Speed Optimization Problem Research Articles

Optimal Time-Complexity Speed Planning for Robot Manipulators

In this paper, we consider the speed planning problem for a robotic manipulator. In particular, we present an algorithm for finding the time-optimal speed law along an assigned path that satisfies velocity and acceleration constraints and respects the maximum forces and torques allowed by the actuators. The addressed optimization problem is a finite-dimensional reformulation of the continuous-time speed optimization problem, obtained by discretizing the speed profile with $n$ points. The proposed algorithm has linear complexity with respect to $n$ and to the number of degrees of freedom. Such complexity is the best possible for this problem. Numerical tests show that the proposed algorithm is significantly faster than algorithms already existing in literature.

Two-phase optimal solutions for ship speed and trim optimization over a voyage using voyage report data

In the daily operations of a shipping line, minimization of a ship's bunker fuel consumption over a voyage comprising a series of waypoints by adjusting its sailing speeds and trim settings plays a critical role in ship voyage management. To quantify the synergetic influence of sailing speed, displacement, trim, and weather and sea conditions on ship fuel efficiency, we first develop a tailored method to build two artificial neural network models using ship voyage report data. We proceed to address the ship sailing speed and trim optimization problem by putting forward three viable countermeasures within an effective two-phase optimal solution framework: sailing speeds of the ship are optimized in an on-shore planning phase, whereas trim optimization is conducted dynamically by the captain in real time when she/he observes the actual weather and sea conditions at sea. In the on-shore speed optimization problem, simultaneous optimization of sailing speeds and trim settings is beneficial in suggesting more informed sailing speeds because both factors influence a ship's fuel efficiency. In the countermeasure 3 proposed by this study, we address speed and trim optimization simultaneously by proposing a two-step global optimization algorithm that combines dynamic programming and a state-of-the-art simulation-based optimization technique. Numerical experiments with two 9000-TEU (twenty-foot equivalent unit) containerships show that (a) the proposed countermeasure 1 saves 4.96% and 5.83% of bunker fuel for the two ships, respectively, compared to the real situation; (b) the proposed countermeasure 2 increases the bunker fuel savings to 7.63% and 7.57%, respectively; and (c) the bunker fuel savings with Countermeasure 3 attain 8.25% on average. These remarkable bunker fuel savings can also translate into significant mitigation of CO2 emissions.

Cellular UAV-to-X Communications: Design and Optimization for Multi-UAV Networks

In this paper, we consider a single-cell cellular network with a number of cellular users (CUs) and unmanned aerial vehicles (UAVs), in which multiple UAVs upload their collected data to the base station (BS). Two transmission modes are considered to support the multi-UAV communications, i.e., UAV-to-infrastructure (U2I) and UAV-to-UAV (U2U) communications. Specifically, the UAV with a high signal to noise ratio (SNR) for the U2I link uploads its collected data directly to the BS through U2I communication, while the UAV with a low SNR for the U2I link can transmit data to a nearby UAV through underlaying U2U communication for the sake of quality of service. We first propose a cooperative UAV sense-and-send protocol to enable the UAV-to-X communications, and then formulate the subchannel allocation and UAV speed optimization problem to maximize the uplink sum-rate. To solve this NP-hard problem efficiently, we decouple it into three sub-problems: U2I and cellular user (CU) subchannel allocation, U2U subchannel allocation, and UAV speed optimization. An iterative subchannel allocation and speed optimization algorithm (ISASOA) is proposed to solve these sub-problems jointly. Simulation results show that the proposed ISASOA can upload 10\% more data than the greedy algorithm.

Optimal Speed and Gear Shift Control of Long-haulage Trucks

Abstract Long haulage trucks consume large amounts of fuel, and fuel savings are desired both from economical and environmental aspects. When the upcoming road topology is known, the speed and gear shifts can be optimized in order to minimize the fuel consumption by e.g. minimizing the braking of the truck. Three different optimal control approaches are evaluated and compared for the speed and gear shift optimization problem. The results are based on simulations, but two of the three evaluated solvers are also implemented on-board a truck using rapid prototyping to investigate the feasibility of such systems. The results indicate that optimal control of the speed reduces the fuel consumption more than finding the optimal gear shift trajectory. The overall optimization problem contains one discrete and one continuous state, which makes the selection of optimization method complex. A sequential optimization scheme where the optimal speed profile is found using linear programming and the optimal gear profile is found using dynamic programming shows similar results as using dynamic programming for the overall problem simultaneously. One drawback with this solution is robustness and several tuning parameters. The driveability of the solutions are found good at the performed on-board tests.

Joint Ship Schedule Design and Sailing Speed Optimization for a Single Inland Shipping Service with Uncertain Dam Transit Time

Inland shipping has received extensive attention in practice and is a high energy-consuming service sensitive to the river streamflow speed and the uncertain lock traversing time of dams. In this study, we propose a joint ship schedule design and sailing speed optimization problem for a single inland shipping service by incorporating the effects of nonidentical streamflow speed and the uncertain dam transit time. A bi-objective programming model is developed for the proposed problem to simultaneously minimize the total bunker consumption and the ship round-trip time with service level constraints. The service level at each port call is captured by the punctual arrival probability of the ship not less than a predefined value. By introducing the term of buffer times, we analytically derive the Pareto optimal solutions of the ship sailing speeds and schedule. The theoretical method is extended to the case with an arbitrary number of dams and the uncertain port service and leg voyage time. We also examine the relationship between the Pareto optimal solution in this study and the solutions of the previous joint sailing speed and schedule optimization problems in the liner shipping service design. Numerical experiments based on the Yangtze River are conducted. The online appendix is available at https://doi.org/10.1287/trsc.2017.0808 .

A Joint Vehicle Routing and Speed Optimization Problem

Classic vehicle routing models usually treat fuel cost as input data, but fuel consumption heavily depends on the travel speed, which leads to the study of optimizing speeds over a route to improve fuel efficiency. In this paper, we propose a joint vehicle routing and speed optimization problem to minimize the total operating cost including fuel cost. The only assumption made on the dependence between fuel cost and travel speed is that it is a strictly convex differentiable function. This problem is very challenging, with medium-sized instances already difficult for a general mixed-integer convex optimization solver. We propose a novel set-partitioning formulation and a branch-cut-and-price algorithm to solve this problem. We introduce new dominance rules for the labeling algorithm so that the pricing problem can be solved efficiently. Our algorithm clearly outperforms the off-the-shelf optimization solver, and is able to solve some benchmark instances to optimality for the first time. The online supplement is available at https://doi.org/10.1287/ijoc.2018.0810 .

Distributed optimization and coordination algorithms for dynamic speed optimization of connected and autonomous vehicles in urban street networks

Dynamic speed harmonization has shown great potential to smoothen the flow of traffic and reduce travel time in urban street networks. The existing methods, while providing great insights, are neither scalable nor real-time. This paper develops Distributed Optimization and Coordination Algorithms (DOCA) for dynamic speed optimization of connected and autonomous vehicles in urban street networks to address this gap. DOCA decomposes the nonlinear network-level speed optimization problem into several sub-network-level nonlinear problems thus, it significantly reduces the problem complexity and ensures scalability and real-time runtime constraints. DOCA creates effective coordination in decision making between each two sub-network-level nonlinear problems to push solutions towards optimality and guarantee attaining near-optimal solutions. DOCA is incorporated into a model predictive control approach to allow for additional consensus between sub-network-level problems and reduce the computational complexity further. We applied the proposed solution technique to a real-world network in downtown Springfield, Illinois and observed that it was scalable and real-time while finding solutions that were at most 2.7% different from the optimal solution of the problem. We found significant improvements in network operations and considerable reductions in speed variance as a result of dynamic speed harmonization.

A Shortest-Path Algorithm for the Departure Time and Speed Optimization Problem

We present a shortest-path algorithm for the departure time and speed optimization problem under traffic congestion. The objective of the problem is to determine an optimal schedule for a vehicle visiting a fixed sequence of customer locations to minimize a total cost function encompassing emissions cost and labor cost. We account for the presence of traffic congestion, which limits the vehicle speed during peak hours. We show how to cast this problem as a shortest-path problem by exploiting some structural results of the optimal solution. We illustrate the solution method and discuss some properties of the problem. The online appendix is available at https://doi.org/10.1287/trsc.2018.0820 .

Speed optimization over a path with heterogeneous arc costs

The speed optimization problem over a path aims to find a set of speeds over each arc of the given path to minimize the total cost, while respecting the time-window constraint at each node and speed limits over each arc. In maritime transportation, the cost represents fuel cost or air pollutant emissions, so study of this problem has significant economic and environmental impacts. To accommodate different fuel and emission models, we allow the dependence of the cost on the speed to be a general continuously differentiable and strictly convex function, and different across the arcs. We develop an efficient algorithm that is able to solve instances of 1000 nodes in less than a second. The algorithm is 20 to 100 times faster than a general convex optimization solver on test instances and requires much less memory. The solutions found at intermediate steps of our algorithm also provide some insights to ship planners on how to balance the operating cost and service quality.

A multiple ship routing and speed optimization problem under time, cost and environmental objectives

The purpose of this paper is to investigate a multiple ship routing and speed optimization problem under time, cost and environmental objectives. A branch and price algorithm as well as a constraint programming model are developed that consider (a) fuel consumption as a function of payload, (b) fuel price as an explicit input, (c) freight rate as an input, and (d) in-transit cargo inventory costs. The alternative objective functions are minimum total trip duration, minimum total cost and minimum emissions. Computational experience with the algorithm is reported on a variety of scenarios.

Speed optimization and bunkering in liner shipping in the presence of uncertain service times and time windows at ports

Recent studies in maritime shipping have concentrated on environmental and economic impacts of ships. In this regard, fuel is considered as one of the important factors for such impacts. In particular, the sailing speed of the vessels affects the fuel consumption directly. In this study, we consider a speed optimization problem in liner shipping, which is characterized by stochastic port times and time windows. The objective is to minimize the total fuel consumption while maintaining the schedule reliability. We develop a dynamic programing model by discretizing the port arrival times to provide approximate solutions. A deterministic model is presented to provide a lower bound on the optimal expected cost of the dynamic model. We also work on the effect of bunker prices on the liner service schedule. We propose a dynamic programing model for bunkering problem. Our numerical study using real data from a European liner shipping company indicates that the speed policy obtained by proposed dynamic model performs significantly better than the ones obtained by benchmark methods. Moreover, our results show that making speed decisions considering the uncertainty of port times will noticeably decrease fuel consumption cost.

A polynomial-time algorithm for sailing speed optimization with containership resource sharing

The sailing speed optimization problem aims to determine the optimal cruising speeds of ships by balancing the number of ships required on services, the fuel consumption, and the level of service provided for customers. The level of service can be incorporated into a sailing speed optimization model from the perspective of supply chain management or from the perspective of shipping lines. We design a polynomial-time algorithm workable to solve the two models based on bi-section search methods. The novelties of the algorithm include constructing a new parameter on which the bi-section search will be executed and deriving a near-optimal solution by taking advantage of the problem structure. We also provide theoretical results that guarantee the validity of the polynomial-time algorithm.

Optimizing Ship Speed to Minimize Total Fuel Consumption with Multiple Time Windows

We study the ship speed optimization problem with the objective of minimizing the total fuel consumption. We consider multiple time windows for each port call as constraints and formulate the problem as a nonlinear mixed integer program. We derive intrinsic properties of the problem and develop an exact algorithm based on the properties. Computational experiments show that the suggested algorithm is very efficient in finding an optimal solution.

Simultaneous Optimization of Container Ship Sailing Speed and Container Routing with Transit Time Restrictions

We introduce a decision support tool for liner shipping companies to optimally determine the sailing speed and needed fleet for a global network. We incorporate cargo routing decisions with tight transit time restrictions on each container such that we get a realistic picture of the utilization of the network. Furthermore, we show that it is possible to extend the model to include optimal time scheduling decisions such that the time associated with transshipments is also reflected accurately. To solve the speed optimization problem, we propose an exact algorithm based on Benders decomposition and column generation that exploits the separability of the problem. Computational results show that the method is applicable to liner shipping networks of realistic size and that it is important to incorporate cargo routing decisions when optimizing speed. The online appendix is available at https://doi.org/10.1287/trsc.2018.0818 .

Formula omitted] policy model for liner shipping refueling and sailing speed optimization problem

This work expounds on implementing an effective dynamic (s,S) policy to solve a liner shipping refueling and speed determination problem under both bunker prices and consumption uncertainties. While solving an optimization model which incorporates a continuous distribution is extremely challenging, we use sample average approximation method to solve it. However, the resulting problem is still a very large-scaled problem. Therefore, we propose two variations of the progressive hedging algorithm to tackle it. Numerical results show that our solution method is efficient and, in addition, our dynamic (s,S) policy model has significant cost reduction potential compared to stationary models.

Optimizing ship speed to minimize fuel consumption

Owing to high fuel costs and environmental regulations, the optimization of ship speed to minimize fuel consumption and reduce carbon emissions has become a hot issue in the maritime industry. In this paper, we study the sailing speed optimization problem for a ship operating on a route having a specified sequence of calling ports with time windows for calling time. The considered problem can be formulated as a non-linear program. We derive the intrinsic properties of the problem and develop an optimal algorithm based on the properties. Computational experiments show that the developed algorithm in this paper is efficient in finding an optimal solution.

Analysis of an exact algorithm for the vessel speed optimization problem

AbstractIncreased fuel costs together with environmental concerns have led shipping companies to consider the optimization of vessel speeds. Given a fixed sequence of port calls, each with a time window, and fuel cost as a convex function of vessel speed, we show that optimal speeds can be found in quadratic time. © 2013 Wiley Periodicals, Inc. NETWORKS, 2013