Surrogate-Assisted Multi-Objective Optimization for Simultaneous Three-Dimensional Packing and Motion Planning Problems Using the Sequence-Triple Representation

Packing problems are classical optimization problems with wide-ranging applications. With the advancement of robotic manipulation, there are growing demands for the automation of packing tasks. However, the simultaneous optimization of packing and the robot's motion planning is challenging because these two decisions are interconnected, and no previous study has addressed this optimization problem. This paper presents a framework to simultaneously determine the robot's motion planning and packing decision to minimize the robot's processing time and the container's volume. This framework comprises three key components: solution encoding, surrogate modeling, and evolutionary computation. The sequence-triple representation encodes complex packing solutions by a sequence of integers. A surrogate model is trained to predict the processing time for a given packing solution to reduce the computational burden. Training data is generated by solving the motion planning problem for a set of packing solutions using the rapidly exploring random tree algorithm. The Non-Dominated Sorting Genetic Algorithm II searches for the Pareto solutions. Experimental evaluations are conducted using a 6-DOF robot manipulator. The experimental results suggest that implementing the surrogate model can reduce the computational time by 91.1%. The proposed surrogate-assisted optimization method can obtain significantly better solutions than the joint angular velocity-based estimation method.