Nested Rollout Policy Adaptation (NRPA) is an approach using online learning policies in a nested structure. It has achieved a great result in a variety of difficult combinatorial optimization problems. In this paper, we propose Meta-NRPA, which combines optimal stopping theory with NRPA for warm-starting and significantly improves the performance of NRPA. We also present several exploratory techniques for NRPA which enable it to perform better exploration. We establish this for three notoriously difficult problems ranging from telecommunication, transportation and coding theory namely Minimum Congestion Shortest Path Routing, Traveling Salesman Problem with Time Windows and Snake-in-the-Box. We also improve the lower bounds of the Snake-in-the-Box problem for multiple dimensions.

People who suffer from paraplegia completely lose sensory and locomotor functions; there are no known treatment methods for their recovery at this time. Exoskeleton robots have the potential to dramatically improve the locomotor ability of these individuals. Although some exoskeleton robots for paraplegic patients have been commercialized and are able to restore walking motion at present, the pilot must acquire the ability to maintain their balance and shift their weight using forearm crutches, which is very challenging for paraplegics. To make this easier, we propose a new automated intelligent gait planning method that integrates a finite-state machine (FSM) model as an underlying foundation and a gait generation model in addition to the exoskeleton system. The underlying FSM model is defined using an inverted pendulum model and a minimum jerk algorithm. To compare the planning gait, 33 volunteers provide normal walking gaits; there are two more volunteers (paraplegic and nonparaplegic) wearing the Shenzhen Institute of Advanced Technology (SIAT) exoskeleton robot to validate the effects of the proposed gait and offer the groups of surface electromyogram (sEMG) data for analysis. As a result, the input of the proposed gait planning method is simplified to two parameters. The proposed walking gait significantly reduces the arm muscle output. Note to Practitioners-This article was motivated by the problem that the four-degree of freedom (DoF) underactuated paraplegic rehabilitation lower limb exoskeleton robot lacks of the center of gravity (COG) transfer process when coordinating with paraplegia patients during the training process for beginner. The existing approach to deal with this problem generally is to train the pilot for obtaining the COG transfer ability by using crutches. This article suggests a gait planning method for the four-DOF underactuated rehabilitation lower limb exoskeleton robot considering the COG transfer process to make the exoskeleton robot coordinate with a pilot and ensure safety. The gait planning method is based on the inverted pendulum model and simplified to several parameters. By adjusting these parameters, the step length, step height, walking speed, and the shape of gait can be adjusted according to the requirements of the exoskeleton robot and pilot. In this article, we mathematically characterize a gait planning method for the exoskeleton control strategy. Preliminary online experiments suggest that this approach is feasible and can significantly reduce the arm muscle output of pilot. In future research, we will adjust the gait by estimating the velocity of center of mass (COM) of the pilot to make the exoskeleton robot coordinate with pilot actively.