Greedy Strategy Research Articles

A Computational Framework for Solving Nonlinear Binary Optimization Problems in Robust Causal Inference

Identifying cause-effect relations among variables is a key step in the decision-making process. Whereas causal inference requires randomized experiments, researchers and policy makers are increasingly using observational studies to test causal hypotheses due to the wide availability of data and the infeasibility of experiments. The matching method is the most used technique to make causal inference from observational data. However, the pair assignment process in one-to-one matching creates uncertainty in the inference because of different choices made by the experimenter. Recently, discrete optimization models have been proposed to tackle such uncertainty; however, they produce 0-1 nonlinear problems and lack scalability. In this work, we investigate this emerging data science problem and develop a unique computational framework to solve the robust causal inference test instances from observational data with continuous outcomes. In the proposed framework, we first reformulate the nonlinear binary optimization problems as feasibility problems. By leveraging the structure of the feasibility formulation, we develop greedy schemes that are efficient in solving robust test problems. In many cases, the proposed algorithms achieve a globally optimal solution. We perform experiments on real-world data sets to demonstrate the effectiveness of the proposed algorithms and compare our results with the state-of-the-art solver. Our experiments show that the proposed algorithms significantly outperform the exact method in terms of computation time while achieving the same conclusion for causal tests. Both numerical experiments and complexity analysis demonstrate that the proposed algorithms ensure the scalability required for harnessing the power of big data in the decision-making process. Finally, the proposed framework not only facilitates robust decision making through big-data causal inference, but it can also be utilized in developing efficient algorithms for other nonlinear optimization problems such as quadratic assignment problems. History: Accepted by Ram Ramesh, Area Editor for Data Science and Machine Learning. Funding: This work was supported by the Division of Civil, Mechanical and Manufacturing Innovation of the National Science Foundation [Grant 2047094]. Supplemental Material: The online supplements are available at https://doi.org/10.1287/ijoc.2022.1226 .

Deadline-Aware Dynamic Task Scheduling in Edge–Cloud Collaborative Computing

In recent years, modern industry has been exploring the transition to cyber physical system (CPS)-based smart factories. As intelligent industrial detection and control technology grows in popularity, massive amounts of time-sensitive applications are generated. A cutting-edge computing paradigm called edge-cloud collaborative computing was developed to satisfy the need of time-sensitive tasks such as smart vehicles and automatic mechanical remote control, which require substantially low latency. In edge-cloud collaborative computing, it is extremely challenging to improve task scheduling while taking into account both the dynamic changes of user requirements and the limited available resources. The current task scheduling system applies a round-robin policy to cyclically select the next server from the list of available servers, but it may not choose the best-suited server for the task. To satisfy the real-time task flow of industrial production in terms of task scheduling based on deadline and time sensitivity, we propose a hierarchical architecture for edge-cloud collaborative environments in the Industrial Internet of Things (IoT) and then simplify and mathematically formulate the time consumption of edge-cloud collaborative computing to reduce latency. Based on the above hierarchical model, we present a dynamic time-sensitive scheduling algorithm (DSOTS). After the optimization of DSOTS, the dynamic time-sensitive scheduling algorithm with greedy strategy (TSGS) that ranks server capability and job size in a hybrid and hierarchical scenario is proposed. What cannot be ignored is that we propose to employ comprehensive execution capability (CEC) to measure the performance of a server for the first time and perform effective server load balancing while satisfying the user’s requirement for tasks. In this paper, we simulate an edge-cloud collaborative computing environment to evaluate the performance of our algorithm in terms of processing time, SLA violation rate, and cost by extending the CloudSimPlus toolkit, and the experimental results are very promising. Aiming to choose a more suitable server to handle dynamically incoming tasks, our algorithm decreases the average processing time and cost by 30% and 45%, respectively, as well as the average SLA violation by 25%, when compared to existing state-of-the-art solutions.

A hybrid greedy political optimizer with fireworks algorithm for numerical and engineering optimization problems

This paper proposes a novel hybrid optimization algorithm named GPOFWA, which integrates political optimizer (PO) with fireworks algorithm (FWA) to solve numerical and engineering optimization problems. The original PO uses subgroup optimal solutions such as party leaders and constituency winners to guide the movement of the search agent. However, the number of such subgroup optimal solutions is limited, which leads to insufficient global exploration capabilities of PO. In addition, the recent past-based position updating strategy (RPPUS) of PO lacks effective verification of the updated candidate solutions, which reduces the convergence speed of the algorithm. The proposed hybrid algorithm uses the spark explosion mechanism in FWA to perform explosion spark and Gauss explosion spark operations on the subgroup optimal solutions (party leader and constituency winner) respectively based on the greedy strategy, which optimizes the subgroup optimal solution and enhances the exploitative ability of the algorithm. Moreover, Gaussian explosion sparks are also used to correct the candidate solutions after RPPUS, which makes up for the shortcomings of the original PO. In addition, a new subgroup optimal solution called the Converged Mobile Center (CMC) based on two-way consideration is designed to guide the movement of search agents and maintain the population diversity. We test the presented hybrid algorithm on 30 well-known benchmark functions, CEC2019 benchmark functions and three engineering optimization problems. The experimental results show that GPOFWA is superior to many statE−of-thE−art methods in terms of the quality of the resulting solution.

An efficient algorithm for task allocation with the budget constraint

This paper studies a heterogeneous task allocation problem with the budget constraint. Existing works on task allocation mainly tackle this well-known NP-hard problem from an optimisation perspective. They have not been able to cater to the extra needs of scalability and robustness in large-scale systems. Furthermore, some general allocation mechanisms do not consider system budget and agent cost. Thus, they cannot guarantee to obtain valid solutions when the budget is constrained. This paper models the task allocation problem as a game whose players are the agents to be assigned to the teams working on the tasks, and align the task allocation objective (i.e., system optimality) with the game-theoretic solution concept of Nash equilibrium. Based on this formulation, a novel algorithm, called CF, is proposed in this paper. CF searches for a valid Nash equilibrium solution using a greedy strategy that aims to improve system utility while takes into consideration of the overall system budget constraint. CF is a scalable, anytime, and monotonic algorithm, which in turn, makes it robust for the deployment in large-scale systems. CF can also be used as a local search algorithm for improving the quality of any existing valid allocation solution. Comprehensive empirical studies have been carried out in this paper to demonstrate that CF is effective in all budget states and achieves a solution quality better than the state-of-the-art algorithms.

An Efficient Improved Greedy Harris Hawks Optimizer and Its Application to Feature Selection.

To overcome the lack of flexibility of Harris Hawks Optimization (HHO) in switching between exploration and exploitation, and the low efficiency of its exploitation phase, an efficient improved greedy Harris Hawks Optimizer (IGHHO) is proposed and applied to the feature selection (FS) problem. IGHHO uses a new transformation strategy that enables flexible switching between search and development, enabling it to jump out of local optima. We replace the original HHO exploitation process with improved differential perturbation and a greedy strategy to improve its global search capability. We tested it in experiments against seven algorithms using single-peaked, multi-peaked, hybrid, and composite CEC2017 benchmark functions, and IGHHO outperformed them on optimization problems with different feature functions. We propose new objective functions for the problem of data imbalance in FS and apply IGHHO to it. IGHHO outperformed comparison algorithms in terms of classification accuracy and feature subset length. The results show that IGHHO applies not only to global optimization of different feature functions but also to practical optimization problems.

A Novel Prediction-Based Temporal Graph Routing Algorithm for Software-Defined Vehicular Networks

Temporal information is critical for routing computation in the vehicular network. It plays a vital role in the vehicular network. Till now, most existing routing schemes in vehicular networks consider the networks as a sequence of static graphs. We need to find an appropriate method to process temporal information into routing computation. Thus, in this paper, we propose a routing algorithm based on the Hidden Markov Model (HMM) and temporal graph, namely, Prediction-Based Temporal Graph Routing Algorithm (PT-GROUT). This new algorithm considers the vehicular network as a temporal graph, in which each data transmission as an edge has its specific temporal information. To better capture the temporal information, we select Software-Defined Vehicular Network (SDVN) as our network architecture, which is a preferred architecture for processing the temporal graph regarding the vehicular network since all vehicle statuses can be easily managed. To compute the future routing path accurately and efficiently, the future temporal graph is predicted by applying HMM, in which we model the current vehicular network with dynamic programming and greedy strategies. With the temporal information and reasonable setting of HMM, PT-GROUT can better evaluate the vehicular network and discover the evolution of the internal structure of the network. The optimal routing path can be achieved more efficiently. The simulation results demonstrate that PT-GROUT can substantially improve the computation efficiency and reduce packet loss and delivery delay compared with its counterparts.

Rapid localization of radioactive leaks based on hybrid adaptive grey wolf algorithm

Radioactive source localization algorithms have been widely used in the detection of nuclear accident areas. But some shortcomings, such as complex algorithm structure, slow localization speed and poor accuracy, were obviously performed to affect mobile robot locating autonomously. In this paper, a potential alternative method was investigated to be a new usage of locating leaks, just via specifying the change of exposure rate. In this model, several key factors, such as gamma ray attenuation, scattering factor, travel angle guide, spatial discretization, etc., were taken into consideration, to demonstrate the effectiveness of the algorithm, which is appropriated in unknown areas of the radioactive waste repository. Since there are three factors with different contribution, such as position, quantity of the source and gamma ray energy, which considered to demonstrate its impact on success. So, a hybrid adaptive grey wolf algorithm (HAGWO) has been adopted and implemented to develop a novel rapid method of radioactive leak location. Three aspects, including the good point set initialization in population size, balanced convergence function, and self-adaptive greedy strategy for population update, were optimized and merged into the locating model. To investigate the effectiveness of the algorithm, results of HAGWO are compared with grey wolf algorithm (GWO), good point set initialization strategy GWO(GGWO) and adaptive head wolf strategy GWO (ALGWO) in convergence speed, accuracy, stability and positioning error of single and double leak points. It is observed that convergence speed is increased by 37.93 ± 2% at the highest; the convergence accuracy is increased by 92.42 ± 2% at the most; the stability is improved by 30% ∼ 50%. The positioning error of single leak point is within 1.08%, and the positioning error of double leak point is less than 8.90%. Besides, compared with GWO, GGWO and ALGWO, the single-point accuracy is improved by 1.36 percentage points (to GWO), and the double-point accuracy is improved by 40.35 percentage points (to ALGWO) at most. It is observed that HAGWO performs the best in locating leaks, with a faster convergence, stronger stability and more accuracy.

Parametric model order reduction for acoustic boundary element method systems through a multiparameter Krylov subspaces recycling strategy

AbstractThe recently introduced framework enabling model order reduction (MOR) for systems arising within the acoustic boundary element method (BEM), allows for fast frequency sweeps to obtain the detailed response of an acoustic system. Nevertheless, in many cases it is desirable to include additional parameters in the MOR scheme to facilitate iterations among different configurations of a specific design. In that context, this work proposes a multiparameter Krylov subspaces recycling scheme, based on the algorithms proposed in Reference 23 for a single parameter, aiming at the parametric MOR of acoustic BEM systems. The proposed scheme allows to include multiple parameters along with the non‐affine wavenumber kernel dependency and thus facilitates the fast solution of parametric acoustic systems. The article distinguishes among three different parametrizations of BEM systems: (i) a right‐hand side parametrization, (ii) an affine, and (iii) a non‐affine parametrization of the system matrix. The two former cases allow for the construction of a cheap residual error estimator and thus facilitate the deployment of a greedy sampling strategy. This work proposes the employment of such a greedy strategy in the context of Krylov subspaces recycling, which combined with the automatic Krylov subspaces recycling (AKR) algorithm, enables the construction of a global reduction basis incorporating such parametric variations. On the contrary, since in case of non‐affine parametrizations a cheap residual error estimator is not directly available, a multiparameter AKR algorithm is deployed to ensure the predefined residual level. The performance of the proposed methods is benchmarked against a reduced basis method‐type approach, which follows the same assumptions as the AKR for the case of non‐affine systems. The potential of the algorithms is demonstrated on academic BEM examples including source position, material, and shape parametrizations and significant reductions in the sampling required for the construction of the respective reduction bases are reported.

RLIM: representation learning method for influence maximization in social networks

A core issue in influence propagation is influence maximization, which aims to find a set of nodes that maximize influence spread by adopting a specific information diffusion model. The limitation of the existing algorithms is they excessively depend on the information diffusion model and randomly set the propagation ability. Therefore, most algorithms are difficult to apply in large-scale social networks. A method to solve the problem is neural network architecture. Based on the architecture, the paper proposes Representation Learning for Influence Maximization (RLIM) algorithm. The algorithm consists of three main parts: the influence cascade of each source node is the premise; the multi-task deep learning neural network to classify influenced nodes and predict propagation ability is the fundamental bridge; the prediction model applying to the influence maximization problem by the greedy strategy is the purpose. Furthermore, the experimental results show that the RLIM algorithm has greater influence spread than the state-of-the-art algorithms in different online social network datasets, and the information diffusion is more accurate.

Complexity of minimum uplink power scheduling with delay bound for Backbone-assisted PD-NOMA wireless networks

Although it has high spectrum utilization ratio, the technique of Power-Domain Non-orthogonal Multiplexing Access (PD-NOMA) has a fatal disadvantage of high power consumptions. Backbone-Assisted PD-NOMA provides a feasible way to lowering power consumptions, since scheduling flexibilities are further enhanced by sharing both decoding capabilities of wireline-connected multiple sinks and the geographical diversity of the sinks. In this paper, we study the problem of minimizing uplink power consumption sum for backbone-assisted PD-NOMA wireless networks, under the constraint of given uplink delay bound. We formulate the problem, and prove that it is NP-Complete by presenting an original reduction from the classic problem of partition into triangles, which is known to be NP-Complete. We further propose a low-complexity heuristic algorithm based on the greedy strategy that as many user equipments as possible are simultaneously scheduled in one slot, which is also the optimal for one sink scenario. The analysis based on experimental results shows that the power consumption sum achieved by the heuristic algorithm will exponentially decrease with linearly-relaxed delay bound, and besides, it is virtually very close to the optimum.

A greedy-based hybrid trajectory optimization method for the “Dyson Ring” building problem

The method used and results found by the team “ASTL-NUAA” from NUAA for the problem of GTOC 11 are presented in the paper. The problem is mainly decomposed into three parts: multiple targets flyby sequence optimization for the Mother Ships, station-building database construction problem of asteroid transfer arcs, and station-building mission planning. Therefore, a three-step optimization framework is proposed to solve the problem. After analyzing the data of all the asteroids and selecting according to the orbital elements and mass of the asteroids, an asteroid candidate set RS1 is chosen as candidate targets for the Mother Ships. A two-level optimization algorithm based on a genetic principle is applied to solve the two-impulse asteroid flyby problem and rapidly determine the asteroid sequence of each Mother Ship. Subsequently, a method of filtering input data for the time-optimal rendezvous problem by the optimal flight time and the corresponding optimal relative phase is proposed to construct a station-building database with less computation burden. The optimal relative phase is obtained by solving free final-phase continuous low-thrust time-optimal problem. The station-building database is composed of the results of continuous low-thrust time-optimal rendezvous problems. At last, a branch-and-bound algorithm based on the greedy strategy is adopted to rapidly get the result by maximizing the minimal mass among the stations. The final score of our solution is 4315.6663, which is obtained after the competition.

On prisoner’s dilemma game with psychological bias and memory learning

Since we live and cooperate in a variable and complex network of relationships, the intricate interactions between individuals emerge amazing complex population dynamics. Combining self-based memory learning, neighbors-based learning and ϵ−greedy strategy selection, we here propose a prisoner’s dilemma game model with diversified behavior change. Results show that individuals’ cooperation behavior could be restrained while the underlying contact network structure with possessing a high average connection. In the case of a small value of psychological bias factor, the ϵ−greedy strategy selection way could just be conducive to better stimulate the individuals’ cooperation behavior in a homogeneity network. However, in the case of a large value of psychological bias factor, ϵ−greedy strategy selection way can enhance the propensity of cooperation regardless of the contact network structure. More comparative analysis of individuals’ gain in a heterogeneity network and a homogeneity network, we find that one’s average gain in former network is significantly greater than that in the latter network. In addition, an optimal value of psychological bias factor exists which can realize benefits maximization in the population while individuals tend to choose strategies at random. Finally, we show that no matter what strategy a player adopted, his average gain shows a significant linear relation with his connection. We try to provide some schemes that can effectively promote the mutual cooperation between people, and offer some reasonable research perspective for the study of evolutionary game related to individuals’ rational.

A Two-Way Update Resource Allocation Strategy in Mobile Edge Computing

Existing studies of mobile edge computing resource allocation strategy problem merely optimize delay and energy cost, seldom considering the benefit of edge servers. So, a two-way update strategy based on game theory (TUSGT) was proposed. TUSGT converts the task competition relationship among edge servers into a noncollaborative game issue and adopts a potential game-based joint optimization strategy, allowing edge servers to determine task selection preference by maximizing their own benefit as the objective. At mobile device side, the EWA algorithm of online learning was used to update parameters, exerting impact on edge server’s task selection preference from a global perspective and improving overall deadline hit rate. The simulation test results show that, compared to BGTA, MILP, greedy strategy, random strategy, and ideal strategy, TUSGT promotes deadline hit rate by up to 30% and increases edge server’s average benefit by up to 65%.

Block Kaczmarz–Motzkin Method via Mean Shift Clustering

Solving systems of linear equations is a fundamental problem in mathematics. Combining mean shift clustering (MS) with greedy techniques, a novel block version of the Kaczmarz–Motzkin method (BKMS), where the blocks are predetermined by MS clustering, is proposed in this paper. Using a greedy strategy, which collects the row indices with the almost maximum distance of the linear subsystem per iteration, can be considered an efficient extension of the sampling Kaczmarz–Motzkin algorithm (SKM). The new method linearly converges to the least-norm solution when the system is consistent. Several examples show that the BKMS algorithm is more efficient compared with other methods (for example, RK, Motzkin, GRK, SKM, RBK, and GRBK).

Adaptive procedures for discriminating between arbitrary tensor-product quantum states

Discriminating between quantum states is a fundamental task in quantum information theory. Given two quantum states ${\ensuremath{\rho}}_{+}$ and ${\ensuremath{\rho}}_{\ensuremath{-}}$, the Helstrom measurement distinguishes between them with minimal probability of error. However, finding and experimentally implementing the Helstrom measurement can be challenging for quantum states on many qubits. Due to this difficulty, there is great interest in identifying local measurement schemes which are close to optimal. In the first part of this work, we generalize previous work by Acin et al. [Phys. Rev. A 71, 032338 (2005)] and show that a locally greedy scheme using Bayesian updating can optimally distinguish between any two states that can be written as a tensor product of arbitrary pure states. We then show that the same algorithm cannot distinguish tensor products of mixed states with vanishing error probability (even in a large subsystem limit), and introduce a modified locally greedy scheme with strictly better performance. In the second part of this work, we compare these simple local schemes with a general dynamic programming approach which finds both the optimal series of local measurements as well as the optimal order in which subsystems are measured.

Cycle Time and Human Fatigue Minimization for Human-Robot Collaborative Assembly Cell

Human fatigue, which is one of the main causes of efficiency decline and health damage, cannot be overlooked in the task scheduling of HRC that is becoming one of the latest frontiers of manufacturing. In this letter, we proposed a task scheduling model that integrated micro-breaks within job-cycles to provide recovery from fatigue accumulation by taking advantage of the characteristic of HRC. Furthermore, an improved Chemical Reaction Optimization (CRO) algorithm is developed to solve the trade-off between cycle time and human fatigue. Greedy strategy is applied in the global and local search reaction of CRO to solve the multi-objective problem which includes two conflicting goals of cycle time and fatigue minimization. The proposed model and algorithm are demonstrated on assembly cases inspired by an industry application. The results from the case study suggest that the proposed model outperforms the comparison model. Finally, computational results have demonstrated that the superiority of the proposed algorithm is proved by comparing with genetic algorithm (GA), imperialist competitive algorithm (ICA), and standard CRO.

Dynamic Virtual Topology Aided Networking and Routing for Aeronautical Ad-Hoc Networks

Aeronautical Ad-hoc Networks (AANETs) have been proposed as the promising complement to terrestrial networks for promoting the global interconnection to provide in-flight network service, emergency communication, vessel traffic service, etc. However, the large network scale of AANETs may induce severe synchronization overhead when the traditional topology-based networking algorithms are adopted. Moreover, the high-dynamic topology and changeable flight routes make the existing position-based routing algorithms suffer loop routing and forwarding failure. Motivated by these problems, this paper aims at developing efficient and low-cost networking and routing algorithms relying on the concept of dynamic virtual topology which organizes the disordered topology of AANETs into a structural and simplified one. The basic idea is that each connected aircraft is assigned with a unique and sequentially increased Virtual Identifier (VID) and thus all the connected aircrafts are organized into a virtual cluster consisting of one trunk and several branches. An event-driven synchronization mechanism is leveraged for maintaining the virtual topology as well as relieving the communication burden imposed by periodical broadcasting. By jointly considering the geographic locations and the virtual locations of aircrafts, we formulate the routing problem in AANETs as a weighted distance minimization problem, and further propose a novel routing algorithm, namely Trunk-Branch Cooperation aided Routing (TBCR) algorithm. Specifically, TBCR employs the geographic greedy forwarding strategy for enhancing its flexibility and boosts the routing efficiency by adopting the loop-free virtual topology based local forwarding. For extending the networking and routing algorithms to the global range, a multi-domain routing solution is also provided. Extensive experimental results show that the proposed Virtual Topology based Networking (VTN) cooperated with TBCR can reduce at least 30% average end-to-end transmission delay in large-scale AANETs and provide more than 90% lower synchronization overhead than the existing solutions.

Energy Efficient Video Decoding for VVC Using a Greedy Strategy-Based Design Space Exploration

IP traffic has increased significantly in recent years, and it is expected that this progress will continue. Recent studies report that the viewing of online video content accounts for a share of 1% of the global greenhouse gas emissions. To reduce the data traffic of video streaming, the new standard Versatile Video Coding (VVC) has been finalized in 2020. In this paper, the energy efficiency of two different VVC decoders is analyzed in detail. Furthermore, we propose a design space exploration that uses an algorithm based on a greedy strategy to derive coding tool profiles that optimize the energy demand of the decoder. We show that the algorithm derives optimal coding tool profiles for a subset of coding tools. Additionally, we propose profiles that reduce the energy demand of VVC decoders and provide energy savings of more than 50% for sequences with 4K resolution. Thereby, we will also show that the proposed profiles can have a lower decoding energy demand than comparable HEVC-encoded bit streams while also having a significantly lower bit rate.

Approximate convex decomposition for 3D meshes with collision-aware concavity and tree search

Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically designed for convex shapes and has been widely used in game engines, physics simulations, and animation. While prior works can capture the global structure of input shapes, they may fail to preserve fine-grained details (e.g., filling a toaster's slots), which are critical for retaining the functionality of objects in interactive environments. In this paper, we propose a novel method that addresses the limitations of existing approaches from three perspectives: (a) We introduce a novel collision-aware concavity metric that examines the distance between a shape and its convex hull from both the boundary and the interior. The proposed concavity preserves collision conditions and is more robust to detect various approximation errors. (b) We decompose shapes by directly cutting meshes with 3D planes. It ensures generated convex hulls are intersection-free and avoids voxelization errors. (c) Instead of using a one-step greedy strategy, we propose employing a multi-step tree search to determine the cutting planes, which leads to a globally better solution and avoids unnecessary cuttings. Through extensive evaluation on a large-scale articulated object dataset, we show that our method generates decompositions closer to the original shape with fewer components. It thus supports delicate and efficient object interaction in downstream applications.

Genetic Algorithm and Greedy Strategy-Based Multi-Mission-Point Route Planning for Heavy-Duty Semi-Rigid Airship.

The large volume and windward area of the heavy-duty semi-rigid airship (HSA) result in a large turning radius when the HSA passes through every mission point. In this study, a multi-mission-point route planning method for HSA based on the genetic algorithm and greedy strategy is proposed to direct the HSA maneuver through every mission point along the optimal route. Firstly, according to the minimum flight speed and the maximum turning slope angle of the HSA during turning, the minimum turning radius of the HSA near each mission point is determined. Secondly, the genetic algorithm is used to determine the optimal flight sequence of the HSA from the take-off point through all the mission points to the landing point. Thirdly, based on the optimal flight sequence, the shortest route between every two adjacent mission points is obtained by using the route planning method based on the greedy strategy. By determining the optimal flight sequence and the shortest route, the optimal route for the HSA to pass through all mission points can be obtained. The experimental results show that the method proposed in this study can generate the optimal route with various conditions of the mission points using simulation studies. This method reduces the total voyage distance of the optimal route by 18.60% on average and improves the flight efficiency of the HSA.