Search Trajectory Research Articles

Towards explainable metaheuristics: Feature extraction from trajectory mining

AbstractExplaining the decisions made by population‐based metaheuristics can often be considered difficult due to the stochastic nature of the mechanisms employed by these optimisation methods. As industries continue to adopt these methods in areas that increasingly require end‐user input and confirmation, the need to explain the internal decisions being made has grown. In this article, we present our approach to the extraction of explanation supporting features using trajectory mining. This is achieved through the application of principal components analysis techniques to identify new methods of tracking population diversity changes post‐runtime. The algorithm search trajectories were generated by solving a set of benchmark problems with a genetic algorithm and a univariate estimation of distribution algorithm and retaining all visited candidate solutions which were then projected to a lower dimensional sub‐space. We also varied the selection pressure placed on high fitness solutions by altering the selection operators. Our results show that metrics derived from the projected sub‐space algorithm search trajectories are capable of capturing key learning steps and how solution variable patterns that explain the fitness function may be captured in the principal component coefficients. A comparative study of variable importance rankings derived from a surrogate model built on the same dataset was also performed. The results show that both approaches are capable of identifying key features regarding variable interactions and their influence on fitness in a complimentary fashion.

Relationship between early life asthma and chronic airway disease in adult life – in search for disease trajectories over the life span- the RELATE study based on the Kongsberg cohort

BackgroundChronic airway disease in adults may have its origin in early life. The purpose of this study is to investigate the long-term prognosis of severe childhood asthma in search for an association between asthma in early life and obstructive lung disease in adulthood.MethodsThis study is based on the Kongsberg cohort, which includes approximately 5000 children with severe asthma with a 4-month stay at the asthma care facility in Kongsberg, Norway during the years 1950 to 1979. An on average 60-year observational study based on a follow-up examination will be performed including questionnaires, blood samples, and tests of lung function and bronchial responsiveness. Blood samples will be stored in a biobank. In addition, we will conduct further analyses of the cohort based on nationwide register data, including socio-economic parameters and mortality.DiscussionChronic airway disease is associated with substantial burden for both the individual patient and society. Our knowledge of early life origins of chronic airway disease later in life has been increasing in recent decades but is still limited. By exploring early life risk factors for chronic airway disease in adulthood, we may gain insights paving the way for future reduction in the burden of chronic airway diseases.

STKST-I: An Efficient Semantic Trajectory Search by Temporal and Semantic Keywords

STKST-I: An Efficient Semantic Trajectory Search by Temporal and Semantic Keywords

Identification of photovoltaic module parameters by implementing a novel teaching learning based optimization with unique exemplar generation scheme (TLBO-UEGS)

The performance evaluation of a Photovoltaic (PV) system heavily relies on accurately estimating the parameters based on its current—voltage relationships. However, due to the PV model’s inherent complexity, obtaining these parameters with precision and efficiency is a challenging task. In this study, a new variant known as teaching learning-based optimization with unique exemplar generation schemes (TLBO-UEGS) is proposed to address PV module parameter estimation problems with robustness and effectiveness. To enhance the performance of TLBO-UEGS, a modified initialization scheme that leverages the strengths of chaotic maps and dynamic oppositional based learning is introduced. This scheme ensures the generation of an initial population with improved solution quality. Furthermore, both the modified teacher phase and modified learner phase are integrated within the TLBO-UEGS optimization framework. This integration allows for different learning strategies to be employed based on the fitness values of each learner, effectively updating their search trajectories. Within the modified teacher phase, two unique exemplar generation schemes are designed to facilitate more effective guidance for learners in the first half of the population while maintaining population diversity. Meanwhile, the modified learner phase emulates a realistic knowledge acquisition process by enabling learners in the second half of the population to engage in collaborative learning with multiple peer learners or retain valuable knowledge from previous learning processes. Extensive simulations demonstrate that TLBO-UEGS achieves superior results, with the minimum root mean square error (RMSE) values of 3.5644 × 10−04 ± 0.0014, 1.3237 × 10−04± 0.0043, and 6.6016 × 10−06± 0.00011 obtained for Photowatt-PWP201, Leibold Solar (LSM 20), and Leybold Solar (STE 4/100) PV modules, respectively.

Semantic segmentation using Firefly Algorithm-based evolving ensemble deep neural networks

Automatic segmentation of salient objects in real-world images has gained increasing interests owing to its popularity in diverse real-world applications, such as autonomous driving, medical diagnosis, aviation security, and underwater surveillance. In this research, we propose Firefly Algorithm (FA)-enhanced evolving ensemble deep networks for semantic segmentation and visual saliency prediction. An improved FA model is proposed to optimize network hyper-parameters. Specifically, it employs mutation operators and a neighbouring search strategy with granular search steps to establish search intensification. It also emphasizes search diversification by adopting multiple dynamic hybrid leaders and diverse adaptive sine and cosine search trajectories in full and randomly selected sub-dimensions to overcome stagnation. Because of its competent segmentation performance, DeepLabV3+ is fine-tuned using transfer learning with FA-based hyper-parameter identification. We optimize the learning rate, momentum and weight decay of the transfer learning network. A number of optimized DeepLabV3+ networks with distinguishing learning configurations are yielded. An ensemble model is subsequently constructed by incorporating three optimized base networks to further strengthen segmentation performance. Evaluated using diverse challenging semantic segmentation and saliency prediction tasks using underwater and medical image data sets, our evolving ensemble deep network illustrates significant superiority over other state-of-the-art deep networks and existing studies. The proposed FA model also outperforms other search methods in solving diverse mathematical landscapes with statistical significance.

Formation flying orbits and GNC design in binary asteroid systems

Formation flying represents a promising opportunity for next space missions, due to its benefits in cost saving, redundancy and fault tolerance given by multiple small and cheap space segments exploitation, with comparable performance of a single, large monolithic spacecraft. That is even more relevant in asteroid exploration, as the harsh environment poses great risks to the probes survival. The low, irregular gravity field, the poor knowledge of shape and composition, and the possible presence of floating particles in the surroundings suggest adopting a low-risk strategy for the exploration of these bodies, delegating proximity operations to multiple nanosatellites, while keeping the main spacecraft at safe distance. As a downside, multiple cooperating spacecraft imply advanced capabilities in accurately reconstructing the relative positions and displacements and in fixing reconfiguration manoeuvres. Moreover, whenever relative distance is very close, agents’ guidance and control shall be autonomously computed by the spacecraft, as promptness of commands is not ensured relying on ground segment only. The partially unknown environment exacerbates this issue, demanding navigation and control schemes capable of withstanding potentially large uncertainties in the dynamics. If a binary system is considered, the multiple gravitational sources complicate even more the setup of the formation, requiring an accurate search and selection of operative orbits. This study will be thus defined by three different steps. First the search and development of suitable trajectories to host a reconfigurable satellite formation is carried out. Then the design of a Model Predictive on-board guidance and control law is performed to assess the capability of the spacecraft to execute successful reconfiguration transfers relying on a simplified dynamical model (namely the Circular Restricted Three-Body Problem). At the end the navigation error requirements are derived, in order to ensure the feasibility of the guidance and control scheme. Inspired by the Hera mission, this study explores the aforementioned aspects of the design of a formation for the exploration of the Didymos binary asteroid system, which comprises many complications but also challenges for many other future missions to fly in unexplored environments.

GEOMETRIC MODELING: TRACKS AND FLOWS

Mathematical models to solve optimization connection problems in nonsimply connected regions under typical technological restrictions on geometric and topological parameters of routes, first of all, on curvature and the number of bends, have been investigated and developed. The models are linked with the extant and prospective topogeodesic models of the territory polygonal images. The solution of connection problems involves search for optimum trajectories of routes and nets within unrestricted geometric shape areas. It needs the development of a plethora of general models as fields where connections are carried out. The connections can be of various types such as bendy, Manhattan, even, solid as well as routes of other types. Smeliakov and Pliekhova observe that the global and local regulation of geometric connections to solve connection problems can be presented as the general optimization connection problem that is defined as the problem of the choice of с, where W is a set of alternatives, R is a principle of optimality. In so doing, the set W can be presented as the totality of the phase space f and the restrictions Q that are applied to the parameters of the phase space f. In turn, it is expedient to imagine that the phase space f is the Cartesian product f = X*Y*Z*U of the output data X, disturbances Y, control parameters U and results Z. The analysis of problem indicates that first and foremost the effectiveness of the modelling of the phase space f is linked with the description of the output data X on the area F and space L of possible highways in F. This research is devoted to the solution of the problem to develop a model for connection tasks within the framework of geometric design.

Distributed Search Planning in 3-D Environments With a Dynamically Varying Number of Agents

In this work, a novel distributed search-planning framework is proposed, where a dynamically varying team of autonomous agents cooperate in order to search multiple objects of interest in three-dimension (3-D). It is assumed that the agents can enter and exit the mission space at any point in time, and as a result the number of agents that actively participate in the mission varies over time. The proposed distributed search-planning framework takes into account the agent dynamical and sensing model, and the dynamically varying number of agents, and utilizes model predictive control (MPC) to generate cooperative search trajectories over a finite rolling planning horizon. This enables the agents to adapt their decisions on-line while considering the plans of their peers, maximizing their search planning performance, and reducing the duplication of work.

Efficient Non-Learning Similar Subtrajectory Search

Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires that the two checking trajectories are similar in their entirety. Many real applications (e.g., trajectory clustering and trajectory join) utilize similar subtrajectory search as a basic operator. It is considered that the time complexity is O ( mn 2 ) for exact algorithms to solve the similar subtrajectory search problem under most trajectory distance functions in the existing studies, where m is the length of the query trajectory and n is the length of the data trajectory. In this paper, to the best of our knowledge, we are the first to propose an exact algorithm to solve the similar subtrajectory search problem in O ( mn ) time for most of widely used trajectory distance functions (e.g., WED, DTW, ERP, EDR and Frechet distance). Through extensive experiments on three real datasets, we demonstrate the efficiency and effectiveness of our proposed algorithms.

Self-supervised contrastive representation learning for large-scale trajectories

Trajectory representation learning aims to embed trajectory sequences into fixed-length vector representations while preserving their original spatio-temporal feature proximity. Existing works either learn trajectory representations for specific mining tasks or fail to utilize large amounts of unlabeled trajectory data for representation learning. In this work, we propose a self-supervised Trajectory representation learning based on Reconstruction Contrastive Learning called TrajRCL. To be specific, TrajRCL first obtains low-distortion and high-fidelity views of trajectories through trajectory augmentation. Then, TrajRCL leverages a Transformer based encoder–decoder network to reconstruct low-distortion view trajectories to approximate high-fidelity trajectories. Self-supervised contrastive learning is finally used to enhance the consistency of the two view’s trajectory representations. Extensive experiments on two real-world demonstrate the superiority of our model over state-of-the-art baselines and significant efficiency on similarity trajectory search and k-NN query.

Transfers between Jupiter–Ganymede and Jupiter–Europa resonant tori in a concentric circular restricted 4-body model

The phenomenon of mean-motion resonance overlapping, which generates heteroclinic connections between unstable resonant orbits, is known to be crucial for the generation of large-scale chaos and global instability in celestial systems. This instability in turn can be profitably leveraged for the purposes of low-energy space mission trajectory design. In most prior work leveraging such phenomena, though, connections were found between orbits resonant with the same moon; however, both Jupiter and Saturn have multiple moons, each having their own set of mean motion resonances. This study will present some results from a search for trajectories between orbits resonant with different Jovian moons, namely Ganymede and Europa. For this, the appropriate model to use is a concentric circular restricted 4-body model, where most unstable mean-motion resonant orbits correspond to 2D tori in a 5D extended phase space. We use GPU-assisted tools inspired by collision detection algorithms from computer graphics to rapidly find near-intersections of Jupiter–Ganymede and Jupiter–Europa resonant orbit manifolds, which correspond to potential transfers. We find the Jupiter–Ganymede 4:3 resonance to be the most promising candidate for trajectories to the key 3:4 Jupiter–Europa resonance, and thus further investigate the properties of 4:3 Jupiter–Ganymede orbits.

An Efficient Evolution-Based Technique for Moving Target Search with Unmanned Aircraft Vehicle: Analysis and Validation

Recent advances in technology have led to a surge in interest in unmanned aerial vehicles (UAVs), which are remote-controlled aircraft that rely on cameras or sensors to gather information about their surroundings during flight. A UAV requires a path-planning technique that can swiftly recalculate a viable and quasi-optimal path in flight if a new obstacle or hazard is recognized or if the target is moved during the mission. In brief, the planning of UAV routes might optimize a specific problem determined by the application, such as the moving target problem (MTP), flight time and threats, or multiobjective navigation. The complexity of MTP ranges from NP-hard to NEXP-complete because there are so many probabilistic variables involved. Therefore, it is hard to detect a high-quality solution for this problem using traditional techniques such as differential calculus. Therefore, this paper hybridizes differential evolution (DE) with two newly proposed updating schemes to present a new evolution-based technique named hybrid differential evolution (HDE) for accurately tackling the MTP in a reasonable amount of time. Using Bayesian theory, the MTP can be transformed into an optimization problem by employing the target detection probability as the fitness function. The proposed HDE encodes the search trajectory as a sequence of UAV motion pathways that evolve with increasing the current iteration for finding the near-optimal solution, which could maximize this fitness function. The HDE is extensively compared to the classical DE and several rival optimizers in terms of several performance metrics across four different scenarios with varying degrees of difficulty. This comparison demonstrates the proposal’s superiority in terms of the majority of used performance metrics.

Swarm Exploration Mechanism-Based Distributed Water Wave Optimization

Using sparrow search hunting mechanism to improve water wave algorithm (WWOSSA), which combines the water wave optimization (WWO) algorithm and the sparrow search algorithm (SSA), has good optimization ability and fast convergence speed. However, it still suffers from insufficient exploration ability and is easy to fall into local optimum. In this study, we propose a new algorithm for distributed population structure, called swarm exploration mechanism-based distributed water wave optimization (DWSA). In DWSA, an information exchange component and an optimal individual evolution component are designed to improve information exchange between individuals. This multi-part information interaction and distributed population structure algorithm can help the population algorithm to establish a balance between exploitation and exploration more effectively. We contrast DWSA with the original algorithms WWOSSA and other meta-heuristics in order to show the effectiveness of DWSA. The test set consists of 22 actual optimization issues from the CEC2011 set and 29 benchmark functions from the CEC2017 benchmark functions. In addition, an experimental comparison of the parameter values introduced in DWSA is included. According to experimental results, the proposed DWSA performs substantially better than its competitors. Assessments of the population diversity and landscape search trajectory also confirmed DWSA’s outstanding convergence.

Scenario trajectory optimization and control on STEP

In this paper we present optimized actuator trajectories, evolving in time and space, of non-inductive ramp-up scenarios for the Spherical Tokamak for Energy Production (STEP). These trajectories are computed by solving a non-linear, multi-objective, constrained, finite-time optimal control problem. A method unique to STEP ramp-up studies that provides an alternative to existing trajectory search strategies which rely on manually adjusting trajectories to reach a desired state. To navigate a non-linear parameter space which is densely populated with local minima, we demonstrate an iterative objective function construction process whereby costs and constraints are included successively and re-optimized after each inclusion to improve convergence and feasibility. This method is particularity useful when the initial trajectory is far from the desired operating space. We use the RApid Plasma Transport simulatOR (RAPTOR) code to self-consistently solve four coupled, 1-D state equations; poloidal flux, electron temperature, ion temperature and electron density. Our STEP actuator trajectories lasting 1500s, consist of 8 Gaussian electron cyclotron heating and current drive beams distributed across the minor radius, a Deuterium/Tritium particle source and plasma current. We also introduce a modified transport Bohm–gyroBohm model and a new actuator module to RAPTOR which were required to adequately simulate the STEP operating scenarios.

Motion and Trajectory Planning and Simulation of a High Frequency Transformer Winding Robot Pose

The application of high-frequency transformers is related to the development of all walks of life in the national economy and people’s livelihood, among which the fast and agile performance of winding knots in the system operation platform is crucial to the production efficiency and quality assurance of transformers. Aiming at the problems of slow attitude movement and trajectory planning time and complicated path trajectory points in the offline system of robots in the traditional production line, this paper proposes an optimization trajectory optimization algorithm based on the combination of accurate unit scanning and Cartesian spatial trajectory planning. When the known effective working space range is determined, the end effector of the robotic arm conducts trajectory search according to a specified time series after obstacle avoidance to find an optimal trajectory that meets the user parameters. At the same time, for the polyline trajectory, this paper uses the multi-dimensional interpolation method, that is, the adopted Cartesian space trajectory planning for smooth processing. Finally, through the MatlabRobot toolbox to end effector arm end angular velocity, angular acceleration for simulation research, according to the simulation results, it can be seen that the arm end angular velocity in three-dimensional space is controlled at −1m/s ~ 1m/s, angular acceleration is basically stable in the Z axis, and controlled in the X axis at −3m/s 2 ~1m/s2, so the control of the fusion algorithm on the motion and trajectory planning of the robot system is reasonable, and it also meets the quantitative needs of users.

Rapid reentry trajectory planning based on geometric-dynamic method

For the maneuvering trajectory planning of hypersonic gliding vehicles under complex constraints, the traditional dynamics methods are complex, and difficult to optimize the control variables to maximize the maneuvering potential of the vehicle. Inspired by the path planning method of low-speed unmanned aerial vehicles, a trajectory planning method combining geometry and dynamics is proposed. Firstly, the feasibility of the method is verified theoretically, the coupling point between the two methods is established, and the information transmission process of joint planning is clarified. Secondly, according to the actual flight, the minimum cost function with angle as the parameter is designed, so that the trajectory search process can meet the complex constraints. The simulation shows that under the premise of rapid trajectory planning, the proposed method can more fully control the change of bank angle and reduce the number of flips, which is conducive to the stability of the whole flight process.

Comprehensive stability analysis of complex hydropower system under flexible operating conditions based on a fast stability domain solving method

This paper aims to study the comprehensive stability of the multi-unit hydropower systems (MUHS) with complex hydraulic coupling under flexible operating conditions and to reduce the time consumption of batch conversions in the stability domain of high-order hydropower systems (HOHSs). Firstly, the models for an actual hydropower system with three-turbine sharing a long tailrace are established considering three typical operating scenarios. Subsequently, a trajectory search algorithm is proposed to improve the speed and flexibility of stable domain solving in HOHSs. On this basis, the stability variation law of the MUHS with the variation of water head and guide vane opening is studied, and the minimum stability domain index is introduced to evaluate the comprehensive stability of systems under full hydroturbine operating conditions. Finally, the comprehensive stability of the MUHS under flexible combination operating conditions is analyzed. Notably, the stability of the MUHS is poor when the hydroturbine is operated at a water head of 215–225 m and a guide vane opening within 55–70%. In addition, the reduction of operating units will significantly deteriorate the comprehensive stability of MUHS. This paper provides a powerful tool for the stability analysis of HOHSs and potentially supports the optimal operation of the MUHS.

Privacy-Preserving Public Route Planning Based on Passenger Capacity

Precise route planning needs huge amounts of trajectory data recorded in multimedia devices. The data, including each user’s location privacy, are stored as cipher text. The ability to plan routes on an encrypted trajectory database is an urgent necessity. In this paper, in order to plan a public route while protecting privacy, we design a hybrid encrypted random bloom filter (RBF) tree on encrypted databases, named the encrypted random bloom filter (eRBF) tree, which supports pruning and a secure, fast k nearest neighbor search. Based on the encrypted random bloom filter tree and secure computation of distance, we first propose a reverse k nearest neighbor trajectory search on encrypted databases (RkNNToE). It returns all transitions, in which each takes the query trajectory as one of its k nearest neighbor trajectories on the encrypted database. The results can be the indicator of a new route’s capacity in route planning. The security of the trajectory and query is proven via the simulation proof technique. When the number of points in the trajectory database and transition database are 1174 and 18,670, respectively, the time cost of an R2NNToE is about 1200 s.

Heuristic Technique for the Search of Interception Trajectories to Asteroids with the Use of Solar Sails

With the advances of space-exploration technologies, a long-lasting concern is finally being addressed: the deflection of potentially hazardous objects (PHOs). Most recently, the first mission of this kind was launched by NASA—the Double Asteroid Redirection Test (DART). Nevertheless, it is estimated that a great number of these PHOs are unattainable by means of current chemical propulsion systems. With that in mind, this study proposes the development of a heuristic technique for the search of interception trajectories with the use of solar sails and its application in determining a set of possible trajectories to intercept hazardous asteroids. As a case study, a hybrid mission inspired by the DART mission is proposed by using a solar sail as means of propulsion after the initial chemical combustion. The dynamics consider a model of the solar radiation pressure acceleration as a function of the orientation of the sail. In turn, the orientation is defined by the application of the developed heuristic technique with the goal of defining alternative trajectories compared to the original mission. These trajectories result in different impact conditions and mission durations. Although the use of solar sails breaks the symmetry in the solutions, the results obtained offer the possibility of fuel economy or even better deflection results by the achievement of greater impact energy with the hazardous objects.

Continuous trajectory similarity search with result diversification

With the continued increasing availability of spatio-temporal data from GPS-equipped devices, online map services, and a variety of location-based social media, trajectory similarity search has become a fundamental operation in location-based data analytics. It is of great importance to enable real-time search of trajectories that satisfy users’ personalized requirements. For the purpose, we study the Diversified Continuous Trajectory Similarity Search (DCTSS) problem. The DCTSS problem aims to process a large number of Continuous Location Set (CLS) queries over a stream of trajectory data while taking result diversity of each query into consideration. To answer the DCTSS problem, we develop a Diversity-Aware Trajectory Publish/Subscribe (DAT-PS) framework, which takes both trajectory data streams and CLS queries as input and performs query-trajectory matching between CLS queries in the query collection and trajectories over the trajectory data stream. Our experimental results on two real-life datasets show that our proposed DAT-PS framework is capable of demonstrating substantial superiority regarding both efficiency and scalability compared against baselines.