A new path plan method based on hybrid algorithm of reinforcement learning and particle swarm optimization

PurposeTo solve the path planning problem of the intelligent driving vehicular, this paper designs a hybrid path planning algorithm based on optimized reinforcement learning (RL) and improved particle swarm optimization (PSO).Design/methodology/approachFirst, the authors optimized the hyper-parameters of RL to make it converge quickly and learn more efficiently. Then the authors designed a pre-set operation for PSO to reduce the calculation of invalid particles. Finally, the authors proposed a correction variable that can be obtained from the cumulative reward of RL; this revises the fitness of the individual optimal particle and global optimal position of PSO to achieve an efficient path planning result. The authors also designed a selection parameter system to help to select the optimal path.FindingsSimulation analysis and experimental test results proved that the proposed algorithm has advantages in terms of practicability and efficiency. This research also foreshadows the research prospects of RL in path planning, which is also the authors’ next research direction.Originality/valueThe authors designed a pre-set operation to reduce the participation of invalid particles in the calculation in PSO. And then, the authors designed a method to optimize hyper-parameters to improve learning efficiency of RL. And then they used RL trained PSO to plan path. The authors also proposed an optimal path evaluation system. This research also foreshadows the research prospects of RL in path planning, which is also the authors’ next research direction.

Power Kripke–Platek set theory and the axiom of choice

While power Kripke–Platek set theory, ${\textbf{KP}}({\mathcal{P}})$, shares many properties with ordinary Kripke–Platek set theory, ${\textbf{KP}}$, in several ways it behaves quite differently from ${\textbf{KP}}$. This is perhaps most strikingly demonstrated by a result, due to Mathias, to the effect that adding the axiom of constructibility to ${\textbf{KP}}({\mathcal{P}})$ gives rise to a much stronger theory, whereas in the case of ${\textbf{KP}}$, the constructible hierarchy provides an inner model, so that ${\textbf{KP}}$ and ${\textbf{KP}}+V=L$ have the same strength. This paper will be concerned with the relationship between ${\textbf{KP}}({\mathcal{P}})$ and ${\textbf{KP}}({\mathcal{P}})$ plus the axiom of choice or even the global axiom of choice, $\textbf{AC}_{\tiny {global}}$. Since $L$ is the standard vehicle to furnish a model in which this axiom holds, the usual argument for demonstrating that the addition of ${\textbf{AC}}$ or $\textbf{AC}_{\tiny {global}}$ to ${\textbf{KP}}({\mathcal{P}})$ does not increase proof-theoretic strength does not apply in any obvious way. Among other tools, the paper uses techniques from ordinal analysis to show that ${\textbf{KP}}({\mathcal{P}})+\textbf{AC}_{\tiny {global}}$ has the same strength as ${\textbf{KP}}({\mathcal{P}})$, thereby answering a question of Mathias. Moreover, it is shown that ${\textbf{KP}}({\mathcal{P}})+\textbf{AC}_{\tiny {global}}$ is conservative over ${\textbf{KP}}({\mathcal{P}})$ for $\varPi ^1_4$ statements of analysis. The method of ordinal analysis for theories with power set was developed in an earlier paper. The technique allows one to compute witnessing information from infinitary proofs, providing bounds for the transfinite iterations of the power set operation that are provable in a theory. As the theory ${\textbf{KP}}({\mathcal{P}})+\textbf{AC}_{\tiny {global}}$ provides a very useful tool for defining models and realizability models of other theories that are hard to construct without access to a uniform selection mechanism, it is desirable to determine its exact proof-theoretic strength. This knowledge can for instance be used to determine the strength of Feferman’s operational set theory with power set operation as well as constructive Zermelo–Fraenkel set theory with the axiom of choice.