Greedy Algorithm Research Articles

Resource Assignment Algorithms for Autonomous Mobile Robots with Task Offloading

This paper deals with the optimization of the operational efficiency of a fleet of mobile robots, assigned with delivery-like missions in complex outdoor scenarios. The robots, due to limited onboard computation resources, need to offload some complex computing tasks to an edge/cloud server, requiring artificial intelligence and high computation loads. The mobile robots also need reliable and efficient radio communication with the network hosting edge/cloud servers. The resource assignment aims at minimizing the total latency and delay caused by the use of radio links and computation nodes. This minimization is a nonlinear integer programming problem, with high complexity. In this paper, we present reduced-complexity algorithms that allow to jointly optimize the available radio and computation resources. The original problem is reformulated and simplified, so that it can be solved by also selfish and greedy algorithms. For comparison purposes, a genetic algorithm (GA) is used as the baseline for the proposed optimization techniques. Simulation results in several scenarios show that the proposed sequential minimization (SM) algorithm achieves an almost optimal solution with significantly reduced complexity with respect to GA.

Application of Graph Theory and Variants of Greedy Graph Coloring Algorithms for Optimization of Distributed Peer-to-Peer Blockchain Networks

This paper investigates the application of graph theory and variants of greedy graph coloring algorithms for the optimization of distributed peer-to-peer networks, with a special focus on private blockchain networks. The graph coloring problem, as an NP-hard problem, presents a challenge in determining the minimum number of colors needed to efficiently allocate resources within the network. The paper deals with the influence of different graph density, i.e., the number of links, on the efficiency of greedy algorithms such as DSATUR, Descending, and Ascending. Experimental results show that increasing the number of links in the network contributes to a more uniform distribution of colors and increases the resistance of the network, whereby the DSATUR algorithm achieves the most uniform color saturation. The optimal configuration for a 100-node network has been identified at around 2000 to 2500 links, which achieves stability without excessive redundancy. These results are applied in the context of a private blockchain network that uses optimal connectivity to achieve high resilience and efficient resource allocation. The research findings suggest that adapting network configuration using greedy algorithms can contribute to the optimization of distributed systems, making them more stable and resilient to loads.

A Two-Stage Greedy Genetic Algorithm for Simultaneous Delivery and Monitoring Tasks with Time Windows

With advancements in drone driving technology, drones can now collaborate with trucks to execute tasks. However, existing drone–truck collaborative systems are limited to single-task objectives and lack efficiency in large-scale multi-task scenarios. Enhancing the efficiency of drone–truck cooperative systems necessitates the coordination of drone and truck paths to execute multiple tasks simultaneously. Addressing time conflicts in such scenarios remains a significant challenge. This study proposes an innovative drone–truck collaborative system enabling the concurrent execution of delivery and monitoring tasks within specified time windows. To minimize travel costs, a two-stage greedy genetic algorithm (TGGA) is introduced. The methodology initially separates tasks, processes them in batches, and subsequently recombines them to determine the final route. The simulation results indicate that TGGA outperforms existing heuristic algorithms.

A robust single-machine scheduling problem with scenario-dependent processing times and release dates

Many uncertainties arise during the manufacturing process, such as changes in the working environment, traffic transportation delays, machine breakdowns, and worker performance instabilities. These factors can cause job processing times and ready times to change. In this study, we address a scheduling model for a single machine where both job release dates and processing times are scenario dependent. The objective is to minimize the total completion time across the worst-case scenarios. Even without the uncertainty factor, this problem is NP-hard. To solve it, we derive several properties and a lower bound used in a branch-and-bound method to find an optimal solution. We propose nine heuristics based on a linear combination of scenario-dependent processing times and release times for approximate solutions. Additionally, we offer an iterated greedy population-based algorithm that efficiently solves this problem by taking advantage of the diversity of solutions. We evaluate the performance of the proposed nine heuristics and the iterated greedy population-based algorithm.

Approximation algorithm of maximizing non-submodular functions under non-submodular constraint

Nowadays, maximizing the non-negative and non-submodular objective functions under Knapsack constraint or Cardinality constraint is deeply researched. Nevertheless, few studies study the objective functions with non-submodularity under the non-submodular constraint. And there are many practical applications of the situations, such as Epidemic transmission, and Sensor Placement and Feature Selection problem. In this paper, we study the maximization of the non-submodular objective functions under the non-submodular constraint. Based on the non-submodular constraint, we discuss the maximization of the objective functions with some specific properties, which includes the property of negative, and then, we obtain the corresponding approximate ratios by the greedy algorithm. What is more, these approximate ratios could be improved when the constraint becomes tight.

An optimized approach for container deployment driven by a two-stage load balancing mechanism.

Lightweight container technology has emerged as a fundamental component of cloud-native computing, with the deployment of containers and the balancing of loads on virtual machines representing significant challenges. This paper presents an optimization strategy for container deployment that consists of two stages: coarse-grained and fine-grained load balancing. In the initial stage, a greedy algorithm is employed for coarse-grained deployment, facilitating the distribution of container services across virtual machines in a balanced manner based on resource requests. The subsequent stage utilizes a genetic algorithm for fine-grained resource allocation, ensuring an equitable distribution of resources to each container service on a single virtual machine. This two-stage optimization enhances load balancing and resource utilization throughout the system. Empirical results indicate that this approach is more efficient and adaptable in comparison to the Grey Wolf Optimization (GWO) Algorithm, the Simulated Annealing (SA) Algorithm, and the GWO-SA Algorithm, significantly improving both resource utilization and load balancing performance on virtual machines.

Randomized greedy methods for weak submodular sensor selection with robustness considerations

We study a pair of budget- and performance-constrained weak submodular maximization problems. For computational efficiency, we explore the use of stochastic greedy algorithms which limit the search space via random sampling instead of the standard greedy procedure which explores the entire feasible search space. We propose a pair of stochastic greedy algorithms, namely, Modified Randomized Greedy (MRG) and Dual Randomized Greedy (DRG) to approximately solve the budget- and performance-constrained problems, respectively. For both algorithms, we derive approximation guarantees that hold with high probability. We then examine the use of DRG in robust optimization problems wherein the objective is to maximize the worst-case of a number of weak submodular objectives and propose the Randomized Weak Submodular Saturation Algorithm (Random-WSSA). We further derive a high-probability guarantee for when Random-WSSA successfully constructs a robust solution. Finally, we showcase the effectiveness of these algorithms in a variety of relevant uses within the context of Earth-observing LEO constellations which estimate atmospheric weather conditions and provide Earth coverage.

Error bounds of Approximate Weak Rescaled Pure Greedy Algorithms

We study the greedy algorithms for [Formula: see text]-term approximation. We propose a modification of the Weak Rescaled Pure Greedy Algorithm (WRPGA) — Approximate Weak Rescaled Pure Greedy Algorithm (AWRPGA) — with respect to a dictionary of a Banach space [Formula: see text]. By using a geometric property of the unit sphere of [Formula: see text], we obtain a general error estimate in terms of some [Formula: see text]-functional. This estimate implies the convergence condition and convergence rate of the AWRPGA. Furthermore, we obtain the corresponding error estimate for the Vector Approximate Weak Rescaled Pure Greedy Algorithm (VAWRPGA). We show that the AWRPGA (VAWRPGA) performs as well as the WRPGA (VWRPGA) when the noise amplitude changes relatively little. Finally, by using the wavelet bases and trigonometric system of Lebesgue spaces, we show that the convergence rate of the AWRPGA is optimal.

Automatic optimisation layout design approach for lightweight and energy-saving additive manufactured hydraulic manifolds

ABSTRACT Additive manufacturing provides advanced technology for producing lightweight and energy-saving hydraulic manifolds. However, current design of additive manufactured hydraulic manifolds relies on manual experience. This study develops a multi-objective optimisation layout design approach to automatically achieve the design of lightweight and energy-saving hydraulic manifolds. The design approach has three parts: (1) a flattened design strategy is introduced to minimise the design difficulty of hydraulic manifolds; (2) a multi-objective performance evaluation function of layout design approach is proposed to establish the relationship between manifolds mass, pressure loss, volume and its layout; (3) a greedy strategy optimisation algorithm is used to automatically find out a global optimum manifold layout based on multi-objective performance evaluation function. Finally, the design approach is applied to optimise a traditional hydraulic manifold. The weight, volume, and pressure loss of the optimised additive manufactured one are reduced by 84%, 44%, and 40%, illustrating the effectiveness of design approach.

A Greedy Tabu Dual Heuristic algorithm for the cyclic pickup and delivery problem with 3D loading constraints

The optimization of auto parts supply chain logistics plays a decisive role in the development of the automotive industry. To reduce logistics costs and improve transportation efficiency, this paper addresses the joint optimization problem of multi-vehicle pickup and delivery transportation paths under time window constraints, coupled with the three-dimensional loading of goods. The model considers mixed time windows, three-dimensional loading constraints, cyclic pickup and delivery paths, varying vehicle loads and volumes, flow balance, and time window constraints. Evaluation rules for the three-dimensional loading test of goods are also set, resulting in constructing a comprehensive optimization model for the inbound logistics of auto parts and components. In this study, a Greedy-Tabu Dual-Heuristic algorithm is proposed, which integrates an Improved Greedy Algorithm with an Enhanced Tabu Search Algorithm based on the -sampling strategy. The overall problem-solving process for the Improved Greedy Algorithm and the Tabu Search Algorithm is outlined. The superiority, efficiency, and stability of the improved algorithm are verified by solving cases of various sizes and analyzing the algorithm’s results before and after improvement. A case study involving the third-party logistics company R Enterprise compares the pickup and delivery-separated Milk-Run mode with the simultaneous delivery and pickup Milk-Run mode. The proposed method shows a 26.67% reduction in total distance traveled and a 46.60% decrease in waiting time compared to the traditional Milk-Run approach. Additionally, when evaluated against the standard 3D loading inspection method, the proposed approach improves average vehicle load utilization by 17% and vehicle volume utilization by 15%. These findings verify the applicability and superiority of the proposed algorithms and models in practical scenarios.

Crop Planting Strategy based on Greedy Algorithm and Monte Carlo Simulation

Crop cultivation is a complex process influenced by a multitude of environmental and market factors. To navigate these complexities and enhance profitability, this paper presents an innovative crop planting strategy. The strategy employs a combination of a greedy algorithm and Monte Carlo simulation techniques to optimize the allocation of crop cultivation. By analyzing historical planting and sales data, the proposed method aims to predict and maximize overall profitability. This approach not only considers immediate conditions but also incorporates a probabilistic assessment of various outcomes, providing a robust framework for decision-making in agricultural planning.

Optimized Bayesian Matching Pursuit for Joint Channel Estimation and Impulse Noise Mitigation

Orthogonal frequency division multiplexing (OFDM) is adopted in most wireless communication systems, and the performance of OFDM is affected by impulse noise (IN). Better channel estimation (CE) performance is required to detect the channel information on the receiving side. The OFDM system is considered with the number of subcarriers carrying the data and pilot symbols. In the OFDM modulator, the symbols of the frequency domain are transformed into the signals of the time domain using inverse discrete Fourier transformation (IDFT). Effective impulsive noise mitigation is crucial for improving the effectiveness of OFDM communication systems, and it improves the signal-to-noise ratio (SNR) at the receiver. A cyclic prefix is then appended before transmission through the channel. In the receiver noise, the effect of IN is mitigated jointly with CE using the Bayesian matching pursuit (BMP) and Moth-flame algorithm (MFA). In this approach, the IN and channel information is considered as a sparse vector. Here, the data symbols used are considered an unknown parameter. The approach incorporating all subcarriers has a lower mean square error (MSE) of IN estimate for impulsive noise reduction. The MFA algorithm is used to optimize the sensor matrix in BMP. The sparsity of the channel and the impulse response are observed in the time domain to represent the channel and IN together. It exactly recovers the sparse signal for finding the convex objectives of the sparse minimizer, and the sparse solution is obtained with fixed point updates. The proposed BMP algorithm improves the CE by explicitly considering the existence of IN. The BMP is a greedy algorithm that selects the most correlated residuals at each column. Under mutual incoherence, it recovers the signal with a higher probability. The simulated outcomes proved that the proposed CE and noise mitigation model achieved better performance based on the bit error rate (BER), throughput and MSE.

On the convergence of generalized kernel-based interpolation by greedy data selection algorithms

We analyze the convergence of generalized kernel-based interpolation methods. This is done under minimalistic assumptions on both the kernel and the target function. On these grounds, we further prove convergence of popular greedy data selection algorithms for totally bounded sets of sampling functionals. Supporting numerical results concerning computerized tomography are provided for illustration.

Layout Optimization for a Large-Scale Grid-Connected Solar Power Plant

A solar power plant provides green electricity to the public via a power grid. As governments worldwide have pledged to reduce carbon emissions and achieve carbon neutrality, large-scale grid-connected solar power plants are booming. Developing such a plant requires significant investment, a large proportion of which covers construction costs. Such costs, together with the energy yield, critically depend on the plant’s layout. The layout planning of a solar power plant involves a series of complex optimization problems such as district partitioning, photovoltaic (PV) component location, and cable routing problems in a solar power plant. These problems have received limited attention in the literature and are highly challenging because they involve large-scale instances, complex design principles, and complicated physical constraints. Motivated by our collaborative projects with an electrical engineering company in China, this paper specifically focuses on the integrated location and routing (ILR) problem, which involves locating service ways, inverters, combiner boxes, and routing cables to connect them. We develop exact algorithms to effectively solve the ILR problem via a decomposition framework (leading to a variant of Benders decomposition (BD)), which is proven to produce an optimal solution. We also develop an exact branch-and-cut scheme to solve each subproblem in the decomposition framework by incorporating cutting planes and separation algorithms. Our solution approach is evaluated on 50 real-world data instances via extensive numerical experiments. Compared with the manual method based on greedy heuristics used in practice, our approach reduces the total cost by approximately 20%. Our decomposition method also achieves an average gap of 0.02% between the obtained lower and upper bounds, significantly smaller than the 16.08% gap achieved with the traditional BD. History: Accepted by Alice E. Smith and David Alderson, Area Editors for Network Optimization: Algorithms & Applications. Funding: This work was partially supported by the Research Grants Council of Hong Kong [Grant 15501221], the National Natural Science Foundation Program of China [Grants 72122006, 72471100, and 72131008], Huazhong University of Science and Technology Double First-Class Funds for Humanities and Social Sciences (Digital Intelligence Decision Optimization Innovation Team), the Interdisciplinary Research Program of HUST [Grant 5003300129], and the Fundamental Research Funds for the Central Universities [Grant 2023WKFZZX101]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0223 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0223 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Joint Task Offloading and Resource Allocation in Mobile Edge Computing-Enabled Medical Vehicular Networks

In medical vehicular networks, medical vehicles can serve as efficient mobile medical service points to provide necessary and critical medical services for patients while in motion. The delay requirement is very vital for medical services to guarantee service quality and save the lives of patients. Mobile Edge Computing (MEC), as an emerging network paradigm, enables the computation extensive tasks to be offloaded to edge servers, efficiently reducing the delay and bandwidth demands. MEC technology is a promising solution to provide high-quality medical services for users in medical vehicular networks. However, task offloading and resource allocation incurs additional service delay and energy consumption, affecting the overall service performance and Quality of Experience (QoE) of users. Thus, realizing the optimal task offloading and resource allocation in MEC-enabled medical vehicular networks, to reduce task completion time and energy consumption, becomes a potential challenge. To address the challenge, we investigate the joint task offloading and resource allocation problem in MEC-enabled medical vehicular networks to improve the QoE of users. Considering the resource requirements and QoS constraint, we formulate a multi-objective optimization model, with the target of average task completion time and average energy consumption minimization. On this basis, we propose a MOEAD-based task offloading and resource allocation (IMO) algorithm to solve it. Furthermore, in order to obtain the optimal solution and speed up the algorithm convergence, we design a greedy strategy-based population initialization algorithm. The extensive simulations demonstrate that compared to existing algorithms, our proposed IMO algorithm can obtain a smaller average completion time, and achieve better tradeoff between task completion time and energy consumption.

Research on an Aerial Docking Strategy for Meta-UAVs Using Aerodynamic Data Surrogate Models

Meta-aircraft, in High-Altitude, Long-Endurance (HALE) unmanned aerial vehicle (UAV) applications, utilize a strategy of formation flying in the stratosphere and aerial docking in the troposphere to enhance flight range and gust resistance. This paper explores an aerial docking strategy for unmanned meta-aircraft using a surrogate model based on aerodynamic data. The study begins with an analysis of the aerodynamic characteristics and the establishment of a dynamic model, followed by the development of a surrogate model using the vortex lattice method and a BP neural network. This model accurately simulates aerodynamic changes near the wingtip. Optimization of the docking process, focusing on impulse and moment of impulse, is achieved using a greedy algorithm. The results show a reduction in drag impulse and rolling moment by 10.89% and 15.76%, respectively, thereby easing the burden on the control system of UAVs.

Multi-Armed Bandit Approaches for Location Planning with Dynamic Relief Supplies Allocation Under Disaster Uncertainty

Natural disasters (e.g., floods, earthquakes) significantly impact citizens, economies, and the environment worldwide. Due to their sudden onset, devastating effects, and high uncertainty, it is crucial for emergency departments to take swift action to minimize losses. Among these actions, planning the locations of relief supply distribution centers and dynamically allocating supplies is paramount, as governments must prioritize citizens’ safety and basic living needs following disasters. To address this challenge, this paper develops a three-layer emergency logistics network to manage the flow of emergency materials, from warehouses to transfer stations to disaster sites. A bi-objective, multi-period stochastic integer programming model is proposed to solve the emergency location, distribution, and allocation problem under uncertainty, focusing on three key decisions: transfer station selection, upstream emergency material distribution, and downstream emergency material allocation. We introduce a multi-armed bandit algorithm, named the Geometric Greedy algorithm, to optimize transfer station planning while accounting for subsequent dynamic relief supply distribution and allocation in a stochastic environment. The new algorithm is compared with two widely used multi-armed bandit algorithms: the ϵ-Greedy algorithm and the Upper Confidence Bound (UCB) algorithm. A case study in the Futian District of Shenzhen, China, demonstrates the practicality of our model and algorithms. The results show that the Geometric Greedy algorithm excels in both computational efficiency and convergence stability. This research offers valuable guidelines for emergency departments in optimizing the layout and flow of emergency logistics networks.

Some constructions for solving routing problems using decompositions and transformations of target sets

Issues related to solving the additive problem of sequential traversal of sets with precedence restrictions and cost functions that allow dependence on the list of tasks are considered. The basic method is a broadly understood dynamic programming (DP), supplemented in the case of problems of appreciable dimension by decompositions of the family of tasks and transformation of the parameters of the original problem. Possible applications are related, in particular, to the problem of tool control in figured sheet cutting of parts on CNC machines. In this problem, an important circumstance is taking into account the precedence conditions, which have, in particular, the following meaning: in the case of a part with holes, cutting of each of the internal contours (corresponding to the holes) should precede cutting of the external contour. The quality criterion itself in this problem, as a rule, is additive. Another type of constraints concerns avoiding thermal deformations of parts. When using the approach with penalties for violating the conditions associated with effective heat dissipation during cutting, cost functions arise that allow dependence on the list of tasks completed to date. Note that in another applied problem, namely, in the problem of dismantling radiation hazardous objects, cost functions arise with dependence on the list of tasks that have not been completed at the moment (and, consequently, concern the objects that have not been dismantled). As a result, we arrive at a very general problem with precedence constraints and cost functions with dependence on the list of tasks. The decomposition applied in the case of a noticeable dimensionality with subsequent implementation of the DP requires, on the one hand, the development of clustering methods, and, on the other, the construction of an adequate structure for distributing global precedence conditions among clusters. In the theoretical part of the work, the case of two clusters is discussed, which makes it possible to cover with a single scheme a number of practically interesting problems of a range (in terms of dimensionality) type. An algorithm for constructing a composite solution is indicated, including a stage of clustering training based on a greedy algorithm. This “composite” algorithm is implemented on a PC; a computational experiment was carried out.

Dynamic thresholding algorithm with memory for linear inverse problems

Abstract The relaxed optimal $k$-thresholding pursuit (ROTP) is a recent algorithm for linear inverse problems. This algorithm is based on the optimal $k$-thresholding technique which performs vector thresholding and error metric reduction simultaneously. Although ROTP can be used to solve small to medium-sized linear inverse problems, the computational cost of this algorithm is high when solving large-scale problems. By merging the optimal $k$-thresholding technique and iterative method with memory as well as optimization with sparse search directions, we propose the so-called dynamic thresholding algorithm with memory (DTAM), which iteratively and dynamically selects vector bases to construct the problem solution. At every step, the algorithm uses more than one or all iterates generated so far to construct a new search direction, and solves only the small-sized quadratic subproblems at every iteration. Thus the computational complexity of DTAM is remarkably lower than that of ROTP-type methods.
It turns out that DTAM can locate the solution of linear inverse problems if the matrix involved satisfies the restricted isometry property. Experiments on synthetic data, audio signal reconstruction and image denoising demonstrate that the proposed algorithm performs comparably to several mainstream thresholding and greedy algorithms, and it works faster than the ROTP-type algorithms especially when the sparsity level of signal is relatively low.

Research on path smoothing optimisation based on improved RRT-Connect algorithm and third-order Bezier curve

Aiming at the deficiencies of the original RRT-Connect path planning algorithm in dealing with obstacle avoidance, planning efficiency and path smoothing in static environments, an improved path optimisation method is proposed by fusing the RRT-Connect path planning algorithm with the greedy search strategy and using a third-order Bezier curve for path smoothing. Firstly, a greedy algorithm is added to the path planning process of the original RRT-Connect algorithm to guide the search direction, so as to make the path search more goal oriented, reduce the time of path planning and improve the efficiency. Secondly, the generated paths are smoothed with third-order Bezier curves to ensure the generation of smooth paths with continuous curvature and improve the quality of the planned paths. Finally, the improved RRT-Connect smoothing optimisation algorithm is simulated with the original RRT-Connect, A* and Dijkstra algorithms in different simulation environments to check the performance of the optimised algorithm. The results show that the success rate of obstacle avoidance in planning paths of the optimised algorithms are all 100%, and compared with the original RRT-Connect algorithm, the improved RRT-Connect smoothing optimisation algorithm has an overall reduction of 12.02% in planning path length, an overall reduction of 40.22% in computation time and an overall improvement of 69.15% in path smoothness. Compared to the A* algorithm, which is based on the graph search shortest path planning algorithm and takes the shortest time, there is an overall reduction of 62.46% in computation time. The improved RRT-Connect smoothing optimisation algorithm has shorter path planning lengths, smoother paths and shortest computation time in different simulation environments. Meanwhile, the stability of the optimisation algorithm is effectively improved in different environments and different running times.