) are used to build the surrogate model, which are sufficient to predict the output at untried points within the design space. Because the predictions obtained from a surrogate model are generally much more efficient than those from numerical analysis code, the computational cost associated with each search in RSM is therefore negligible. Surrogate-model-based optimizations are of particular interest for engineering design when coupled with high-fidelity and expensive analysis codes, such as computation fluid dynamics (CFD) and computational structural dynamics (CSD) [13]. In many studies, RSM together with design of experiment (DOE) was used to construct the surrogate models and find the best-fitting solutions [14; 15; 16; 17]. Some researchers applied the adaptive RSM to search for the global optima of complex mechanical systems [18; 19; 20]. However, in these cases, they did not consider the situation of multi-objective functions with conflicting properties [21] which may lead to being trapped into a local optimum solution during the design optimization process. In this paper, the shape design optimization of robot arms for high speed performance via the surrogate-based evolutionary approach is investigated. First, based on the CAD model of a robot arm, the design variables, constraints, and objective functions of the optimization problem are defined. Next, a quadratic RSM together with Box-Behnken design (BBD) and FEM is used to construct the surrogate model. In solving the optimization problem, the multi-objective evolutionary algorithm by decomposition (DE variant) (MOEA/D-DE) technique which includes evolutionary operators of selection, recombination, and mutation is employed to address the multiple objective functions with conflicting features and search for the Pareto-optimal sets of global optimization. The weighted sum method is finally used to determine the best candidate among the generated population samples through fitness checking. The proposed paper is able to make two significant contributions: one is to provide a surrogate-based evolutionary optimization approach to deploy in the robot arm design optimization process to obtain higher performance and efficiency, as well as to reduce computational cost; the other one is to solve the shape design optimization problem of robot arms considering multiple, conflicting objectives for higher accuracy and controllability simultaneously. The rest of the paper is organized as follows. The techniques for robot arm analysis and design, which involve the target performance to be achieved and the framework of the proposed surrogate-based evolutionary optimization (SBEO) method, are described in Section 2. The procedure for the optimal shape design of a specific robot arm is given in Section 3. Some optimal-design-related simulation results, such as Pareto front history, improvement of performance, computational efficiency, and sensitivity analysis, are given in Section 4. Section 5 presents a discussion on the advantages, limitations, and future works of the proposed method.