The aim of this study is to investigate market depth as a stock market liquidity dimension. A new methodology for market depth measurement exactly based on Shannon information entropy for high-frequency data is introduced and utilized. The proposed entropy-based market depth indicator is supported by an algorithm inferring the initiator of a trade. This new indicator seems to be a promising liquidity measure. Both market entropy and market liquidity can be directly measured by the new indicator. The findings of empirical experiments for real-data with a time stamp rounded to the nearest second from the Warsaw Stock Exchange (WSE) confirm that the new proxy enables us to effectively compare market depth and liquidity for different equities. Robustness tests and statistical analyses are conducted. Furthermore, an intra-day seasonality assessment is provided. Results indicate that the entropy-based approach can be considered as an auspicious market depth and liquidity proxy with an intuitive base for both theoretical and empirical analyses in financial markets.

A single anti-collision trajectory generation problem for an “own” vessel only is significantly different from the challenge of generating a whole set of safe trajectories for multi-surface vehicle encounter situations in the open sea. Effective solutions for such problems are needed these days, as we are entering the era of autonomous ships. The article specifies the problem of anti-collision trajectory planning in many-to-many encounter situations. The proposed original multi-surface vehicle beam search algorithm (MBSA), based on the beam search strategy, solves the problem. The general idea of the MBSA involves the application of a solution for one-to-many encounter situations (using the beam search algorithm, BSA), which was tested on real automated radar plotting aid (ARPA) and automatic identification system (AIS) data. The test results for the MBSA were from simulated data, which are discussed in the final part. The article specifies the problem of anti-collision trajectory planning in many-to-many encounter situations involving moving autonomous surface vehicles, excluding Collision Regulations (COLREGs) and vehicle dynamics.

The biggest challenges in the maritime environment are accidents and excessive fuel consumption. In order to improve the safety of navigation at sea and to reduce fuel consumption, the strategy of anti-collision, shortest trajectory planning is proposed. The strategy described in this paper is based on the beam search method. The beam search algorithm (BSA) takes into account many safe trajectories for the present ship and chooses the best in terms of length and other criteria. The risk of collision of present ship with any target ships is detected when the closest point of approach (CPA) of the present ship is violated by the target ship’s planned trajectory. Only course alteration of the present ship is applied, and not speed alteration. The algorithm has been implemented in the decision support system NAVDEC and tested in a real navigation environment on the m/f Wolin, a Polish ferry. Almost all BSA trajectories calculated were shorter in comparison to the standard NAVDEC-calculated algorithm.

The Vehicle Routing Problem belongs to graph optimization and its goal is to find shortest routes visiting a given set of customers with additional constraints present. The article presents the ant colony optimization metaheuristic which solves vehicle routing problems and its real-life application in transport logistics (finding routes for delivery companies). The metaheuristic generated high-quality solutions (superior to compared methods). Our tool is flexible and enables us to solve various variants of routing problems so it is well suited to specific needs of transportation companies.