Greedy Heuristic Solution Research Articles

Joint Deployment of Sensors and Chargers in Wireless Rechargeable Sensor Networks

As a promising technology to achieve the permanent operation of battery-powered wireless sensor devices, wireless rechargeable sensor networks (WRSNs) by radio-frequency radiation have attracted considerable attention in recent years. Determining how to save the deployment cost of WRSNs has been a hot topic. Previous scholars have mainly studied the cost of deploying chargers, thus ignoring the impact of sensor deployment on the network. Therefore, we consider the new problem of joint deployment of sensors and chargers on a two-dimensional plane, i.e., deploying the minimum number of sensors and chargers used to monitor points of interest (PoIs). Considering the interaction of deployed sensors and chargers, we divide the problem into two stages, P1 and P2. P1 addresses the sensor deployment, while P2 addresses the deployment of chargers. Both P1 and P2 have proved to be NP-hard. Meanwhile, we notice that the aggregation effect of sensors can effectively reduce the number of chargers deployed; therefore, we propose a greedy heuristic approximate solution for deploying sensors by using the aggregation effect (GHDSAE). Then, a greedy heuristic (GH) solution and a particle swarm optimization (PSO) solution are proposed for P2. The time complexity of these solutions is analyzed. Finally, extensive simulation results show that the PSO solution can always reduce the number of chargers deployed based on the GHDSAE solution sensor deployment approach. Therefore, it is more cost-effective to jointly deploy sensors and chargers by using the GHDSAE solution and the PSO solution.

Bi-Objective Incentive Mechanism for Mobile Crowdsensing With Budget/Cost Constraint

In recent years, mobile crowdsensing (MCS) has been widely adopted as an efficient method for large-scale data collection. In MCS systems, insufficient participation and unstable data quality have become two crucial issues that prevent crowdsensing from further development. Thus designing a valid incentive mechanism is essentially significant. Most of the existing works on incentive mechanism design focus on single-objective optimization with various constraints. However, in the real-world crowdsensing, it is common that several objectives to be optimized exist. Furthermore, constraints on budget or cost are often seen in MCS systems as the feasibility of implementing incentive mechanism is indispensable. This paper studies a bi-objective optimization scenario of MCS to simultaneously optimize total value function and coverage function with budget/cost constraint through a set of problem transformations. Then a budget- or cost-feasible bi-objective incentive mechanism is further proposed to solve the aforementioned bi-objective optimization problem through the combination of binary search and greedy heuristic solution under budget or cost constraint, respectively. Through both rigorous theoretical analysis and extensive simulations, the obtained results demonstrate that the mechanisms achieve computation efficiency, individual rationality, truthfulness, and budget or cost feasibility, while one mechanism obtains an approximation.

Location of urban micro‐consolidation centers to reduce the social cost of last‐mile deliveries of cargo: A heuristic approach

AbstractUrban deliveries of goods have become a rising challenge due to the increase of online shopping in addition to the traditional business‐to‐business (B2B) dynamics. To maintain a satisfactory level of service, carriers must conduct delivery operations under restrictive environments, creating undesirable externalities such as congestion and pollution. Urban micro‐consolidation centers (UMCs) are defined as on‐street or off‐street spaces where all the deliveries within a certain radius are dropped and reconsolidated to be delivered by more sustainable last‐leg modes. Their main purpose is to mitigate such negative externalities. This work formulates the last‐mile delivery problem assisted by UMCs as a mixed‐integer quadratically‐constrained program and develops a greedy heuristic solution, inspired by the decomposition algorithms for large‐scale optimization. The simulation results and a case study in Manhattan, New York show how the heuristic provides reasonable results with respect to the exact solution while also shedding light on how its solution can be utilized for freight‐efficient urban design and policy planning.

An improved performance of greedy heuristic solutions for a bi-criteria mixture packaging problem of two types of items with bounded weights

An improved performance of greedy heuristic solutions for a bi-criteria mixture packaging problem of two types of items with bounded weights

Charging While Moving: Deploying Wireless Chargers for Powering Wearable Devices

With the promising technology of far-field wireless power transfer, wearable devices are able to harvest radio frequency (RF) energy from RF-based chargers and thus operate continuously. Rational planning of the quantity and positions of the chargers provide an effective way to improve the recharging efficiency and save the charger deployment budget. Existing work on RF-based charger placement mainly considers the situation where the devices are static, or adopt very simple mobility model. In this paper, we consider wireless charging service provision for wearable devices worn by users in a two-dimensional area, with users having a specific stay-move behavior pattern characterized by the trajectories, stay points, and stay time distribution. Based on this mobility pattern, we formulate the problem as how to find a charger placement to minimize the charging service budget, subject to the power non-outage probability requirement of the wearable devices. We further transform this problem to several equivalent problems for easier tractability and prove that it is NP-complete. Both greedy heuristic and particle swarm optimization (PSO) based solutions are proposed to solve the problem with certain approximation ratio. Finally, performances of the proposed solutions are compared with exhaustive search and existing point provisioning algorithm through extensive simulations. Simulation results show that both greedy heuristic and PSO-based solutions outperform the baseline algorithms, while PSO-based solution requires least number of chargers and thus is the most cost-effective.

A Dynamic Placement Mechanism of Service Function Chaining Based on Software-defined Networking

To cope with the explosive growth of Internet services, Service Function Chaining (SFC) based on Software-defined Networking (SDN) is an emerging and promising technology that has been suggested to meet this challenge. Determining the placement of Virtual Network Functions (VNFs) and routing paths that optimize the network utilization and resource consumption is a challenging problem, particularly without violating service level agreements (SLAs). This problem is called the optimal SFC placement problem and an Integer Linear Programming (ILP) formulation is provided. A greedy heuristic solution is also provided based on an improved two-step mapping algorithm. The obtained experimental results show that the proposed algorithm can automatically place VNFs at the optimal locations and find the optimal routing paths for each online request. This algorithm can increase the average request acceptance rate by about 17.6% and provide more than 20-fold reduction of the computational complexity compared to the Greedy algorithm. The feasibility of this approach is demonstrated via NetFPGA-10G prototype implementation.

A greedy heuristic for shift minimization personnel task scheduling problem

Shift Minimization Personnel Task Scheduling Problem (SMPTSP) is assigning a given set of predetermined tasks (with known start and finish times) to a minimum number of heterogeneous workers with predetermined shifts. Each task can be performed only by a specific subset of workers. Every task must be assigned to a worker. A worker cannot perform more than one task at a time, and tasks cannot be pre-empted. SMPTSP is NP-hard, but there is practical interest in solving very large instances of it in ground crew scheduling of a large airline in a large airport. Recently, there have been a few papers reporting various solution methods for large instances of SMPTSP. However, solving very large instances of SMPTSP remains a challenge. In this paper, we propose a novel greedy heuristic solution method for SMPTSP. A reduced problem is solved iteratively by selecting the best possible assignment of tasks to one worker. We have tested the Greedy heuristic method on 3 sets of available large test problems. The results show that the heuristic method performs well relative to the current solution methods, and has the added advantage of being able to solve very large instances fast.

Reputation-Aware, Trajectory-Based Recruitment of Smart Vehicles for Public Sensing

With the abundant on-board resources in smart vehicles, they have become major candidates for providing ubiquitous services, including public sensing. One of the challenges facing such ubiquitous utilization is the recruitment of the participating vehicles. In this paper, we present the reputation-aware, trajectory-based recruitment (RTR) framework that handles recruitment of vehicles for public sensing. The framework considers the spatiotemporal availability of participants along with their reputation to select vehicles that achieve desired coverage of an area of interest within a budget cap. The framework consists of a reputation assessment scheme, a pricing model, and a selection scheme collaborating for a main recruitment objective; maximizing coverage with minimum cost. We propose greedy heuristic solutions targeting the selection problem in real-time. The RTR framework generalizes the basic selection problem to handle some practical scenarios, including departing vehicles and varying redundancy requirements. We also propose a reputation assessment scheme and a pricing model as parts of the framework. Extensive performance evaluation of the proposed framework is conducted and the evaluation shows that the proposed greedy heuristics are able to achieve results close to previously obtained optimal benchmarks under different scenarios, and that the framework succeeds in achieving high levels of coverage even when vehicles do not stick to their announced trajectories.

Dynamic traffic engineering for high-throughput data forwarding in wireless mesh networks

High-throughput data delivery in Wireless Mesh Networks (WMNs) is a challenging problem due to dynamic changes of link quality, interference and congestion. In this work, we first develop an optimization framework for Dynamic Traffic Engineering (O-DTE) in WMNs that aims to minimize the interference and congestion at each hop through joint power and rate control so as to achieve high-throughput data delivery. Due to NP-hardness of the O-DTE framework, we then develop a greedy heuristic alternate solution (G-DTE) that enables routers, at each hop, to select outgoing links offering higher data rates and reduced interferences. Thus, the proposed G-DTE produces near optimal results by taking multi-path data forwarding decisions in distributed fashion; it exploits single-hop neighborhood information only and thus it is scalable. The simulation results, carried out in ns-3, demonstrate that the proposed G-DTE significantly outperforms the state-of-the-art works in terms of throughput, delay, reliability and fairness performances.

Joint ground and air emergency medical services coverage models: A greedy heuristic solution approach

Aeromedical and ground ambulance services often team up in responding to trauma crashes, especially when the emergency helicopter is unable to land at the crash scene. We propose location-coverage models and a greedy heuristic for their solution to simultaneously locate ground and air ambulances, and landing zones (transfer points). We provide a coverage definition based on both response time and total service time, and consider three coverage options; only ground emergency medical services (EMS) coverage, only air EMS coverage, or joint coverage of ground and air EMS in which the patient is transferred from an ambulance into an emergency helicopter at a transfer point. To analyze this complex coverage situation we develop two sets of models, which are variations of the Location Set Covering Problem (LSCP) and the Maximal Covering Location Problem (MCLP). These models address uncertainty in spatial distribution of motor vehicle crash locations by providing coverage to a given set of both crash nodes and paths. The models also consider unavailability of ground ambulances by drawing upon concepts from backup coverage models. We illustrate our results on a case study that uses crash data from the state of New Mexico. The case study shows that crash node and path coverage percentage values decrease when ground ambulances are utilized only within their own jurisdiction.

Vertical partitioning for flash and HDD database systems

Recent advances in flash memory technology have greatly enhanced the capability of flash memory to address the I/O bottleneck problem. Flash memory has exceptional I/O performance compared to the hard disk drive (HDD). The superiority of flash memory is especially visible when dealing with random read patterns. Even though the cost of flash memory is higher than that of HDD storage, the popularity of flash memory is increasing at such a pace that it is becoming a common addition to the average computer. Recently, flash memory has been made into larger devices called solid state drives (SSDs). Although these devices can offer capacities comparable to HDDs, they are considerably more expensive per byte. Our research aims to increase the I/O performance of database systems by using a small amount of flash memory alongside HDD storage. The system uses a fully vertically partitioned storage structure where each column is stored separately on either the HDD or SSD. Our approach is to assign the columns into the SSD which will benefit the most from the characteristics of flash memory. We prove this problem is NP-complete and propose an optimal dynamic programming solution and a faster greedy heuristic solution. A system simulator has been implemented and experiments show that the overall I/O costs can be greatly reduced using only a limited amount of flash memory. The results show the greedy heuristic solution performed similarly to the more expensive dynamic programming solution for the situations tested.

Scheduling Agreeable Jobs On A Single Machine To Minimize Weighted Number Of Early And Tardy Jobs

The problem of non-preemptive (NP) scheduling of number of jobs on a single machine to minimize weighted number of early and tardy jobs where the earliest start times and latest due date are agreeable (i.e. earliest start time must increase in the same sequence as latest due dates) has been considered. The problem has been shown to be NP complete in the strong sense and finding an optimal solution appeared unlikely. Two greedy heuristic solutions were obtained, and extensive computational trials indicated that the heuristics performed better than other existing solutions. Journal of Applied Science and Technology Vol. 12 (1&2) 2007: pp. 12-17

Analysis of some greedy algorithms for the single-sink fixed-charge transportation problem

The single-sink fixed-charge transportation problem (SSFCTP) consists of finding a minimum cost flow from a number of nodes to a single sink. Beside a cost proportional to the amount shipped, the flow cost encompass a fixed charge. The SSFCTP is an important subproblem of the well-known fixed-charge transportation problem. Nevertheless, just a few methods for solving this problem have been proposed in the literature. In this paper, some greedy heuristic solutions methods for the SSFCTP are investigated. It is shown that two greedy approaches for the SSFCTP known from the literature can be arbitrarily bad, whereas an approximation algorithm proposed in the literature for the binary min-knapsack problem has a guaranteed worst case bound if adapted accordingly to the case of the SSFCTP.

Strict-product-ordering approach in the vertical product-line design problem

We consider a Vertical Product-line Design (VPD) problem for a monopolist where products are designed with quality-type attributes and customer segments exhibit an ordered pattern in the attribute part-worth structure. In this paper, we examine the appropriateness of a strict-product-ordering approach across products in designing a vertical product line. We show that the approach, although used widely in practice, is not a property of an optimal solution and can lead to an arbitrarily bad design. Furthermore, we present a sufficient condition where the strict-product-ordering approach is the property of an optimal solution in a general product line design problem. We also show that the VPD problem with a strict-product-ordering approach is computationally intractable, and develop a greedy heuristic solution procedure that exploits the problem structure. A computational study shows that the heuristic results in an average performance ratio of 98.7% compared with optimal solutions. In addition, our computational study shows that insisting on the strict-product-ordering approach results in on-average 3% less profit for the firm if it is enforced in inappropriate conditions.

First-best, second-best, and heuristic solutions in conservation reserve site selection

Previous studies which dealt with the conservation reserve site selection problem used either optimization methods, specifically linear integer programming (IP), or heuristic algorithms. The trade-off between computational efficiency versus optimality has been discussed in some articles and conflicting messages were signaled. Although the problem of suboptimality was acknowledged, some authors argued that heuristics may be preferable to exact optimization because IP models are computationally complex and may not be solvable when too many reserve sites are involved. On the other hand, some studies reported that fairly large problems could be solved easily. This paper shows that although the computational complexity argument can be valid for large reserve selection problems, by properly guiding the solver and exploiting the problem structure, formal optimization can deliver second-best (near-optimal) solutions that dominate the greedy heuristic solutions.

Locating Discretionary Service Facilities, II: Maximizing Market Size, Minimizing Inconvenience

Discretionary service facilities are providers of products and/or services that are purchased by customers who are traveling on otherwise preplanned trips such as the daily commute. Optimum location of such facilities requires them to be at or near points in the transportation network having sizable flows of different potential customers. N. Fouska (Fouska, N. 1988. Optimal Location of Discretionary Service Facilities. MS Thesis, Operations Research Center, MIT, Cambridge, Mass.) and O. Berman, R. Larson and N. Fouska (BLF [Berman, O., R. C. Larson, N. Fouska. 1992. Optimal location of discretionary service facilities. Trans. Sci. 26(3) 201–211.]) formulate a first version of this problem, assuming that customers would make no deviations, no matter how small, from the preplanned route to visit a discretionary service facility. Here the model is generalized in a number of directions, all sharing the property that the customer may deviate from the preplanned route to visit a discretionary service facility. Three different generalizations are offered, two of which can be solved approximately by greedy heuristics and the third by any approximate or exact method used to solve the p-median problem. We show for those formulations yielding to a greedy heuristic approximate solution, including the formulation in BLF, that the problems are examples of optimizing submodular functions for which the G. Nemhauser, L. Wolsey and M. Fisher (Nemhauser, G. L., L. A. Wolsey, M. L. Fisher. 1978. An analysis of approximations for maximizing sub-modular set functions, I. Math. Prog. 14 265–294.) bound on the performance of a greedy algorithm holds. In particular, the greedy solution is always within 37% of optimal, and for one of the formulations we prove that the bound is tight.

Absolute bounds on optimal cost for a class of set covering problems

We study the class of (m constraint,n variable) set covering problems which have no more thank variables represented in each constraint. Letd denote the maximum column sum in the constraint matrix, letr=[m/d]−1, and letZ g denote the cost of a greedy heuristic solution. Then we prove $$\begin{gathered} Zg \leqslant 1 + r + m - d - \left[ {mk \cdot MAX\left\{ {\frac{{2r}}{{2n - r - 1}},\ln \frac{n}{{n - r}}} \right\}} \right. \hfill \\ \left. { - kd \cdot MIN\left\{ {\frac{{r(r + 1)}}{{2(n - r)}},n \cdot \ln \frac{{n - 1}}{{n - r - 1}} - 1} \right\}} \right]. \hfill \\ \end{gathered} $$ This provides the firsta priori nontrivial upper bound discovered on heuristic solution cost (and thus on optimal solution cost) for the set covering problem. An example demonstrates that this bound is attainable, both for a greedy heuristic solution and for the optimal solution. Numerical examples show that this bound is substantially better than existing bounds for many problem instances. An important subclass of these problems occurs when the constraint matrix is a circulant, in which casem=n andk=d=[αη] for some 0<α<1. For this subclass we prove $$\mathop {\lim }\limits_{n \to \infty } Zg/n \leqslant \frac{{\alpha ^2 }}{2}[1/\alpha ][1/\alpha ].$$

An analysis of the greedy algorithm for the submodular set covering problem

We consider the problem: min $$\{ \mathop \Sigma \limits_{j \in s} f_j :z(S) = z(N),S \subseteqq N\} $$ wherez is a nondecreasing submodular set function on a finite setN. Whenz is integer-valued andz(O)=0, it is shown that the value of a greedy heuristic solution never exceeds the optimal value by more than a factor $$H(\mathop {\max }\limits_j z(\{ j\} ))$$ where $$H(d) = \sum\limits_{i = 1}^d {\frac{1}{i}} $$ . This generalises earlier results of Dobson and others on the applications of the greedy algorithm to the integer covering problem: min {fy: Ay ≧b, y e {0, 1}} wherea ij ,b i } ≧ 0 are integer, and also includes the problem of finding a minimum weight basis in a matroid.