Speed Optimization Problem Research Articles

Ship speed optimization method combining Fisher optimal segmentation principle

An iterative optimization method that combines the principle of ordered clustering was proposed to address the strong correlation among route segmentation, weather loading, and ship speed optimization. Focusing on a single voyage task on a given route, the speed of an ocean-going container ship was optimized to achieve the minimum fuel consumption of the ship. The verified data-driven method was used to build a ship fuel consumption prediction model, and the Fisher optimal segmentation method was applied to segment ship routes. Subsequently, the speed optimization problem was solved using an iterative optimization method. The optimization results confirmed that the iterative optimization method has significant advantages in realizing route segmentation with the highest weather similarity within the segment. Extensive empirical studies on six case routes revealed the significant fuel-saving potential of the proposed iterative optimization method. Under different routes and weather conditions, the proposed iterative optimization method achieves a ship fuel-saving rate of 2.4 %–5.4 % and provides a reliable technical reference for the shipping industry to reduce the energy consumption and emissions of ships.

An integrated assignment, routing, and speed model for roadway mobility and transportation with environmental, efficiency, and service goals

Managing all the mobility and transportation services with autonomous vehicles for users of a smart city requires determining the assignment of the vehicles to the users and their routing in conjunction with their speed. Such decisions must ensure low emission, efficiency, and high service quality by also considering the impact on traffic congestion caused by other vehicles in the transportation network.In this paper, we first propose an abstract trilevel multi-objective formulation architecture to model all vehicle routing problems with assignment, routing, and speed decision variables and conflicting objective functions. Such an architecture guides the development of subproblems, relaxations, and solution methods. We also propose a way of integrating the various urban transportation services by introducing a constraint on the speed variables that takes into account the traffic volume caused across the different services. Based on the formulation architecture, we introduce a (bilevel) problem where assignment and routing are at the upper level and speed is at the lower level. To address the challenge of dealing with routing problems on urban road networks, we develop an algorithm that alternates between the assignment-routing problem on an auxiliary complete graph and the speed optimization problem on the original non-complete graph. The computational experiments show the effectiveness of the proposed approach in determining approximate Pareto fronts among the conflicting objectives.

Differential Flatness of Slider–Pusher Systems for Constrained Time Optimal Collision Free Path Planning

Abstract In this work, we show that the differential kinematics of slider–pusher systems are differentially flat assuming quasi-static behavior and frictionless contact. Second, we demonstrate that the state trajectories are invariant to time-differential transformations of the path parametrizing coordinate. For one this property allows to impose arbitrary velocity profiles on the slider without impacting the geometry of the state trajectory. This property implies that certain path planning problems may be decomposed approximately into a strictly geometric path planning and an auxiliary throughput speed optimization problem. Building on these insights, we elaborate a numerical approach tailored to constrained time optimal collision free path planning and apply it to the slider–pusher system.

UAV Trajectory Optimization for Time-Constrained Data Collection in UAV-Enabled Environmental Monitoring Systems

This article studies the unmanned aerial vehicle (UAV) trajectory planning problem in a UAV-enabled environmental monitoring system and considers a typical data collection scenario where a UAV is dispatched to a geographical area to collect time-constrained data in a set of monitoring areas and transmit collected data to a ground base station (GBS). We formulate the UAV trajectory planning problem as an optimization problem with the objective to minimize the UAV’s mission completion time by jointly optimizing the UAV’s flying speeds, hovering positions, and visiting sequence, taking into account the Age of Information (AoI) of data in monitoring areas, and the on-board energy of the UAV. To solve the problem, we decompose the formulated optimization problem into two subproblems: a UAV speed optimization problem and a UAV path optimization problem, and propose successive convex approximation (SCA) method-based and generic algorithm (GA)-based algorithms to solve the subproblems. Based on the proposed algorithms, we further propose an AoI-and-energy-aware trajectory optimization (AoI-EaTO) algorithm to solve the main problem. Simulation results show that the proposed AoI-EaTO algorithm can find a better solution to the problem than two benchmark algorithms. Moreover, given the UAV’s on-board energy and maximum speed as well as the positions of the GBS and monitoring areas, the AoI limitation threshold that the system is able to satisfy can be obtained through simulation results. This threshold can be used to decide if the UAV is able to finish a particular data collection mission, which is useful to the deployment of the mission.

A Stochastic Sailing Speed Optimization and Vessel Deployment Problem in Liner Shipping

In this research, we consider the stochastic sailing speed optimization and vessel deployment problem and examine the trade-off between sailing speed and the number of vessels required to provide a certain service in international liner shipping. Solving this kind of stochastic program is a challenging task. To address this issue, we construct a mathematical formulation based on Ng (1) and Ng (2) and enhance the linearization techniques from Wang and Meng (3) so that problem instances of an even larger scale can be solved. The proposed formulation has been numerically applied to solve realistic cases, and the empirical results show that the proposed framework is effective in solving this stochastic programming problem. The managerial insights from our work can help liner shipping companies determine bunker consumption and vessel deployment strategies.

Predictive energy-efficient driving strategy design of connected electric vehicle among multiple signalized intersections

Signalized intersections dominate traffic flow in urban areas, resulting in increased energy consumption and travel delay for the vehicles involved. To mitigate the negative effect of traffic lights on eco-driving control of electric vehicles, a multi-intersections-based eco-approach and departure strategy (M-EAD) is proposed to improve vehicle energy efficiency, traffic throughput, and battery life, while maintaining acceptable driving comfort. M-EAD is a two-stage control scheme that includes efficient green signal window planning and speed trajectory optimization. In the upper stage, the traffic light green signal window planning is formulated as a shortest path problem, which is solved using an A* algorithm for travel delay reduction. In the lower stage, the speed optimization problem is solved by resorting to a receding horizon framework, in which the energy consumption and battery life losses are minimized using an iterative dynamic programming algorithm. Finally, Monte Carlo simulation with randomized traffic signal parameters is conducted to evaluate the performance of the proposed M-EAD strategy. The results show the various advancements of the proposed M-EAD strategy over two benchmark methods, constant speed and isolated-intersection-based eco-approach and departure strategies in terms of energy efficiency, travel time, and battery life in stochastic traffic scenarios. In addition, the performance of M-EAD on actual road conditions is validated by on-road vehicle test.

Optimizing fuel consumption on inland waterway networks: Local search heuristic for lock scheduling

Fuel consumption and CO2 emission are among the main criteria to assess the environmental and economical impact of vessels on inland waterways. Both criteria, however, are directly affected by the vessels’ sailing speed. In this paper, we present a mathematical programming formulation of the speed optimization problem, which aims at minimizing the aggregated fuel consumption on an inland waterway network. The network can consist of multiple river segments, connected by a set of locks, without restrictions on the configuration. To allow scalability towards realistic waterway networks, we also propose a local-search based heuristic to optimize the speed for individual vessels. We evaluate the effectiveness of the heuristic by comparing it to solving the exact mathematical programming formulation. For all computational experiments, we make use of real AIS data from a section of the Dutch river network. We observe that the heuristic is able to construct a high quality solution in realistic problem settings within reasonable amount of computation time.

A Fast Macroscopic Speed Planner for Electric Vehicle Platooning

Electric vehicles (EVs) have demonstrated significant advantages of high fuel economy and low maintenance cost over gasoline-powered vehicles and hybrid electric vehicles in moving people and goods. However, range anxiety remains as one of the main barriers in market penetration for EVs. Platooning has proven to be an effective approach to reduce aerodynamic drag resistance and thus extend EV ranges. However, taking full advantage of platooning to reduce energy consumption during a trip while satisfying the time constraint is a challenge. This paper is focused on the design and validation of the high-level speed planner of a two-level real-time platooning framework for EVs. The speed optimization problem in the high-level speed planner for the entire trip is reformulated into two speed profile optimization problems in two processes: 1) catch-up and then platooning, and 2) platooning and then break-away. Analytical solutions are derived for the optimal speed profiles in both processes. The analytical solutions capture the impacts of critical parameters such as initial and final inter-vehicle distances, and the leading vehicle speed.

A Two-Phase Method for Production Planning and Machine Speed Optimization Problem

A Two-Phase Method for Production Planning and Machine Speed Optimization Problem

An ACO-based heuristic approach for a route and speed optimization problem in home health care with synchronized visits and carbon emissions

An ACO-based heuristic approach for a route and speed optimization problem in home health care with synchronized visits and carbon emissions

Liner sailing speed optimization considering wind and waves

This paper proposes a new sailing speed optimization problem considering sea conditions such as wind and waves for a container shipping company. Since wind and waves, as exterior factors, can reduce speed, more power is employed as compensation to maintain regular service frequency and avoid delay, resulting in additional bunker consumption and higher cost. Hence, it is necessary to optimize the sailing speed according to the wind and waves. A power model was built to determine the reduced speed caused by the wind and waves for quantifying the speed reduction. On the basis of the proposed model, we developed a mixed-integer nonlinear programming model for a sailing speed optimization problem considering the wind and waves. In view of the complexity of the function for determining the speed reduction, a discrete method is proposed to transform the proposed mixed-integer nonlinear programming model into a mixed-integer linear programming model. Finally, a numerical experiment was conducted to verify and validate the applicability.

Vessel velocity decisions in inland waterway transportation under uncertainty

Recent studies have concentrated on environmental and economic impacts of ships. In this regard, fuel and CO2 emission is considered as one of the important factors for such impacts. In particular, the sailing speed of the vessels affects the fuel consumption and therefore the emission directly. In this study, we consider a speed optimization problem in inland waterway, which is characterized by stochastic waiting times at the lock caused by uncertainty in lock processing time estimations of other vessels. The objective is to minimize fuel consumption of an approaching ship, such that it traverses the river segment in a set deadline. We introduce a mathematical model for this problem and evaluate the effectiveness and attractiveness of two solution approaches: an optimal solution and a simple heuristic. This creates intuitive guidelines for skippers based on information provision to select an appropriate speed decision approach to minimize the total expected fuel consumption and CO2 emission of inland waterway transportation.

Liner Shipping Service Planning Under Sulfur Emission Regulations

Air emissions from ships have become an important issue in sustainable shipping because of the low quality of the marine fuel consumed by ships. To reduce sulfur emissions from shipping, the International Maritime Organization has established emission control areas (ECAs) where ships must use low-sulfur fuel with at most 0.1% sulfur or take equivalent emission-reduction measures. The use of low-sulfur fuel increases the costs for liner shipping companies and affects their operations management. This study addresses a holistic liner shipping service planning problem that integrates fleet deployment, schedule design, and sailing path and speed optimization, considering the effect of ECAs. We propose a nesting algorithmic framework to address this new and challenging problem. Semianalytical solutions are derived for the sailing path and speed optimization problem, which are used in the schedule design. A tailored algorithm is applied to solve schedule design problems, and the solutions are used in fleet deployment. The fleet deployment problem is then addressed by a dynamic programming-based pseudo-polynomial time algorithm. Numerical experiments demonstrate that considering the effect of ECAs in liner shipping operations management can reduce over 2% of the costs, which is significant considering that the annual operating cost of a shipping company’s network can be as high as several billion dollars.

Autonomous Driving Trajectory Optimization With Dual-Loop Iterative Anchoring Path Smoothing and Piecewise-Jerk Speed Optimization

This letter presents a free space trajectory optimization algorithm for autonomous driving, which decouples the collision-free trajectory generation problem into a Dual-Loop Iterative Anchoring Path Smoothing (DL-IAPS) problem and a Piecewise-Jerk Speed Optimization (PJSO) problem. The work leads to remarkable driving performance improvements including more robust and precise collision avoidance, higher control feasibility, higher computation efficiency and stricter driving comfort guarantee, compared with other existing algorithms. The advantages of our algorithm are attributed to our fast iterative collision checks with exact vehicle/obstacle shapes, strict non-holonomic dynamic constraints and accurate kinematics-based speed optimization. It has been validated that, through batch simulation and road experiments, compared with prior works, our algorithm is with the highest robustness and capable to maintain the lowest failure rate (~7%) at nearly all test conditions, achieves 10x faster computational speed than other planners, fulfills 100% driving-comfort standards in complex driving scenarios, and does not induce significant time increase as boundaries or obstacles scale up.

Optimization of Speed Profile with RTA Constraints under Wind Uncertainty

Four-dimensional (4D) trajectory is considered to be one of the effective means to reduce the environmental impact of aviation while increasing capacity and safety. This paper proposes an approach to optimize cruise speed profile subject to wind uncertainty, aiming to reduce the fuel burn complying with the Required Time of Arrival (RTA) constraints. The approach is based on a probabilistic framework, and the uncertainty propagation is analyzed using a Probability Transformation Method, and the probability distributions of arrival time and fuel consumption are determined. In addition, from an airborne operation perspective, transition profiles need to be considered in the reference speed optimization problem, aiming to improve the rationale of the reference trajectory. Numerical simulations are presented, and the results demonstrate that the speed profiles optimized by this method are able to meet the RTA constraints in the presence of wind uncertainty, with an average reduction of 7.04% in fuel consumption compared with that of the flight data.

Eco-Approach With Traffic Prediction and Experimental Validation for Connected and Autonomous Vehicles

This work proposes a fuel efficient vehicle speed control strategy for a connected and autonomous vehicle to pass the intersection (the eco-approach application). A control framework is developed to integrate traffic prediction (enabled by connectivity) and speed optimization. The traffic prediction is based on traffic flow model and can be applied to mixedtraffic scenarios where both connected and non-connected vehicles are on the road. Real-time information from connected vehicles and signal lights provides `partial' measurement of the traffic states. The unknown traffic states are estimated using an observer (Unscented Kalman Filter). Uncertainties in the traffic prediction are systematically considered during the vehicle speed optimization to improve the robustness of the optimal control. Effects of powertrain states (the transmission gear ratio) on fuel consumption are considered as well. The vehicle speed optimization problem is real-time implementable using an efficient nonlinear programming solver. The optimal speed control strategy is evaluated in both a simulated traffic scenario and a real-world traffic scenario. In the simulated traffic scenario, fuel benefits vary from 5.3% to 9.4% as the penetration rate of connectivity increases. This is satisfactory compared to 11.7% fuel benefits with perfect traffic prediction. In the realworld traffic scenario, experimental results show that 6.9% fuel benefits can be achieved with two connected preceding vehicles and 11.2% fuel benefits can be obtained with perfect prediction. The results demonstrate the effectiveness of the traffic prediction and the optimal vehicle speed control strategy.

Speed optimization algorithm with routing to minimize fuel consumption under time-dependent travel conditions

ABSTRACT With increasing interest in reducing fuel consumption and related pollution caused by transportation services, a speed optimization problem that derives speeds of a vehicle given a fixed route to customers has become significant, given that fuel consumption of vehicles is a function of their speeds. Following this interest, we address a speed optimization problem under time-dependent travel conditions. Motivated by the fact that altering the fixed route in response to the time-dependent condition would contribute to minimizing fuel consumption for transportation services, a routing decision is also involved in the problem formulation. To solve this problem, we propose an exact approach with approximation schemes to handle its complexity. Through the experiments, we verify the performance of the proposed approach in terms of finding near-optimal solutions within a short computation time as well as how the routing decision contributes to minimizing fuel consumption for transportation services.

A Green Routing and Scheduling Problem in Home Health Care

The growing concern about the influences of anthropogenic pollutions has forced researchers and scholars to study the environmental concerns. This paper addresses a green routing and scheduling problem in home health care (HHC) with the constraints of synchronized visits and carbon emissions. In this work, the objective is to design a reasonable logistics route meanwhile reduce the effect on the environment for the HHC company. The formulated mixed-integer programming (MIP) model is solved for a set of small scale instances using Gurobi solver with a time limit of 1 hour. An efficient two-phase heuristic approach through decomposing the studied problem into a routing problem and a speed optimization problem is proposed. The heuristic approach is based on two exact methods using Gurobi solver and dynamic programming (DM) method. The proposed heuristic approach is examined by a total of 19 instances with different scales. The experimental results for the studied problem highlight the effectiveness and efciency of the proposed heuristic approach.

Liner ship bunkering and sailing speed planning with uncertain demand

Liner shipping is an important branch of maritime transportation. As bunker fuel consumption causes high operating cost and harmful gas emissions, bunker fuel management is a great challenge and a hot research topic in liner shipping. Bunker charging can be achieved at ports with diverse prices, and it is recognized that appropriately managing bunker fuel and sailing speed can improve liner shipping performance and reduce environmental pollution. Most existing works assume that the container demand is deterministic. However, in practice, it is usually difficult to exactly estimate the volume of containers to be shipped due to various factors. This paper studies a liner ship bunkering and speed optimization problem under uncertain container demand. For the problem, a two-stage stochastic and non-linear programming formulation is proposed. To split the complexity of the problem, the complicated bunker consumption function is approximated by piecewise linear ones. To solve the problem, a classic sample average approximation (SAA) method, and the SAA based on scenario reduction, and an L-shaped method are developed and compared. Numerical results show that the L-shaped method outperforms the two SAA methods, in terms of solution quality and computational time.

Tramp Ship Routing and Scheduling with Speed Optimization Considering Carbon Emissions

The International Maritime Organization (IMO) proposed to reduce the total CO2 emissions of the maritime sector by 50% by 2050, and strive to gradually achieve the zero-carbon target. Therefore, shipping companies need to consider environmental impacts while pursuing benefits. In view of the tramp ship scheduling with speed optimization problem, considering carbon emissions, the configuration of owner ships and charter ships, and the impact of sailing speed on ship scheduling with the target of minimizing the total costs of shipping companies, multi-type tramp ship scheduling and speed optimization considering carbon emissions is established. A genetic simulated annealing algorithm based on a variable neighborhood search is proposed to solve the problem. Firstly, the ship type is matched with the cargo. Then the route is generated according to the time constraint, and finally, the neighborhood search strategy is adopted to improve the solution quality. The effectiveness of the proposed model and algorithm is verified by an example, which also confirms that ship scheduling and sailing speed joint optimization can reduce costs and carbon emissions. Research results can not only deepen the study of the theory of tramp scheduling but also to effectively solve the tramp shipping schedule considering carbon emissions problems faced by companies to provide theoretical guidance.