Showing papers on "Integer programming published in 2021"

A Clustering-Based Coverage Path Planning Method for Autonomous Heterogeneous UAVs

Abstract: Unmanned aerial vehicles (UAVs) have been widely applied in civilian and military applications due to their high autonomy and strong adaptability. Although UAVs can achieve effective cost reduction and flexibility enhancement in the development of large-scale systems, they result in a serious path planning and task allocation problem. Coverage path planning, which tries to seek flight paths to cover all of regions of interest, is one of the key technologies in achieving autonomous driving of UAVs and difficult to obtain optimal solutions because of its NP-Hard computational complexity. In this paper, we study the coverage path planning problem of autonomous heterogeneous UAVs on a bounded number of regions. First, with models of separated regions and heterogeneous UAVs, we propose an exact formulation based on mixed integer linear programming to fully search the solution space and produce optimal flight paths for autonomous UAVs. Then, inspired from density-based clustering methods, we design an original clustering-based algorithm to classify regions into clusters and obtain approximate optimal point-to-point paths for UAVs such that coverage tasks would be carried out correctly and efficiently. Experiments with randomly generated regions are conducted to demonstrate the efficiency and effectiveness of the proposed approach.

MIPLIB 2017: data-driven compilation of the 6th mixed-integer programming library

Abstract: We report on the selection process leading to the sixth version of the Mixed Integer Programming Library, MIPLIB 2017. Selected from an initial pool of 5721 instances, the new MIPLIB 2017 collection consists of 1065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, these sets were compiled using a data-driven selection process supported by the solution of a sequence of mixed integer optimization problems, which encode requirements on diversity and balancedness with respect to instance features and performance data.

Optimal Scheduling of Isolated Microgrids Using Automated Reinforcement Learning-based Multi-period Forecasting

Abstract: To reduce the negative impact of the uncertainty of load and renewable energies outputs on microgrid operation, an optimal scheduling model is proposed for isolated microgrids by using automated reinforcement learning-based multi-period forecasting of renewable power generations and loads. Firstly, a prioritized experience replay automated reinforcement learning (PER-AutoRL) is designed to simplify the deployment of deep reinforcement learning (DRL)-based forecasting model in a customized manner, the single-step multi-period forecasting method based on PER-AutoRL is proposed to address the error accumulation issue suffered by existing multi-step forecasting methods, then the prediction values are revised via the error distribution to improve the prediction accuracy; secondly, a scheduling model considering demand response is constructed to minimize the total microgrid operating costs, where the revised forecasting values are used as the dispatch basis, and a spinning reserve chance constraint is set according to the error distribution; finally, by transforming the original scheduling model into a readily solvable mixed integer linear programming via the sequence operation theory (SOT), the transformed model is solved by using CPLEX solver. The simulation results show that compared with traditional scheduling models without forecasting, this approach manages to significantly reduce the system operating costs by improving the prediction accuracy.

Cost-Effective App Data Distribution in Edge Computing

Abstract: Edge computing, as an extension of cloud computing, distributes computing and storage resources from centralized cloud to distributed edge servers, to power a variety of applications demanding low latency, e.g., IoT services, virtual reality, real-time navigation, etc. From an app vendor's perspective, app data needs to be transferred from the cloud to specific edge servers in an area to serve the app users in the area. However, according to the pay-as-you-go business model, distributing a large amount of data from the cloud to edge servers can be expensive. The optimal data distribution strategy must minimize the cost incurred, which includes two major components, the cost of data transmission between the cloud to edge servers and the cost of data transmission between edge servers. In the meantime, the delay constraint must be fulfilled - the data distribution must not take too long. In this article, we make the first attempt to formulate this Edge Data Distribution (EDD) problem as a constrained optimization problem from the app vendor's perspective and prove its $\mathcal {NP}$ NP -hardness. We propose an optimal approach named EDD-IP to solve this problem exactly with the Integer Programming technique. Then, we propose an $O(k)$ O ( k ) -approximation algorithm named EDD-A for finding approximate solutions to large-scale EDD problems efficiently. EDD-IP and EDD-A are evaluated on a real-world dataset and the results demonstrate that they significantly outperform three representative approaches.

Top- k Feature Selection Framework Using Robust 0–1 Integer Programming

Abstract: Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine learning and has been widely studied in recent years. Most FS methods rank the features in order of their scores based on a specific criterion and then select the $k$ top-ranked features, where $k$ is the number of desired features. However, these features are usually not the top- $k$ features and may present a suboptimal choice. To address this issue, we propose a novel FS framework in this article to select the exact top- $k$ features in the unsupervised, semisupervised, and supervised scenarios. The new framework utilizes the $\ell _{0,2}$ -norm as the matrix sparsity constraint rather than its relaxations, such as the $\ell _{1,2}$ -norm. Since the $\ell _{0,2}$ -norm constrained problem is difficult to solve, we transform the discrete $\ell _{0,2}$ -norm-based constraint into an equivalent 0–1 integer constraint and replace the 0–1 integer constraint with two continuous constraints. The obtained top- $k$ FS framework with two continuous constraints is theoretically equivalent to the $\ell _{0,2}$ -norm constrained problem and can be optimized by the alternating direction method of multipliers (ADMM). Unsupervised and semisupervised FS methods are developed based on the proposed framework, and extensive experiments on real-world data sets are conducted to demonstrate the effectiveness of the proposed FS framework.

Fuzzy integrated cell formation and production scheduling considering automated guided vehicles and human factors

Abstract: In today's competitive environment, it is essential to design a flexible-responsive manufacturing system with automatic material handling systems. In this study, a fuzzy Mixed Integer Linear Programming (MILP) model is designed for Cell Formation Problem (CFP) including the scheduling of parts within cells in a Cellular Manufacturing System (CMS) where several Automated Guided Vehicles (AGVs) are in charge of transferring the exceptional parts. Notably, using these AGVs in CMS can be challenging from the perspective of mathematical modeling due to consideration of AGVs’ collision as well as parts pickup/delivery. This paper tries to investigate the role of AGVs and human factors as indispensable components of automation systems in the cell formation and scheduling of parts under fuzzy processing time. The proposed objective function includes minimizing the makespan and inter-cellular movements of parts. Due to the NP-hardness of the problem, a hybrid Genetic Algorithm (GA/heuristic) and a Whale Optimization Algorithm (WOA) are developed. The experimental results reveal that our proposed algorithms have a high performance compared to CPLEX and other two well-known algorithms, i.e., Particle Swarm Optimization (PSO) and Ant Colony Optimization (ACO), in terms of computational efficiency and accuracy. Finally, WOA stands out as the best algorithm to solve the problem.

Confidence Interval Based Distributionally Robust Real-Time Economic Dispatch Approach Considering Wind Power Accommodation Risk

Abstract: This article proposes a confidence interval based distributionally robust real-time economic dispatch (CI-DRED) approach, which considers the risk related to accommodating wind power. In this article, only the wind power curtailment and load shedding due to wind power disturbances are evaluated in the operational risk. The proposed approach can strike a balance between the operational costs and risk even when the wind power probability distribution cannot be precisely estimated. A novel ambiguity set is developed based on the imprecise probability theory, which can be constructed based on the point-wise or family-wise confidence intervals. The worst pair of distributions in the established ambiguity set is then identified, and the original CI-DRED problem is transformed into a determined nonlinear dispatch problem accordingly. By using the sequential convex optimization method and piecewise linear approximation method, the nonlinear dispatch model is reformulated as a mixed integer linear programming problem, for which off-the-shelf solvers are available. A fast inactive constraint filtration method is also applied to further relieve the computational burden. Numerical results on the IEEE 118-bus system and a real 445-bus system verify the effectiveness and efficiency of the proposed approach.

Ambulance routing in disaster response considering variable patient condition: NSGA-II and MOPSO algorithms

Abstract: The shortage of relief vehicles capacity is a common issue throughout disastrous situations due to the abundance of injured people who need urgent medical aid. Hence, ambulances fleet management is highly important to save as many injured individuals as possible. In this regard, the present paper defines different patient groups based on their needs and characteristics. In order to provide the affected people with proper and timely medical aid, changes in their health status are also considered. A Mixed-integer Linear Programming (MILP) model is proposed to find the best sequence of routes for each ambulance and minimize the latest service completion time (SCT) as well as the number of patients whose condition gets worse because of receiving untimely medical services. Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Multi-Objective Particle Swarm Optimization (MOPSO) are used to find high-quality solutions over a short time. In the end, Lorestan province, Iran, is considered as a case study to assess the model's performance and analyze the sensitivity of solutions with respect to the major parameters, which results in insightful managerial suggestions.

Exact methods for the traveling salesman problem with drone

Abstract: Efficiently handling last-mile deliveries becomes more and more important nowadays. Using drones to support classical vehicles allows improving delivery schedules as long as efficient solution meth...

Energy-Efficient Wireless Communications with Distributed Reconfigurable Intelligent Surfaces

Abstract: This paper investigates the problem of resource allocation for a wireless communication network with distributed reconfigurable intelligent surfaces (RISs). In this network, multiple RISs are spatially distributed to serve wireless users and the energy efficiency of the network is maximized by dynamically controlling the on-off status of each RIS as well as optimizing the reflection coefficients matrix of the RISs. This problem is posed as a joint optimization problem of transmit beamforming and RIS control, whose goal is to maximize the energy efficiency under minimum rate constraints of the users. To solve this problem, two iterative algorithms are proposed for the singleuser case and multi-user case. For the single-user case, the phase optimization problem is solved by using a successive convex approximation method, which admits a closed-form solution at each step. Moreover, the optimal RIS on-off status is obtained by using the dual method. For the multi-user case, a low-complexity greedy searching method is proposed to solve the RIS on-off optimization problem. Simulation results show that the proposed scheme achieves up to 33% and 68% gains in terms of the energy efficiency in both single-user and multi-user cases compared to the conventional RIS scheme and amplify-and-forward relay scheme, respectively.

Joint Target Assignment and Power Allocation in Multiple Distributed MIMO Radar Networks

Abstract: The “defocused transmit-focused receive” (DTFR) mode in the distributed multiple-input multiple-output (MIMO) radar network is very effective in multitarget tracking. In this mode, a completely defocused beam is transmitted and a focused receive beam is synthesized so that the MIMO radar is capable of tracking targets independently. A joint target assignment and power allocation (TAPA) strategy is developed for multiple distributed MIMO radar networks in cluttered environment using the DTFR mode. Our aim is to achieve the better system tracking accuracy under the constraints of receive beam direction capability and power budget. We derive the posterior Cramer-Rao lower bound (PCRLB) and adopt it as the objective function, since it quantifies the precision of target state estimates. It is shown that the TAPA problem is a mixed integer programming and NP-hard problem, where two involved parameters, i.e., the target-radar assignment and power allocation, are both coupled in the objective and in the constraints. By introducing an intermediate variable, we propose an efficient two-step-based solution for solving this problem. The simulation results show the superior performance and adaptivity compared with existing algorithms.

Reliability-Aware Offloading and Allocation in Multilevel Edge Computing System

Abstract: Mobile edge computing system provides cloud computing capabilities at the edge of wireless mobile networks, ensuring low latency, highly efficient computing, and improved user experience. At the same time, computationally intensive components are offloaded from mobile devices to edge servers and distributed among the servers. Due to the special constraints (mobile devices’ battery capacities, limited computing resources of one single edge server, inevitable edge server failure, etc.), there emerges a following problem. 1) How to guarantee the reliability of the offloaded computing? This problem brings in the following two other problems. 2) How to find the appropriate offloading point in the mobile program such that the computing tasks offloaded to cloud can be maximized, while the transmission energy consumption is minimized? 3) What is the achievable minimum latency tasks allocation strategy among multiple users’ mobile devices and multiple edge servers? In this paper, we try to address the aforementioned problems. First, for the appropriate offloading point problem, we consider the offloading valuable basic constraint and propose a task merging strategy based on mobile program component call graphs to minimize the computational complexity of the program partition. Second, we formulate the second problem as a combinatorial optimization problem and transform it into an n -fold integer programming problem by mapping the remaining computing resources to a virtual component. Third, we design a reliable shadow component scheme between multilevel severs for the reliability problem. Finally, we develop a fast algorithm for the mix problem and analyze its performance and conduct experiments to prove the accuracy of our theoretical results.

Improving Post Training Neural Quantization: Layer-wise Calibration and Integer Programming

Abstract: Lately, post-training quantization methods have gained considerable attention, as they are simple to use, and require only a small unlabeled calibration set. This small dataset cannot be used to fine-tune the model without significant over-fitting. Instead, these methods only use the calibration set to set the activations' dynamic ranges. However, such methods always resulted in significant accuracy degradation, when used below 8-bits (except on small datasets). Here we aim to break the 8-bit barrier. To this end, we minimize the quantization errors of each layer separately by optimizing its parameters over the calibration set. We empirically demonstrate that this approach is: (1) much less susceptible to over-fitting than the standard fine-tuning approaches, and can be used even on a very small calibration set; and (2) more powerful than previous methods, which only set the activations' dynamic ranges. Furthermore, we demonstrate how to optimally allocate the bit-widths for each layer, while constraining accuracy degradation or model compression by proposing a novel integer programming formulation. Finally, we suggest model global statistics tuning, to correct biases introduced during quantization. Together, these methods yield state-of-the-art results for both vision and text models. For instance, on ResNet50, we obtain less than 1\% accuracy degradation --- with 4-bit weights and activations in all layers, but the smallest two. Our code is available at, https://github.com/papers-submission/CalibTIP

Optimal decision trees for categorical data via integer programming

Abstract: Decision trees have been a very popular class of predictive models for decades due to their interpretability and good performance on categorical features. However, they are not always robust and tend to overfit the data. Additionally, if allowed to grow large, they lose interpretability. In this paper, we present a mixed integer programming formulation to construct optimal decision trees of a prespecified size. We take the special structure of categorical features into account and allow combinatorial decisions (based on subsets of values of features) at each node. Our approach can also handle numerical features via thresholding. We show that very good accuracy can be achieved with small trees using moderately-sized training sets. The optimization problems we solve are tractable with modern solvers.

Network planning with deep reinforcement learning

Abstract: Network planning is critical to the performance, reliability and cost of web services. This problem is typically formulated as an Integer Linear Programming (ILP) problem. Today's practice relies on hand-tuned heuristics from human experts to address the scalability challenge of ILP solvers. In this paper, we propose NeuroPlan, a deep reinforcement learning (RL) approach to solve the network planning problem. This problem involves multi-step decision making and cost minimization, which can be naturally cast as a deep RL problem. We develop two important domain-specific techniques. First, we use a graph neural network (GNN) and a novel domain-specific node-link transformation for state encoding, in order to handle the dynamic nature of the evolving network topology during planning decision making. Second, we leverage a two-stage hybrid approach that first uses deep RL to prune the search space and then uses an ILP solver to find the optimal solution. This approach resembles today's practice, but avoids human experts with an RL agent in the first stage. Evaluation on real topologies and setups from large production networks demonstrates that NeuroPlan scales to large topologies beyond the capability of ILP solvers, and reduces the cost by up to 17% compared to hand-tuned heuristics.

READ: Robustness-oriented Edge Application Deployment in Edge Computing Environment

Abstract: Edge computing (EC) can overcome several limitations of cloud computing. In the EC environment, a service provider can deploy its application instances on edge servers to serve users with low latency. Given a limited budget K for deploying applications in a particular geographical area, some approaches have been proposed to achieves various optimization objectives, e.g., to maximize the servers' coverage, to minimize the average network latency, etc. However, the robustness of the services collectively delivered by the service provider's applications deployed on the edge servers has not been considered at all. This is a critical issue, especially in the highly distributed, dynamic and volatile EC environment. We make the first attempt to tackle this challenge. Specifically, we formulate this Robustness-oriented Edge Application Deployment(READ) problem as a constrained optimization problem and prove its NP-hardness. Then, we provide an integer programming based approach READ-O for solving it precisely, and an approximation algorithm READ-A for efficiently finding near-optimal solutions to large-scale problems. READ-A's approximation ratio is not worse than K/2, which is constant regardless of the total number of edge servers. Evaluation of the widely-used real-world dataset against five representative approaches demonstrates that our approaches can solve the READ problem effectively and efficiently.

Improving flex-route transit services with modular autonomous vehicles

Abstract: With the advent of modular autonomous vehicles (MAVs), this paper presents a novel operational design for flex-route transit services to reduce operation costs of vehicles and improve the service quality of customers. The regime allows the simultaneous dispatch of a certain amount of MAVs from a bus terminal at a departure time. Each MAV is allowed to visit customers freely outside of checkpoints. Self-adaptive capacity and flexible service mode adapt time- and space-dependent demand characteristics. The presented operational design is formulated as a mixed-integer linear program that is NP-hard. A two-stage solution framework is developed to decompose the proposed mathematical programming cautiously. In the first stage, customized dynamic programming with valid cuts is designed to solve a bus scheduling problem efficiently. In the second stage, an effective and fast heuristic is proposed to solve a variant of the dial-a-ride problem and satisfy the technical requirements for developing on-line applications. Numerical examples and a case study show the effectiveness of the proposed design by comparing the flex-route transit services using traditional vehicles.

Sustainable supply chain network design problem: Using the integrated BWM, TOPSIS, possibilistic programming, and ε-constrained methods

Abstract: This paper proposes a two-stage multi-objective possibilistic integer linear programming sustainable supply chain network design model, minimizing the economic, environmental goals and maximizing the social sustainability goals. The proposed model determines the openings of facilities and the amount of flow of goods across the supply chain. It introduces supplier green image factors in the design of the supply chain network. The model has considered epistemic uncertainty to model the unknown capacity, cost, and demand. The proposed study has been carried out in two stages. In the first stage, BWM (Best-Worst method) and TOPSIS are applied to evaluate the green image weights of suppliers. Further, these green weights are being used in the second phase for the supply chain network design. The study has adopted combined possibilistic programming and Epsilon (e) constraint method, which was reported infrequently in the literature. Epsilon (e) constraint method generates distinct Pareto-optimal solutions, which provided a large combination of the trade-off between the cost, emission, and social sustainability. The results facilitate decision-makers to take the decision in an uncertain environment.

A Survey on Mixed-Integer Programming Techniques in Bilevel Optimization

Abstract: Bilevel optimization is a field of mathematical programming in which some variables are constrained to be the solution of another optimization problem. As a consequence, bilevel optimization is able to model hierarchical decision processes. This is appealing for modeling real-world problems, but it also makes the resulting optimization models hard to solve in theory and practice. The scientific interest in computational bilevel optimization increased a lot over the last decade and is still growing. Independent of whether the bilevel problem itself contains integer variables or not, many state-of-the-art solution approaches for bilevel optimization make use of techniques that originate from mixed-integer programming. These techniques include branch-and-bound methods, cutting planes and, thus, branch-and-cut approaches, or problem-specific decomposition methods. In this survey article, we review bilevel-tailored approaches that exploit these mixed-integer programming techniques to solve bilevel optimization problems. To this end, we first consider bilevel problems with convex or, in particular, linear lower-level problems. The discussed solution methods in this field stem from original works from the 1980's but, on the other hand, are still actively researched today. Second, we review modern algorithmic approaches to solve mixed-integer bilevel problems that contain integrality constraints in the lower level. Moreover, we also briefly discuss the area of mixed-integer nonlinear bilevel problems. Third, we devote some attention to more specific fields such as pricing or interdiction models that genuinely contain bilinear and thus nonconvex aspects. Finally, we sketch a list of open questions from the areas of algorithmic and computational bilevel optimization, which may lead to interesting future research that will further propel this fascinating and active field of research.

Warm Start of Mixed-Integer Programs for Model Predictive Control of Hybrid Systems

Abstract: In hybrid model predictive control (MPC), a mixed-integer quadratic program (MIQP) is solved at each sampling time to compute the optimal control action. Although these optimizations are generally very demanding, in MPC, we expect consecutive problem instances to be nearly identical. This article addresses the question of how computations performed at one time step can be reused to accelerate ( warm start ) the solution of subsequent MIQPs. Reoptimization is not a rare practice in integer programming: for small variations of certain problem data, the branch-and-bound algorithm allows an efficient reuse of its search tree and the dual bounds of its leaf nodes. In this article, we extend these ideas to the receding-horizon settings of MPC. The warm-start algorithm we propose copes naturally with arbitrary model errors, has a negligible computational cost, and frequently enables an a priori pruning of most of the search space. Theoretical considerations and experimental evidence show that the proposed method tends to reduce the combinatorial complexity of the hybrid MPC problem to that of a one-step look-ahead optimization, greatly easing the online computation burden.

Joint Task Partitioning and User Association for Latency Minimization in Mobile Edge Computing Networks

Abstract: Mobile edge computing (MEC) is a promising solution to support emerging delay-sensitive mobile applications, such as self-driving, augment/virtual reality, and various Internet of Things (IoT) applications. By deploying MEC servers at network edge, e.g., close to cellular base stations (BSs), the computational tasks generated by these applications can be offloaded to edge nodes (ENs) and be quickly executed there. At the same time, with the projected large number of IoT devices, the communication and computational resources allocated to each user can be quite limited, making it challenging to provide low-latency MEC services. In this paper, we investigate the problem of task partitioning and user association in an MEC system, aiming to minimize the average latency of all users. We assume that each task can be partitioned into multiple subtasks that can be executed on local devices (e.g., vehicles), MEC servers, and/or cloud servers; each user can be associated with one of the nearby ENs. The subtasks can be independent of or dependent on each other. For each case, we formulate the joint optimization of task partitioning ratios and user association as a mixed integer programming problem. Each problem is solved by decomposing it into two subproblems. The lower-level subproblem is task partitioning under a given user association, which can be solved optimally. The higher-level subproblem is user association, we propose a dual decomposition-based approach and a matching-based approach to derive near-optimal solutions. Simulation results show that compared to benchmark schemes, the proposed schemes reduce the average latency by about 50% and 40% for the cases of independent and dependent subtasks, respectively.

The electric vehicle routing problem with capacitated charging stations

Abstract: Much of the existing research on electric vehicle routing problems (E-VRPs) assumes that the charging stations (CSs) can simultaneously charge an unlimited number of electric vehicles, but this is not the case. In this research, we investigate how to model and solve E-VRPs taking into account these capacity restrictions. In particular, we study an E-VRP with non-linear charging functions, multiple charging technologies, en route charging, and variable charging quantities, while explicitly accounting for the capacity of CSs expressed in the number of chargers. We refer to this problem as the E-VRP with non-linear charging functions and capacitated stations (E-VRP-NL-C). This problem advances the E-VRP literature by considering the scheduling of charging operations at each CS. We first introduce two mixed integer linear programming formulations showing how CS capacity constraints can be incorporated into E-VRP models. We then introduce an algorithmic framework to the E-VRP-NL-C, that iterates between two main components: a route generator and a solution assembler. The route generator uses an iterated local search algorithm to build a pool of high-quality routes. The solution assembler applies a branch-and-cut algorithm to select a subset of routes from the pool. We report on computational experiments comparing four different assembly strategies on a large and diverse set of instances. Our results show that our algorithm deals with the CS capacity constraints effectively. Furthermore, considering the well-known uncapacitated version of the E-VRP-NL-C, our solution method identifies new best-known solutions for 80 out of 120 instances.

A branch-and-cut algorithm for the vehicle routing problem with drones

Abstract: Increasing online purchases and higher customer requirements in terms of speed, flexibility, and costs of home deliveries are challenges to every company involved in last mile delivery. Technological advances have paved the way for last mile deliveries by unmanned aerial vehicles (UAV). Yet, the limited range and capacity of UAVs remain a challenge. This makes the possibility of pairing drones with well-established means of transportation highly attractive. However, the optimization problem arising in joint delivery by truck and drone has only recently been considered in the literature. We develop a new mixed integer linear programming (MILP) model for the vehicle routing problem with drones (VRPD) with two different time-oriented objective functions. Additionally, we introduce new valid inequalities based on problem properties to strengthen the linear relaxation. One type of valid inequalities is an extension of the well known subtour elimination constraints. As the number of these constraints grows exponentially with instance size, we provide a separation routine that identifies violated cuts in relaxed solutions to add them efficiently. We therefore derive the first branch-and-cut algorithm for the VRPD. Extensive numerical experiments are performed to demonstrate the competitiveness of our MILP formulation and to show the impact of different combinations of valid inequalities. We optimally solve instances with unrestricted drone ranges with up to 20 nodes and instances with range-limited drones with up to 30 nodes. These are significantly larger instance sizes than the previously known exact approaches are able to handle. In addition, we introduce a relaxation of the VRPD that provides good lower bounds in notable reduced run times. To provide managerial insights, we show that integrating truck-drone tandems into transportation systems can not only lead to improvements regarding the speed of deliveries, but can also be used to reduce the fleet size without slowing down the delivery process and increasing the workload of truck drivers.

The cooperative sorting strategy for connected and automated vehicle platoons

Abstract: This paper presents a "cooperative vehicle sorting" strategy that seeks to optimally sort connected and automated vehicles (CAVs) in a multi-lane platoon to reach an ideally organized platoon In the proposed method, a CAV platoon is firstly discretized into a grid system, where a CAV moves from one cell to another in discrete time-space domain Then, the cooperative sorting problem is modeled as a path-finding problem in the graphic domain The problem is solved by the deterministic A* algorithm with a stepwise strategy, where only one vehicle can move within a movement step The resultant shortest path is further optimized with an integer linear programming algorithm to minimize the sorting time by allowing multiple movements within a step To improve the algorithm running time and address multiple shortest paths, a distributed stochastic A* algorithm (DSA*) is developed by introducing random disturbances to the edge costs to break uniform paths (with equal path cost) Numerical experiments are conducted to demonstrate the effectiveness of the proposed DSA* method The results report shorter sorting time and significantly improved algorithm running time due to the use of DSA* In addition, we find that the optimization performance can be further improved by increasing the number of processes in the distributed computing system