• Safe Reinforcement Learning (RL) as Deep Deterministic Policy Gradient is used. • Deep Deterministic Policy Gradient (DDPG) is combined with metaheuristic SMA. • The approach mitigates the drawbacks of DDPG-based safe RL optimal control. • SMA initializes the parameters of the neural network-based controller. • State safety constraints are incorporated into the search process of SMA. This paper presents a novel optimal control approach resulting from the combination between the safe Reinforcement Learning (RL) framework represented by a Deep Deterministic Policy Gradient (DDPG) algorithm and a Slime Mould Algorithm (SMA) as a representative nature-inspired optimization algorithm. The main drawbacks of the traditional DDPG-based safe RL optimal control approach are the possible instability of the control system caused by randomly generated initial values of the controller parameters and the lack of state safety guarantees in the first iterations of the learning process due to (i) and (ii): (i) the safety constraints are considered only in the DDPG-based training process of the controller, which is usually implemented as a neural network (NN); (ii) the initial values of the weights and the biases of the NN-based controller are initialized with randomly generated values. The proposed approach mitigates these drawbacks by initializing the parameters of the NN-based controller using SMA. The fitness function of the SMA-based initialization process is designed to incorporate state safety constraints into the search process, resulting in an initial NN-based controller with embedded state safety constraints. The proposed approach is compared to the classical one using real-time experimental results and performance indices popular for optimal reference tracking control problems and based on a state safety score.

In this paper, we provide a proof of concept on how to model and forecast average Vessel Service Time (VST)̅ using Long Short-Term Memory (LSTM) Recurrent Neural Networks (RNNs). The proposed model is learned from the Automatic Identification System (AIS) data by using machine learning. Geohash area (GeoArea) with a certain precision, convex hull area (ConvArea), and average vessel proximity (Δ) are mined for the port of Singapore every hour. These three metrics are used to calculate port spatial complexity (SpComplexity) and port spatial density (SpDensity) indicators. In addition, we propose an algorithm to mine the (VST)̅ and associate that with the mined GeoArea, ConvArea, and Δ and the calculated indicators (i.e., SpDensity and SpComplexity). Then, an LSTM model is trained and subsequently tested to forecast future (VST)̅, as Port Authorities are increasingly relying on data-driven insights for decision-making purposes. We trained and tested several LSTM models with four different time aggregation granularities (2, 4, 6, and 8 hours) and provided performance comparisons between them in terms of Mean Square Error (MSE). The experiments emphasized the feasibility of the proposed LSTM model to forecast (VST)̅.

The Automatic Identification System (AIS) is a vessel tracking system that automatically provides updates on a vessel's movement and other relevant voyage data to vessel traffic management centres and operators. Aside from assisting in real-time tracking and monitoring marine traffic, this system is used in the analysis of historical navigation patterns. In this work, we mined and aggregated vessel speeds from AIS messages within geohashed regions at different precision levels. This granulated, real-world information was brought into the formulation of a Speed-based Vessel Schedule Recovery Problem (S-VSRP). The goal is to mitigate disruptions in vessel schedule by adjusting the speeds while also conforming to the historical navigation patterns reflected in the AIS data. We introduce a new model for vessel schedule speed recovery problem by formulating it as a multi-objective optimization (MOO) problem called the Big-Data-enabled Granular S-VSRP (G-S-VSRP) and propose meta-heuristic optimization methods to find Pareto-optimal solutions. The three objectives are: (1) minimizing the total delay between origin and destination ports, (2) minimizing total financial loss, and (3) maximizing the average speed compliance with historical speed limits. Three evolutionary multi-objective optimizers (EMOO) were investigated and utilized to approximate the Pareto-optimal solutions providing vessel voyage speeds. The Pareto front gives the ability to inspect the tradeoff among the three conflicting objectives. To the best of our knowledge, this is the first time historical AIS data has been exploited in the published literature to mitigate disruptions in vessel schedules.