Minimum Time Problem Research Articles

Optimization of the Process of Batch Distillation of Binary Mixtures

The method of dynamic optimization, known as maximum principle of Pontryagin, is presented. It is applied to the process of batch rectification of binary mixtures, with aim of solving the problem of minimum time (for given distillate quantity of specified composition) or maximum distillate quantity of specified composition (for given batch time). The optimum profiles of reflux ratio are found for seven different separation tasks, based on semi-rigorous model without holdups. The results obtained for distillate quantity are compared to respective results obtained with constant reflux ratio and constant distillate composition working policies, and also with the results of other authors. The solution algorithms for all the three working policies are given. Computer implementation of the algorithms is performed in programming language FORTRAN.

Time-optimal ergodic search: Multiscale coverage in minimum time

Search and exploration capabilities are essential for robots to inspect hazardous areas, support scientific expeditions in extreme environments, and potentially save human lives in natural disasters. The variability of scale in these problems requires robots to reason about time alongside their dynamics and sensor capabilities to effectively assess and explore for information. Recent advances in ergodic search methods have shown promise in supporting trajectory planning for exploration in continuous, multiscale environments with dynamics consideration. However, these methods are still limited by their inability to effectively reason about and adapt the time to explore in response to their environment. This ability is crucial for adapting exploration to variable-resolution information-gathering tasks. To address this limitation, this paper poses the time-optimal ergodic search problem and investigates solutions for fast, multiscale, and adaptive robotic exploration trajectories. The problem is formulated as a minimum-time problem with an ergodic inequality constraint whose upper bound specifies the amount of coverage needed. We show the existence of optimal solutions using Pontryagin’s conditions of optimality, and we demonstrate effective, minimum-time coverage numerically through a direct transcription optimization approach. The efficacy of the approach in generating time-optimal search trajectories is demonstrated in simulation under several nonlinear dynamic constraints, and in a physical experiment using a drone in a cluttered environment. We find that constraints such as obstacle avoidance are readily integrated into our formulation, and we show through an ablation study the flexibility of search capabilities at various scales. Last, we contribute a receding-horizon formulation of time-optimal ergodic search for sensor-driven information-gathering and demonstrate improved adaptive sampling capabilities in localization tasks.

Schwarz decomposition for parallel minimum lap-time problems: evaluating against ADMM

The Minimum Lap Time Problem (MLTP) remains a significant area of research, particularly in the motorsport context. This form of Optimal Control Problem (OCP) aims to minimise lap times on a specific track with a given vehicle. Various complexities in both vehicle and track models are employed across the literature to address optimal trajectory planning. While previous works have tackled MLTP as a singular task using a serial approach, the increasing model complexity and horizon length demands the utilisation of parallelisation techniques. This paper introduces a novel application of the Overlapping Schwarz Decomposition algorithm to address the MLTP. The algorithm divides the problem into smaller sub-problems based on different sectors of a track, distributing them among multiple processors. We validate and compare the Schwarz approach against a serial approach and the Alternating Direction Method of Multipliers (ADMM) in solving MLTP with over 2.5 million variables. Despite the general efficiency improvement of parallelisation compared to the serial approach, the Schwarz algorithm demonstrates superior speed, accuracy and robustness compared to ADMM. As a result of our findings, it emerges as the preferred choice when large-scale MLTPs need to be solved.

Age of Information-Inspired Data Collection and Secure Upload Assisted by the Unmanned Aerial Vehicle and Reconfigurable Intelligent Surface in Maritime Wireless Sensor Networks

This paper proposes an age of information (AoI)-inspired secure transmissions strategy for secure transmission from the maritime wireless sensor network to the onshore base station (BS) with the assistance of the unmanned aerial vehicle (UAV) and reconfigurable intelligent surface (RIS), in which eavesdroppers exist near the BS. In the proposed scheme, the secure transmission process is divided into the data collection period and the data upload period according to the time sequence to minimize the age of information (AoI) for the privacy information. In the data collection period, we design two scheduling schemes by selecting the sensor with the smallest current AoI or the largest difference in the adjacent AoI. In addition, we propose two heuristic algorithms by adopting the particle swarm optimization algorithm (PSO) and genetic algorithm (GA) to solve the above two problems. In the data uploading period, the uploading time minimization problem is converted to the secrecy rate maximization problem. We design an iterative optimization algorithm with auxiliary variables that are introduced to optimize the reflection coefficient of the RIS. Simulation results show that the proposed scheme can reduce the average AoI by about 10 s compared to the current methods.

New bounds for single-machine time-dependent scheduling with uniform deterioration

We consider the single-machine time-dependent scheduling problem with linearly deteriorating jobs arriving over time. Each job i is associated with a release time ri and a processing time pi(si)=αi+βisi, where αi,βi>0 are parameters and si is the job's start time. In this setting, the approximability of both single-machine minimum makespan and total completion time problems remains open. We develop new bounds and approximation results for the special case of the problems with uniform deterioration, i.e. βi=β, for each i. The main contribution is a O(1+1/β)-approximation algorithm for the makespan problem and a O(1+1/β2) approximation algorithm for the total completion time problem. Further, we propose greedy constant-factor approximation algorithms for instances with β=O(1/n) and β=Ω(n), where n is the number of jobs. Our analysis is based on an approach for comparing computed and optimal schedules via bounding pseudomatchings.

Influence of the Road Model on the Optimal Maneuver of a Racing Motorcycle

Motorcycle motion is largely influenced by the road geometry, which alters the allowable accelerations in longitudinal and lateral directions and influences the vertical wheel loads. Recently, a method for three-dimensional road reconstruction and its incorporation into transient and quasi-steady-state (QSS) minimum lap time simulations (MLTSs) has been proposed. The main purpose of this work is to demonstrate how significantly different results from a minimum lap time optimal control problem can be obtained when using inappropriate elevation data sources in the track reconstruction problem, and how the road model reconstructed using poor input data can lead to misleading conclusions when analyzing real vehicle and driver performances. Two road models derived from high- and low-resolution digital elevation models (DEMs) are compared and their impact on the optimal maneuver of a racing motorcycle is examined. The essentials of track identification are presented, as well as vehicle positioning on the 3D road and the generalized QSS motorcycle model. Obtained 3D and 2D road models are analyzed in detail, on a case example of the Road Atlanta racetrack, and used in minimum lap time simulations, which are validated by the experimental data recorded on the Supersport motorcycle. The comparative analysis showed that great care should be taken when selecting the elevation dataset in the track reconstruction process, and that the 1 m resolution local DEMs seem to be sufficient to obtain MLTS results close to the measured ones. The example of using the 3D free-trajectory QSS minimum lap time problem to localize the track segments where real driver actions can be improved is also presented. The differences between simulation results on different road models of the same racetrack can be large and influence the interpretation of optimal maneuver.

Comparative dynamic optimization study of batch hydrothermal liquefaction of two microalgal strains for economic bio-oil production

This work presents dynamic optimization strategies of batch hydrothermal liquefaction of two microalgal species, Aurantiochytrium sp. KRS101 and Nannochloropsis sp. to optimize the reactor temperature profiles. Three dynamic optimization problems are solved to maximize the endpoint biocrude yield, minimize the final time, and minimize the reactor thermal energy. The biocrude maximization and time minimization problems demonstrated 11% and 6.18% increment in the optimal biocrude yields and reduction of 78.2% and 61.66% in batch times compared to the base cases for the microalgae with higher lipid and protein fractions, respectively. The energy minimization problem revealed a significant reduction in the reactor thermal energies to generate the targeted biocrude yields compared to the biocrude maximization. Therefore, the identified optimal temperature trajectories outperformed the conventional fixed temperature profiles and could improve the overall economics of the batch bio-oil production from the algal-based biorefineries by significantly enhancing the reactor performance.

Tighter bounds on the minimum broadcast time

Given a connected graph and a subset of its vertices referred to as the sources, the minimum broadcast time problem asks for the shortest time necessary for communicating a message from the sources to all other vertices in the graph. Information exchange is possible only between neighbors, and each vertex can transmit the message to at most one neighbor at a time. Since early works on complexity theory, the problem has been known to be NP-hard. Contributions from the current text to the understanding of the minimum broadcast time problem are threefold. Through considerations of the shortest distances between sources and other vertices, a new lower bound on the broadcast time is derived. Analytical expressions of this bound are given in the single source instances of several graph classes. Fast procedures for computing upper bounds are studied next, including both the construction of feasible solutions, and the improvement of existing ones. Finally, with a focus on a new stable-set interpretation of the problem, integer programming formulations are studied, and for their theoretical interest, associated facet-defining valid inequalities are given. The computational performance of the novel methodology is evaluated in numerical experiments applied to standard benchmark instances and to instances larger than those studied in preceding recent works.

Semiconcavity for the minimum time problem in presence of time delay effects

Semiconcavity for the minimum time problem in presence of time delay effects

Energy optimization for full-duplex wireless-powered IoT networks using rotary-wing UAV with multiple antennas

In this paper, we propose a novel design for the rotary-wing unmanned aerial vehicle (UAV)-enabled full-duplex (FD) wireless-powered Internet of Things (IoT) networks. In this network, the UAV is equipped with an antenna array, and the K IoT sensors, which are distributed randomly, use single-antenna to communicate. By sending the energy, the UAV as a hybrid access point, charges the sensors and collects information from them. Then, to manage the time and optimize the energy, the sensors are divided into N groups, so that the UAV equipped with multi-input multi-output (MIMO) technology can serve the sensors in a group, during the total time T. We provide a simple implementation of the wireless power transfer protocol in the sensors by using the time division multiple access (TDMA) scheme to receive information from the users. In other words, the sensors of each group receive energy from the UAV, when it hovers over the sensors of the previous group, and also when the UAV flies over the previous group to the current group. The sensors of each group send their information to the UAV, when the UAV is hovering over their group. Under these assumptions, we formulate two optimization problems: a sum throughput maximization problem, and a total time minimization problem. Numerical results show that our proposed optimal network provides better performance than the existing networks. In fact, our novel design can serve more sensors at the cost of using more antennas compared to that of the conventional networks.

A theoretical and empirical study of job scheduling in cloud computing environments: the weighted completion time minimization problem with capacitated parallel machines

A theoretical and empirical study of job scheduling in cloud computing environments: the weighted completion time minimization problem with capacitated parallel machines

Deep Reinforcement Learning-Based Rescue Resource Distribution Scheduling of Storm Surge Inundation Emergency Logistics

A high-intensity storm surge hazard exposes residents and facilities to inundation danger. A continuously operating robust inundation emergency logistics system is vital to guarantee lives and support the control of hazardous materials. A massive inundation area, large number of affected facilities, and instantly changing flooding situation bring tremendous challenges to rescue resource allocation. In this article, a rescue resource distribution scheduling of storm surge inundation logistics is proposed to quantitatively formulate the rescue time minimization problem in emergency logistics. The mixed-integer linear programming (MILP) method is proposed for the emergency logistics scheduling model validation and optimality comparison. To enhance the efficiency of creating a good quality allocation strategy when facing large-scale problems, a deep reinforcement learning algorithm—deep deterministic policy gradient (DDPG)—is utilized to search the solutions. Based on a rescue resource scheduling model of storm surge inundation logistics targeting storm surge Mangkhut in September, 2018, a case study of the Futian District, Shenzhen, China, was conducted to verify the correctness and efficiency of the MILP and the DDPG. The optimal schedule solution designed by the MILP had a duration of 3.5138 h, while the solution calculated by DDPG had a duration of 5.065 h for the rescue. The execution time of DDPG was stable and under a second, while the execution time of the MILP was over two hours.

Task Assignment Optimization in Multi-UAV-Assisted WSNs Considering Energy Budget and Sensor Distribution Characteristics.

In emergency situations, such as disaster area monitoring, deadlines for data collection are strict. The task time minimization problem concerning multi-UAV-assisted data collection in wireless sensor networks (WSNs), with different distribution characteristics, such as the geographical or importance of the information of the sensors, is studied. Our goal is to minimize the mission time for UAVs by optimizing their assignment, trajectory, and deployment locations, while the UAV energy constraint is taken into account. For the coupling relationship between the task assignment, trajectory, and hover position, it is not easy to solve the mixed integer non-convex problem directly. The problem is divided into two sub-problems: (1) UAV task assignment problem and (2) trajectory and hover position optimization problem. To solve this problem, an assignment algorithm, based on sensor distribution characteristics (AASDC), is proposed. The simulation results show that the collection time of our scheme is shorter than that of existing comparison schemes when using the same data size.

An Analytic Method to Determine the Optimal Time for the Induction Phase of Anesthesia

We obtain an analytical solution for the time-optimal control problem in the induction phase of anesthesia. Our solution is shown to align numerically with the results obtained from the conventional shooting method. The induction phase of anesthesia relies on a pharmacokinetic/pharmacodynamic (PK/PD) model proposed by Bailey and Haddad in 2005 to regulate the infusion of propofol. In order to evaluate our approach and compare it with existing results in the literature, we examine a minimum-time problem for anesthetizing a patient. By applying the Pontryagin minimum principle, we introduce the shooting method as a means to solve the problem at hand. Additionally, we conducted numerical simulations using the MATLAB computing environment. We solve the time-optimal control problem using our newly proposed analytical method and discover that the optimal continuous infusion rate of the anesthetic and the minimum required time for transition from the awake state to an anesthetized state exhibit similarity between the two methods. However, the advantage of our new analytic method lies in its independence from unknown initial conditions for the adjoint variables.

Automated Federated Learning in Mobile-Edge Networks—Fast Adaptation and Convergence

Federated Learning (FL) can be used in mobile edge networks to train machine learning models in a distributed manner. Recently, FL has been interpreted within a Model-Agnostic Meta-Learning (MAML) framework, which brings FL significant advantages in fast adaptation and convergence over heterogeneous datasets. However, existing research simply combines MAML and FL without explicitly addressing how much benefit MAML brings to FL and how to maximize such benefit over mobile edge networks. In this paper, we quantify the benefit from two aspects: optimizing FL hyperparameters (i.e., sampled data size and the number of communication rounds) and resource allocation (i.e., transmit power) in mobile edge networks. Specifically, we formulate the MAML-based FL design as an overall learning time minimization problem, under the constraints of model accuracy and energy consumption. Facilitated by the convergence analysis of MAML-based FL, we decompose the formulated problem and then solve it using analytical solutions and the coordinate descent method. With the obtained FL hyperparameters and resource allocation, we design a MAML-based FL algorithm, called Automated Federated Learning (AutoFL), that is able to conduct fast adaptation and convergence. Extensive experimental results verify that AutoFL outperforms other benchmark algorithms regarding the learning time and convergence performance.

Two-Phases Flying Process Based Cruise Time Minimization for Collecting Data in a UAV-Enabled Untraveled Wireless IoT Network

This work studies a practical scenario where the unmanned aerial vehicle (UAV) is dispatched from the data center to collect the data from the Internet of Things (IoT) devices and return to the data center. These IoT devices with different amounts of data and are sparsely located in an untraveled area. In this scenario, we consider minimizing the UAV's cruise time by jointly optimizing the clustering strategy of the IoT devices, the association strategy between the UAV and the IoT devices, the UAV's trajectory, and the bandwidth allocation strategy. Traditionally, the minimal cruise time is obtained by visiting all IoT devices one by one and this will lead to huge cost. To address this problem, affinity propagation (AP) algorithm is proposed to cluster all these IoT devices first of all. Then, to avoid visiting all devices one by one and realize parallel computation of data collection time, the entire UAV's flying process is divided into two phases, namely, the inter-cluster phase and the intra-cluster phase. For the inter-cluster phase, the minimal cruise time is formulated to minimize total distance among clusters using the traveling salesman problem with a neighborhood (TSPN)-based algorithm. Subsequently, for the intra-cluster phase, we formulate the collecting time minimization problem in each cluster as a mix-integer non-convex optimization problem. To address these issues, we design a two-loop algorithm involving the bisection search, the altering optimization (AO), and the successive convex approximation (SCA) methods. Simulation results validate the effectiveness of our proposed scheme.

Lunar descent and landing via two-phase explicit guidance and pulse-modulated reduced-attitude control

This work considers the three-dimensional descent path of a space vehicle, from periselenium of its operational orbit to the lunar surface. The trajectory is split in two arcs: (1) descent path, up to an altitude of 50 m, and (2) terminal approach and soft touchdown. For phase 1, a new, three-dimensional locally-flat near-optimal guidance is introduced that is based on the local projection of the position and velocity variables. A minimum-time problem is defined using the locally flat coordinates of position and velocity. This leads to identifying closed-form functions of time for the two thrust angles, which identify the commanded thrust direction. During terminal approach (phase 2), correct vertical alignment, modest velocity, and negligible angular rate at touchdown are pursued. With this intent, a predictive bang-off-bang guidance algorithm is proposed that is capable of guaranteeing the desired final conditions. In both phases, the attitude control system has the objective of aligning the actual thrust direction with the commanded one, provided by the guidance algorithm. The resulting reduced-attitude control problem is addressed through the use of a new quaternion-based nonlinear control algorithm, which is proven to enjoy asymptotic stability properties. The attitude actuation system is composed of 12 monopropellant thrusters, ignited using pulse width modulation. Monte Carlo simulations are run, assuming significant displacements from the nominal initial conditions and including several harmonics of the selenopotential. The numerical results unequivocally prove that the guidance and control architecture proposed in this study is effective to achieve lunar descent and safe touchdown in nonnominal flight conditions.

Comparative Analysis of Nonlinear Programming Solvers: Performance Evaluation, Benchmarking, and Multi-UAV Optimal Path Planning

In this paper, we propose a set of guidelines to select a solver for the solution of nonlinear programming problems. We conduct a comparative analysis of the convergence performances of commonly used solvers for both unconstrained and constrained nonlinear programming problems. The comparison metrics involve accuracy, convergence rate, and computational time. MATLAB is chosen as the implementation platform due to its widespread adoption in academia and industry. Our study includes solvers which are either freely available or require a license, or are extensively documented in the literature. Moreover, we differentiate solvers if they allow the selection of different optimal search methods. We assess the performance of 24 algorithms on a set of 60 benchmark problems. We also evaluate the capability of each solver to tackle two large-scale UAV optimal path planning scenarios, specifically the 3D minimum time problem for UAV landing and the 3D minimum time problem for UAV formation flying. To enrich our analysis, we discuss the effects of each solver’s inner settings on accuracy, convergence rate, and computational time.

Multi-UAV Collaborative Sensing and Communication: Joint Task Allocation and Power Optimization

Compared to a single UAV with limited sensing coverage and communication capability, multi-UAV cooperation is able to provide more effective sensing and transmission (S&T) services. Nevertheless, most existing works on multi-UAV sensing mainly focus on mutually exclusive task allocation and independent data transmission, which did not fully exploit the benefit of multi-UAV sensing and communication. Motivated by this, we propose a novel multi-UAV cooperative S&T scheme with replicated sensing task allocation. Although replicated task allocation may sound counter-intuitive, it can actually foster cooperative transmission among multiple UAVs and thus reduce the overall sensing mission completion time. To obtain the optimal task allocation and transmit power of the proposed scheme, a mission completion time minimization problem is formulated. To solve this problem, a necessary condition for replicated sensing task allocation is derived. For the cases of replicated sensing, the considered problem is transformed into a monotonic optimization and is solved by the generic Polyblock algorithm. To efficiently evaluate the mission completion time in each iteration of the Polyblock algorithm, new auxiliary variables are introduced to decouple the otherwise sophisticated joint optimization of transmission time and power. While for the degenerated case of non-replicated sensing, the closed-form expression of the optimal transmission time is derived

Machine learning assisted delay minimization in full duplex energy constrained cooperative communication network

Cooperative communication is key in attaining high network throughput and better coverage area for a wireless powered communication network. The conventional solution methodologies proposed in the literature for these networks suffer from high run-time complexity. This paper presents an efficient polynomial-time machine learning approach for solving the total transmission time minimization problem through relay selection and scheduling of the users in a full duplex wireless powered cooperative communication network. Exploiting the simplicity offered by the tree ensemble models, a distributed gradient-boosted decision tree based model (XGBoost) is incorporated. The inputs of the model are the uplink channel coefficients and energy harvesting rates of the relays and the users, and outputs are the optimal completion time of the relays and users, relay selection and schedule of the users. Simulation results indicate that the proposed model very well approximates the true outputs, i.e., performs very close to the optimal solution of the optimization problem, while maintaining a very low run-time computational complexity. Specifically, for a network of 9 users, the run-time of the proposed model is just 25% of the optimal solution, and this ratio grows as the number of users increases in the network.