Set Of Schedules Research Articles

KMOEA: A Knowledge-Based Multiobjective Algorithm for Distributed Hybrid Flow Shop in a Prefabricated System

In this article, a distributed hybrid flow shop scheduling problem with variable speed constraints is considered. To solve it, a knowledge-based adaptive reference points multiobjective algorithm (KMOEA) is developed. In the proposed algorithm, each solution is represented with a 3-D vector, where the factory assignment, machine assignment, operation scheduling, and speed setting are encoded. Then, four problem-specific lemmas are proposed, which are used as the knowledge to guide the main components of the algorithm, including the initialization, global, and local search procedures. Next, an efficient initialization approach is presented, which is embedded with several problem-related initialization rules. Furthermore, a novel Pareto-based crossover heuristic is designed to learn from more promising solutions. To enhance the local search abilities, a speed adjustment local search method is investigated. Finally, a set of instances generated based on the realistic prefabricated production system is tested to verify the efficiency and effectiveness of the proposed algorithm.

A Two-Workshop Collaborative, Integrated Scheduling Algorithm considering the Prescheduling of the Root-Subtree Processes.

Aiming at the existing two-workshop integrated scheduling algorithm with the same equipment resources, a unified vertical or horizontal scheduling rule is used to sort all processes and ignore the vertical and horizontal characteristics of the associated process position in the process tree, which affects the scheduling results. A two-workshop collaborative, integrated scheduling algorithm considering the prescheduling of the Root-Subtree processes is proposed. The algorithm proposes a process conflict adjustment strategy for the horizontal equipment constraints. The same equipment Root-Subtree processes are sorted and loaded into the corresponding equipment queue through the vertical and horizontal prescheduling method in a single-workshop environment, and it combines with the schedulable process set to dequeue the first process of the queue. To enhance the flexibility of process scheduling, it proposes a process conflict adjustment strategy for the vertical process tree constraints in the two workshops to determine the processing workshop of the processes and the actual start time, which narrows the search comparison for schedulable processes. The example tests show that the algorithm not only excavates and utilizes the effectiveness of the vertical and horizontal characteristics of the process tree, but also considers the process migration time. Therefore, the effect is better and more practical.

Multi-Channel Data Aggregation Scheduling Based on the Chaotic Firework Algorithm for the Battery-Free Wireless Sensor Network

The emergence of battery-free wireless sensor networks (benefiting from the ability to collect energy from the surroundings) has broken through the energy and lifetime limitations of traditional wireless sensor network systems, but also brings challenges to the sharing of network resources. In the multi-channel wireless communication environment, in particular, how to coordinate the communication time and occupied channels of a large number of sensor nodes from the perspective of optimizing the global network has become a research problem that must be solved. To reduce the transmission delay and the usage of wireless channels, a new multi-channel data aggregation scheduling method based on the chaotic firework algorithm is proposed in this paper. With the help of the generation function of feasible solutions, one scheduling set and a firework individual can be rapidly converted to each other. By the operations of firework explosions, the Gaussian mutation, and chaotic exploration, a sub-optimal scheduling set could be found during an acceptable time period. Finally, simulation results show that the new scheduling method has advantages in aggregation delay and occupied channels when compared with existing methods.

A new Internet of Things based optimization scheme of residential demand side management system

The steady increase in the energy demand and the growing carbon footprint has forced electricity-based utilities to shift from their use of non-renewable energy sources to renewable energy sources. Furthermore, there has been an increase in the integration of renewable energy sources in the electric grid. Hence, one needs to manage the energy consumption needs of the consumers, more effectively. Consumers can connect all the devices and houses to the internet by using Internet of Things (IoT) technology. In this study, the researchers have developed and proposed a novel 2-stage hybrid method that schedules the power consumption of the houses possessing a distributed energy generation and storage system. Stage 1 modeled the non-identical Home Energy Management Systems (HEMSs) that can contain the DGS like WT and PV. The HEMS organise the controllable appliances after taking into consideration the user preferences, electricity prices and the amount of energy produced /stored. The set of optimal consumption schedules for every HEMS was estimated using a BPSO and BSA. On the other hand, Stage 2 includes a Multi-Agent-System (MAS) based on the IoT. The system comprises two portions: software and hardware. The hardware comprises the Base Station Unit (BSU) and many Terminal Units (TUs).

Camera traps are an effective tool for monitoring insect-plant interactions.

Insect and pollinator populations are vitally important to the health of ecosystems, food production, and economic stability, but are declining worldwide. New, cheap, and simple monitoring methods are necessary to inform management actions and should be available to researchers around the world. Here, we evaluate the efficacy of a commercially available, close‐focus automated camera trap to monitor insect–plant interactions and insect behavior. We compared two video settings—scheduled and motion‐activated—to a traditional human observation method. Our results show that camera traps with scheduled video settings detected more insects overall than humans, but relative performance varied by insect order. Scheduled cameras significantly outperformed motion‐activated cameras, detecting more insects of all orders and size classes. We conclude that scheduled camera traps are an effective and relatively inexpensive tool for monitoring interactions between plants and insects of all size classes, and their ease of accessibility and set‐up allows for the potential of widespread use. The digital format of video also offers the benefits of recording, sharing, and verifying observations.

From Spectrum Bonding to Contiguous-Resource Batching Task Scheduling

We formulate and analyze a generic task scheduling problem: a set of tasks need to be executed on a pool of continuous resource such as spectrum and memory, each requiring a certain amount of time and contiguous resource; some tasks can be executed simultaneously in batch by sharing the resource, while others requiring exclusive use of the resource. We seek an optimal resource allocation and the related scheduling policy maximizing the overall system utility. This problem, termed as the contiguous-resource batching task scheduling problem, arises in a variety of engineering fields, where communication and storage resources are potential bottlenecks and thus need to be carefully scheduled. Two motivating examples are the spectrum bonding problem in dynamic spectrum access systems and the dynamic storage allocation problem in computer systems. In this paper, we investigate both offline and online scheduling settings. We first establish the NP-hardness of the offline setting and the inapproximability of the online setting in its generic form. Given the theoretical performance limit, we then develop approximation algorithms with mathematically proven performance guarantee in terms of approximation and competitive ratios for the offline and online settings.

Bi-objective optimization using an improved NSGA-II for energy-efficient scheduling of a distributed assembly blocking flowshop

In this study, an Energy-Efficient Distributed Assembly Blocking FlowShoP (EEDABFSP) is considered. An improved Non-dominated Sorting Genetic Algorithm-II (NSGA-II) is developed to solve it. Two objectives have been considered, i.e. minimizing the maximum completion time and total energy consumption. To begin, each feasible solution is encoded as a one-dimensional vector with the factory assignment, operation scheduling and speed setting assigned. Next, two initialization schemes are presented to improve both quality and diversity, which are based on distributed assembly attributes and the slowest allowable speed criterion, respectively. Then, to accelerate the convergence process, a novel Pareto-based crossover operator is designed. Because the populations have different initialization strategies, four different mutation operators are designed. In addition, a distributed local search is integrated to improve exploitation abilities. Finally, the experimental results demonstrate that the proposed algorithm is more efficient and effective for solving the EEDABFSP.

An approach for bi-objective maintenance scheduling on a networked system with limited resources

Preventive maintenance activities are often the cause of downtime of technical multi-component systems. To minimize maintenance costs and maximize productivity, maintenance tasks are often grouped and carried out simultaneously. We consider the problem of obtaining an optimal maintenance schedule when the multi-component system is also a networked system and can be modeled as a directed graph, where nodes represent machines or workers, and edges represent the exchange of material, information, or work between these nodes. To find efficient maintenance schedules, we formulate a bi-objective optimization problem, which considers the limited availability of maintenance personnel, and we propose an algorithm that finds a set of maintenance schedules, which are a good approximation of the Pareto front in terms of costs and productivity. Through sensitivity analysis we show the extent to which adding maintenance personnel improves system productivity at the expense of increased maintenance costs and idle time of some resources. Besides solving the Pareto-optimal schedules, we show how the developed model is useful in maintenance personnel planning, and we outline limitations and future developments of the present work.

A Binary Integer Linear Programming Approach for Risk Minimization of a Multi-Mode Resource-Constrained Project Scheduling Problem with Discrete Time-Cost-Quality-Risk Trade-Off

The multi-mode resource-constrained project scheduling problem (MRCPSP) allows project managers to assign schedules and limited resources to project activities while minimizing total duration. This time objective has been extended to include the trade-offs of cost and quality called the discrete time-cost-quality trade-off problem (DTCQTP) to provide project managers an overview of indicators affecting project performance. However, the impacts of the COVID-19 pandemic have led project managers and consultants to assess their projects’ risks regarding scheduling and resource assignment decisions. Hence, this paper aims to extend the MRCPSP and the DTCQTP to include risk at the resource level to highlight the importance of hiring the proper resources in project scheduling. A binary integer linear programming model named the multi-mode resource-constrained project scheduling with discrete time-cost-quality-risk trade-off (MRCPSP-DTCQRT) was developed with risk minimization as the objective function. A case study from prior literature was used to illustrate the model using the open-sourced Python-MIP package, which uses the branch-and-cut methodology for generating optimal solutions. A set of schedules that either prioritize time, cost, quality, risk, or a balance among the four was generated for the use of the project manager to make decisions based on the current situation. Future research may extend the model further to include resource skills, test large-scale case studies, and use other methodologies such as metaheuristics and machine learning to arrive at optimal solutions within reasonable computing time.

The Impact of the COVID-19 Pandemic on the Psychological Well-being of Healthcare Workers in Obstetrics and Gynaecology: An Observational Study at an Apex Institute.

Background and objectiveThe coronavirus disease 2019 (COVID-19) pandemic has affected the health, social, and economic sectors all over the world. With a view to assessing the impact of COVID-19 on the mental health of healthcare workers (HCWs), we conducted a study to find out the incidence and severity of depression, anxiety, and post-traumatic stress disorder (PTSD) among HCWs.Material and methodsThis was an observational cross-sectional study conducted in the Department of Obstetrics and Gynaecology in collaboration with the Department of Psychiatry at AIIMS, New Delhi from March 2021 to June 2021. One hundred HCWs working in the Department of Obstetrics and Gynaecology were surveyed using a set of semi-structured interview schedules and structured questionnaires distributed via email or manually. The structured questionnaire included the demographic profile; other baseline information; the 42-item Depression, Anxiety, and Stress Scale (DASS-42); and the Impact of Event Scale-Revised (IES-R) instrument. Data analysis was carried out using the statistical package STATA version 14.0 (StataCorp LLC, College Station, TX).ResultsA total of 100 HCWs participated in the study, out of which 39 (39%), 45 (45%), and 16 (16%) were doctors, nursing staff, and supporting staff, respectively. Overall, 92 (92%) of the participants were women, and the mean age of the participants was 29.87 ±4.85 years. Out of the 100 participants, 17 (17%), 25 (25%), 13 (13%), and two (2%) participants had depression, anxiety, stress, and PTSD, respectively. Occupation-wise, among the nursing staff, doctors, and supporting staff, the incidence of depression was 24.4%, 15.4%, 0.0%, respectively; the anxiety rate was 33.3%, 25.6%, and 0.0%, respectively; and the rate of stress was 17.8%, 12.8%, and 0.0%, respectively. The IES-R score was significantly higher among unmarried as compared to married participants (2.70 ±7.935 vs. 1.60 ±3.583, p=0.000). Participants living in joint families had a higher DASS-42 score (DASS-D: 4.00 ±5.299 vs. 3.77 ±7.727, p=0.889; DASS-A: 4.31 ±4.398 vs. 4.12 ±7.496, p=0.905; DASS-S: 4.08 ±4.816 vs. 3.88 ±7.567, p=0.016) and lower IES-R score (1.31 ±4.922 vs. 2.66 ±9.947, p=0.752) as compared to those living in nuclear families. Depression (4.86 ±8.165 vs. 2.00 ±4.388, p=0.054), anxiety (5.31 ±7.538 vs. 2.14 ±4.704, p=0.024), stress (5.20 ±7.651 vs. 1.67 ±4.733, p=0.014) and PTSD (3.61 ±10.900 vs. 1.44 ±2.634, p=0.245) were all higher among HCWs having exposure to COVID-19 more than 10 hours per week compared to participants with an exposure of less than 10 hours per week. The participants having psychiatric illness in the family showed significantly higher mean values for DASS-42 (DASS-D: 20.00 ±26.870 vs. 3.50 ±6.264, p=0.001; DASS-A: 18.50 ±20.506 vs. 3.88 ±6.215, p=0.002; DASS-S: 18.00 ±21.213 vs. 3.64 ±6.346, p=0.003) as compared to those without any psychiatric illness in the family.ConclusionBased on our findings, occupational and environmental factors at the workplace play a key role in mental health outcomes, and COVID-19 has had a significant impact on the mental health of HCWs. Furthermore, we have also observed that effective planning can significantly reduce mental stress.

Design and Development of Feeding Automation System and Water Quality Monitoring on Freshwater Fish Cultivation

Feeding is one of the most critical aspects of freshwater fish farming in order to get optimal aquaculture outcomes. It has been widely acknowledged that feeding is often done directly by cultivators, who distribute the feed by employing hand. This common strategy can result in two outcomes. The first outcome is an increase in feed costs owing to excessive feeding, while the second outcome is an increase in feed costs due to excessive feeding. Overfeeding, as a matter of a fact, may lead to the result in leftover feed that is not devoured by the fish, contaminating the pond water and disrupting the pH stability of the pond water. In addition, the second effect that may occur is a shortage of nutrition and nutrients in fish, which can lead to poor fish development. Another issue in aquaculture is the high mortality rate of fish, which actually contain several reasons, one of which is poor water quality, which is not conducive to maximal fish growth and development. Cultivators must thus regularly examine the quality of pond water, specifically the pH of pond water. In light of these concerns, we require a system that can assist farmers in controlling feed scheduling, determining the amount of feed required based on the age of the fish, and monitoring water quality. The device in question is an automated fish feeding and water quality monitoring system. This automated solution has shown to provide a number of benefits. The benefit is that feeding can be scheduled, the amount of feed can be changed according to the age and demands of the fish, and the pond water quality, in this case the pH of the water, can be automatically monitored. Further, the research was carried out at different stages. Planning and data gathering, needs analysis, implementation, and system testing were all aspects of the research. The RTC sensor, pH sensor, and temperature sensor were all employed in the automation system. The RTC sensor was utilized to time the feeding schedule for the fish. The pH sensor detected the pH value of the pool water, while the temperature sensor detected the temperature of pool water. The data collected from the three sensors was then processed by the NodeMCU ESP8266 microcontroller. The NodeMCU ESP8266 microcontroller chip houses the system’s logic and software instructions. The data of the sensor was transferred and recorded to a Google spreadsheet, where it was utilized as an indication to control actuators such as servo motors and relays. Further more, the fish feed was opened and closed by utilizing a servo motor. The pH pump was turned on and off using the relay as a switch. This pH pump contained fluids to keep the pH levels in the water stable. Through employing NodeMCU ESP8266 microcontroller, this study has revealed to be able to create an automated system for feeding and monitoring water quality. The automation system then was able to perform the feeding activity in accordance to schedule set, and also was able to perform it according to the specified amount of feed. In addition, the quality of the pond water was also able to be monitored.

Stable routing scheduling algorithms in multi-hop wireless networks

Stability is an important issue in order to characterize the performance of a network, and it has become a major topic of study in the last decade. Roughly speaking, a communication network system is said to be stable if the number of packets waiting to be delivered (backlog) is finitely bounded at any one time.In this paper we introduce a number of routing scheduling algorithms which, making use of certain knowledge about the network's structure, guarantee stability for certain injection rates.First, we introduce two new families of combinatorial structures, which we call universally strong selectors and generalized universally strong selectors, that are used to provide a set of transmission schedules. Making use of these structures, we propose two local-knowledge packet-oblivious routing scheduling algorithms. The first proposed routing scheduling algorithm only needs to know some upper bounds on the number of links and on the network's degree, and is asymptotically optimal regarding the injection rate for which stability is guaranteed. The second proposed routing scheduling algorithm is close to be asymptotically optimal, but it only needs to know an upper bound on the number of links. For such algorithms, we also provide some results regarding both the maximum latencies and queue lengths. Furthermore, we also evaluate how the lack of global knowledge about the system topology affects the performance of the routing scheduling algorithms.

OPTIMALISASI OPERASIONAL TOWER CRANE PADA PEKERJAAN ARSITEKTURAL PELAKSANAAN KONSTRUKSI GEDUNG BERTINGKAT TINGGI 168 METER (PROYEK HOLLAND VILLAGE JAKARTA)

ABSTRACT
 This thesis discusses the operation of tower cranes in high-rise building construction. In the implementation of high-rise building projects, tower crane vertical transportation operations are very decisive as the most important means for lifting and transporting material supply on each working floor. The Holland Village Jakarta project is experiencing obstacles to the efficiency of construction completion which has not been in accordance with duration of the time schedule set. For this reason, an analysis of the optimization of tower crane operations is carried out in terms of human resource factors, material resources, method resources, and environmental conditions. And also carried out an analysis of risk management so as to achieve optimization of tower crane vertical transportation operations. The approach taken is to use risk management based on the dominant risk response analysis to make relevant strategic decisions. The configuration of 3 tower cranes is carried out by analyzing hierarchical decisions using the Analytical Hierarchy Process (AHP) method with the selection of the best alternative configuration. The results of the hierarchy of dominant response criteria in sequence, namely: economic/cost criteria, time efficiency, ease of implementation, and criteria for transportation of architectural materials. The alternative configuration of the KTC-3 tower crane is effective as a weight value of 33.78% with a change in position configuration from the existing tower configuration. The duration of construction can be optimized by 10 days in 5.5%.
 Keywords: tower crane, risk response, AHP, configuration, duration

On permutation schedules for two-machine flow shops with buffer constraints and constant processing times on one machine

The two-machine flow shop problem with buffers where one of the machines has constant processing times is studied. It is investigated if optimal permutation schedules exist, i.e., schedules which minimize the makespan within the set of all schedules and where the job sequence on both machines is the same. Two standard buffer models (an intermediate buffer that a job occupies between its processing on the two machines and a spanning buffer which is occupied by a job over all of its processing steps) are considered for two types of buffer usage: i) all jobs occupy the same buffer amount and ii) for each job the occupied buffer amount equals its processing time on the machine with non-constant times. For (i) and both buffer models, it is shown that the set of optimal schedules always contains at least one permutation schedule. For (ii) the existence of optimal permutation schedules is only guaranteed for instances with n jobs for all n≤6 (spanning buffer) and for all n≤3 (intermediate buffer). For each n>6 (spanning buffer) and each n>3 (intermediate buffer) exists an instance which does not have an optimal permutation schedule. For (ii) and both buffer models, an upper bound and a lower bound for ratio between the makespan of a best permutation schedule and the makespan of an optimal schedule is given. It is also shown for (ii) and both buffer models that in general it is NP-hard to decide if an optimal permutation schedule exists.

Rural-Urban Migration Among Women Farmers: Science Education, Survey, and Implication for Food Crop Production in Cross River State, Nigeria

The main objectives of the study were to: identify the socio-economic characteristics of the respondents, assess factors influencing women’s food production activities and identify measures for reducing rural-urban migration among women farmers in the study area. A sample size of 200 farmers was randomly selected for the study. Data were collected using a set of structured questionnaires and interview schedules. The result obtained showed that most of the farmers were between the ages of 51-60 years (50.0%). Farmers’ levels of education were the non-formal level of education (45.0%), primary level of education (35.0%), and secondary level of education (15%). Farming was their major occupation (52.5%) and trading (40.0%). 8-10 household size was the highest which promotes labour within the family (40.0%), 11 and above (30.0%). Family labour was the main source of labour supply (75.0%), and exchange labour (22.5%). Factors influencing women’s crop production activities were lack of fertile farmland, old age, active engagement in domestic activities, and high cost of farm inputs, which were 22.5, 17.5, 13.5, and 11.5%, respectively. The findings showed that mechanization can reduce migration among women farmers. The study recommended that government should mechanise agriculture, loans should be given to corporative farmers while land tenure system should be reviewed to favour farming which will also help to reduce rural-urban migration among women farmers in Cross River State, Nigeria.

Forecasting and modeling of the COVID-19 pandemic in the USA with a timed intervention model

We propose a novel Timed InterventionS, P, E, I, Q, R, D model for projecting the possible futures of the COVID-19 pandemic in the USA. The proposed model introduces a series of timed interventions that can account for the influence of real time changes in government policy and social norms. We consider three separate types of interventions: (i) Protective interventions: Where population moves from susceptible to protected corresponding to mask mandates, stay-at-home orders and/or social distancing. (ii) Release interventions: Where population moves from protected to susceptible corresponding to social distancing mandates and practices being lifted by policy or pandemic fatigue. (iii) Vaccination interventions: Where population moves from susceptible, protected, and exposed to recovered (meaning immune) corresponding to the mass immunization of the U.S. Population. By treating the pandemic with timed interventions, we are able to model the pandemic extremely effectively, as well as directly predicting the course of the pandemic under differing sets of intervention schedules. We show that without prompt effective protective/vaccination interventions the pandemic will be extended significantly and result in many millions of deaths in the U.S.

Two sets of initial conditions on boreal forest carbon storage economics

Two sets of initial conditions are used in the investigation of capital return rate and carbon storage in boreal forests. Firstly, a growth model is applied in young stands as early as the inventory-based model is applicable. Secondly, the growth model is applied to observed wooded stands. Four sets of thinning schedules are investigated in either case. The two sets of initial conditions yield similar results. The capital return rate is a weak function of rotation age, which results in variability in the optimal number of thinnings. Reducing the number of thinnings to one increases timber stock but induces a capital return rate deficiency. The deficiency per excess volume unit is smaller if the severity of any thinning is restricted by the removal of large trees only. Omission of thinnings best applies to spruce-dominated stands with stem count less than 2000/ha. Restricted thinning intensity applies to deciduous stands and dense pine stands. The albedo effect increases the benefits of restricted thinnings and increased clearcuttings instead of contradicting the carbon storage.

An Optimization Model for Highway Work Zones Considering Safety, Mobility, and Project Cost

Highway Work Zones (HWZs) are associated with significant adverse impacts on safety, mobility, and work costs. The objective of this paper is two-fold: First, to quantify the impacts of HWZs on safety, mobility, and work costs. Second, to develop an optimization model to minimize the total costs associated with HWZs by controlling site geometry, Temporary Traffic Control (TTC), and work management. This model implements a location-based schedule within the cost evaluation. A genetic algorithm is used to determine a set of optimal scheduling and decision variables. The performance of the model is demonstrated in a case study. The results reveal that crash costs, which were often ignored or only included indirectly in previous works, are a substantial cost component. Their explicit inclusion in the optimization process significantly affects the total cost and the optimal operations of the HWZ. Furthermore, the inclusion of a location-based schedule in the model is instrumental and affects the optimal solution since all HWZ cost components are affected by the work processes and project duration. Moreover, consideration of the effects of TTC on the optimized function has a substantial influence on the total cost. The model can support transportation agencies and local authorities in mitigating the adverse impacts associated with HWZs.

Scheduling in parallel machines with two objectives: analysis of factors that influence the Pareto frontier

This paper explores the characteristics of solutions when scheduling jobs in a shop with parallel machines. Three classical objective functions were considered: makespan, total completion time, and total tardiness. These three criteria were combined in pairs, resulting in three bi-objective formulations. These formulations were solved using the ε-constraint method to obtain a Pareto frontier for each pair. The objective of the research is to evaluate the Pareto set of efficient schedules to characterize the solution sets. The characterization of the solutions sets is based on two performance metrics: the span of the objective functions' values for the points in the frontier and their closeness to the ideal point. Results that consider four experimental factors indicate that when the makespan is one of the objective functions, the range of the processing times among jobs has a significant influence on the characteristics of the Pareto frontier. Simultaneously, the slack of due dates is the most relevant factor when total tardiness is considered.

A theoretical framework to accelerate scheduling improvement heuristics using a new longest path algorithm in perturbed DAGs

ABSTRACT Job-shop scheduling problems are complex and still well-studied manufacturing problems. Improvement heuristic algorithms have been proposed to solve the scheduling problems using makespan as their performance measure. All these heuristics iteratively perturb trial schedules by selecting a new schedule from a set of nearby schedules (neighbourhood); then, recalculate and compare the makespan until a sufficient schedule is determined. Unlike previous studies, we did not generate a new heuristic or a novel neighbourhood calculation. Instead, we proposed a theoretical framework, Algorithm to Visit Affected Node (AVAN), which can be incorporated in qualified heuristics while using their current neighbourhood structure to accelerate the recalculation of the makespan in each iteration. We modelled the system by Directed Acyclic Graph (DAG) where the length of the longest path equals the makespan. The scheduling perturbations are represented by adding and deleting edges. AVAN investigates the configuration of scheduling perturbations (added/deleted edges) to find an appropriate starting point to traverse the graph. AVAN is mathematically more efficient than previous longest path algorithms for perturbed DAG. Its time complexity is , where is the number of affected nodes and is the number of incoming and outgoing edges of the affected nodes.