This document summarizes an improved heuristic algorithm for solving permutation flow shop scheduling problems. The heuristic modifies the well-known NEH algorithm by generating more initial partial job sequences and selecting the best sequences at each step, aiming to find sequences with lower makespans. An example is provided showing the improved heuristic finds sequences with makespans equal to the best makespan found by the original NEH algorithm. The improved heuristic maintains the same quadratic computational complexity as the original NEH algorithm while generating solutions of equal or better quality.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
The document summarizes a queueing model with two component mixture of doubly truncated exponential service times. The service time distribution is a two component mixture of doubly truncated exponential distributions, which can characterize heterogeneous and finite range service times. Assuming Poisson arrivals, the embedded Markov chain technique is used to analyze the system. Explicit expressions are derived for performance measures like average number of customers, average waiting time, throughput, and probability of idleness. Numerical analysis studies the sensitivity of performance measures to parameter changes. The model includes two component mixture of exponential, doubly truncated exponential, and exponential service time models as special cases.
Implementation and evaluation of novel scheduler of UC/OS (RTOS)Editor Jacotech
The document summarizes proposed modifications to the scheduler of the UC/OS real-time operating system (RTOS) to allow tasks with the same priority level to be queued. The proposed scheduler uses time-slicing to schedule multiple tasks at the same priority level. Amendments were made to task management structures and system calls related to scheduling and time management. Evaluation on a hardware board showed the modified scheduler added minimal overhead.
The document discusses concurrency issues in operating systems and solutions to the critical section problem. It begins by introducing the critical section problem and describing software and hardware solutions. It then defines key concurrency concepts like critical sections, mutual exclusion, deadlocks, livelocks, race conditions, and starvation. Specific hardware approaches like interrupt disabling and test-and-set instructions are presented. Software approaches using semaphores are also introduced as a way for processes to signal each other and synchronize access to shared resources.
This document presents a comparative study of two genetic algorithm-based task allocation models in distributed computing systems. It aims to minimize turnaround time, where the previous model aimed to maximize reliability. The models are implemented on two example cases, with the minimum turnaround time model finding an allocation with a turnaround of 14 units and slightly lower reliability than the maximum reliability model's allocation of 20 units. In conclusion, minimizing turnaround time leads to slightly reduced reliability compared to maximizing reliability.
Study of average losses caused by ill processing in a production line with im...Alexander Decker
This academic article analyzes average losses caused by ill-processing in a production line with immediate feedback and multi-server facilities at each processing unit. The authors model the production line as a queuing network with an arbitrary number of processing units in series, where each unit has multi-server capacity. They analyze the stationary behavior and find the solution in product form. Considering processing costs, the average loss to the system due to rejection of items from ill-processing is obtained.
This document summarizes a research paper on the operational fixed job scheduling problem with working time constraints. The paper considers the problem of maximizing the total weight of jobs that can be processed within working time limits on parallel machines. It analyzes preemptive and non-preemptive versions of the problem and provides polynomial-time algorithms for some special cases of the preemptive problem. For the non-preemptive problem, the paper shows it is strongly NP-hard and proposes a branch-and-bound algorithm with computational testing showing it can solve instances with up to 100 jobs in reasonable time.
The document summarizes research on task scheduling techniques for dynamically reconfigurable systems. It presents (1) an integer linear programming model to formally define the scheduling problem, (2) the Napoleon heuristic scheduler to solve the problem in reasonable time based on the ILP model, and (3) experimental results validating that Napoleon obtains an average 18.6% better schedule length than other algorithms. Future work is outlined to integrate Napoleon into a general design framework and scheduling-aware partitioning flow.
Process synchronization is required when multiple processes access shared data concurrently. Peterson's solution solves the critical section problem for two processes using shared variables - an integer "turn" and a boolean flag array. Synchronization hardware uses atomic instructions like TestAndSet() and Swap() to implement locks for mutual exclusion. Semaphores generalize locks to control access to multiple resources.
Welcome to International Journal of Engineering Research and Development (IJERD)IJERD Editor
The document summarizes a queueing model with two component mixture of doubly truncated exponential service times. The service time distribution is a two component mixture of doubly truncated exponential distributions, which can characterize heterogeneous and finite range service times. Assuming Poisson arrivals, the embedded Markov chain technique is used to analyze the system. Explicit expressions are derived for performance measures like average number of customers, average waiting time, throughput, and probability of idleness. Numerical analysis studies the sensitivity of performance measures to parameter changes. The model includes two component mixture of exponential, doubly truncated exponential, and exponential service time models as special cases.
Implementation and evaluation of novel scheduler of UC/OS (RTOS)Editor Jacotech
The document summarizes proposed modifications to the scheduler of the UC/OS real-time operating system (RTOS) to allow tasks with the same priority level to be queued. The proposed scheduler uses time-slicing to schedule multiple tasks at the same priority level. Amendments were made to task management structures and system calls related to scheduling and time management. Evaluation on a hardware board showed the modified scheduler added minimal overhead.
The document discusses concurrency issues in operating systems and solutions to the critical section problem. It begins by introducing the critical section problem and describing software and hardware solutions. It then defines key concurrency concepts like critical sections, mutual exclusion, deadlocks, livelocks, race conditions, and starvation. Specific hardware approaches like interrupt disabling and test-and-set instructions are presented. Software approaches using semaphores are also introduced as a way for processes to signal each other and synchronize access to shared resources.
This document presents a comparative study of two genetic algorithm-based task allocation models in distributed computing systems. It aims to minimize turnaround time, where the previous model aimed to maximize reliability. The models are implemented on two example cases, with the minimum turnaround time model finding an allocation with a turnaround of 14 units and slightly lower reliability than the maximum reliability model's allocation of 20 units. In conclusion, minimizing turnaround time leads to slightly reduced reliability compared to maximizing reliability.
Study of average losses caused by ill processing in a production line with im...Alexander Decker
This academic article analyzes average losses caused by ill-processing in a production line with immediate feedback and multi-server facilities at each processing unit. The authors model the production line as a queuing network with an arbitrary number of processing units in series, where each unit has multi-server capacity. They analyze the stationary behavior and find the solution in product form. Considering processing costs, the average loss to the system due to rejection of items from ill-processing is obtained.
This document summarizes a research paper on the operational fixed job scheduling problem with working time constraints. The paper considers the problem of maximizing the total weight of jobs that can be processed within working time limits on parallel machines. It analyzes preemptive and non-preemptive versions of the problem and provides polynomial-time algorithms for some special cases of the preemptive problem. For the non-preemptive problem, the paper shows it is strongly NP-hard and proposes a branch-and-bound algorithm with computational testing showing it can solve instances with up to 100 jobs in reasonable time.
The document summarizes research on task scheduling techniques for dynamically reconfigurable systems. It presents (1) an integer linear programming model to formally define the scheduling problem, (2) the Napoleon heuristic scheduler to solve the problem in reasonable time based on the ILP model, and (3) experimental results validating that Napoleon obtains an average 18.6% better schedule length than other algorithms. Future work is outlined to integrate Napoleon into a general design framework and scheduling-aware partitioning flow.
Process synchronization is required when multiple processes access shared data concurrently. Peterson's solution solves the critical section problem for two processes using shared variables - an integer "turn" and a boolean flag array. Synchronization hardware uses atomic instructions like TestAndSet() and Swap() to implement locks for mutual exclusion. Semaphores generalize locks to control access to multiple resources.
The document shares hopes for the new year 2008, quoting a Bible verse about God meeting all needs. It expresses the hope that people focus on their relationship with God as the most important thing in life. It also hopes that people experience peace beginning with themselves and spreading out, and that faith, hope and love grow in their hearts each day with God's blessing on the coming year.
This document summarizes a paper on a multi-objective genetic algorithm for flowshop scheduling. [1] It discusses how large companies must deal with multiple scheduling objectives simultaneously. It then reviews a weighted multi-objective genetic algorithm that was presented in another paper to solve a 20 job, 10 machine flowshop scheduling problem by evaluating 48,600 solutions. The algorithm compares solution pairs to identify non-dominated solutions and select the best overall schedule. While classic scheduling methods are useful, heuristic algorithms like this multi-objective approach can better handle complex industrial scenarios. Scheduling remains an important tool for coordinating work and improving objectives in manufacturing companies.
Bicriteria in n x 2 flow shop scheduling problem under specified rental polic...Alexander Decker
This document presents an algorithm for solving a bicriteria scheduling problem involving n jobs and 2 machines in a flow shop configuration. The processing times and setup times are associated with probabilities. Jobs also have weights indicating their relative importance. The objectives are to minimize the total rental cost of the machines and the total elapsed time. An equivalent job block theorem and Johnson's algorithm are used. A computer program and numerical example are provided to illustrate the algorithm. The algorithm finds a sequence that minimizes rental cost while minimizing the total elapsed time.
11.bicriteria in nx0002www.iiste.org call for paper flow shop scheduling incl...Alexander Decker
This document discusses minimizing bicriteria (total rental cost and makespan) in an n x 2 flow shop scheduling problem where processing times and setup times are associated with probabilities and job blocks are considered. A heuristic algorithm is proposed to find optimal or near optimal job sequences. The algorithm calculates expected processing and setup times, expected flow times, and equivalent job blocks. It then aims to minimize machine rental costs while minimizing makespan by finding job sequences under the specified rental policy. A computer program and numerical example are provided to illustrate the algorithm.
The document discusses how students today are immersed in technology such as cell phones, MP3 players, laptops, and social media. It notes that 76% of secondary students have cell phones, with 30% having smartphones. It also discusses how students want to use their own technology for learning. The document provides examples of how some schools are integrating students' personal technology into the classroom, such as allowing cell phone use for assignments. It emphasizes that schools must prepare students for the technological workplace of the future.
This document discusses flow shop scheduling, which involves sequencing jobs through a set of machines or processes where each job must visit the machines in the same order. It defines flow shop scheduling and provides examples of its applications in industries that require a strict production order. The document then describes two common methods for flow shop scheduling - preemptive and non-preemptive - and provides an example to illustrate the difference. Finally, it discusses algorithms for solving flow shop scheduling problems, focusing on Johnson's algorithm, which provides an optimal solution for problems with two machines.
This document discusses job shop scheduling, which involves scheduling jobs at general purpose work stations. It describes factors like arrival patterns, number of machines, work sequences, and performance criteria. For arrival patterns, it notes static and dynamic types. For work sequences, it discusses fixed and random types. It provides examples of performance criteria like makespan and machine utilization. It also introduces Gantt charts for scheduling displays and discusses scenarios like scheduling n jobs on 1 machine, n jobs on a flow shop with 2 machines, and n jobs on m machines in general. Heuristics for the n jobs on m machines case include shortest processing time, earliest due date, and critical ratio rules.
This document discusses job shop scheduling, which involves scheduling jobs at general purpose work stations. It describes factors like arrival patterns, number of machines, work sequences, and performance criteria. Two common arrival patterns are static and dynamic. Work sequences can be fixed or random. Performance is often evaluated based on makespan (total time) and machine utilization. Gantt charts are used to graphically display schedules. Several scenarios for job shop scheduling are presented, including strategies for 1 machine, flow shops with 2 machines, and systems with multiple jobs and machines. Heuristics like shortest processing time are commonly used to generate schedules.
Application of branch and bound method for optimal two stage flow shop schedu...Alexander Decker
The document presents a study on solving a two-stage flow shop scheduling problem using the branch and bound method. It describes the problem of scheduling jobs on two machines (A and B) to minimize total elapsed time. An algorithm is provided using branch and bound to evaluate lower bounds at each node and branch to the lowest bound. A numerical example with 5 jobs is solved step-by-step and the optimal sequence is found to be 1-3-5-2-4 with a minimum elapsed time of 138 units.
11.application of branch and bound method for optimal two stage flow shop sch...Alexander Decker
This document summarizes a research paper that examines optimal scheduling for a two-stage flow shop problem using the branch and bound method. It presents the mathematical model and provides a numerical example to illustrate the algorithm. The paper studies a flow shop problem where equivalent jobs are defined for group jobs. The objective is to minimize total elapsed time. The branch and bound method is applied to obtain the optimal job sequence. A 5-job, 2-machine problem is used to demonstrate the step-by-step approach to determining the optimal schedule with minimum completion time of 138 units.
The International Journal of Engineering and Science (The IJES)theijes
This document summarizes a research paper on using work-stealing scheduling algorithms to effectively balance workloads across multiple processors in real-time systems. It discusses how work stealing allows tasks to be distributed from busy processors to idle ones, improving system throughput. The authors propose a priority-based approach where tasks are stolen following an earliest deadline first policy. Their EDF-HSB scheduling algorithm uses work stealing combined with periodic servers to ensure real-time tasks meet deadlines while also efficiently executing best-effort jobs opportunistically during idle periods. The system model and overall approach are described to integrate real-time and best-effort work using global scheduling with work stealing.
This document discusses different models for multiprocessor real-time scheduling, including identical, uniform, and unrelated processor models. It also covers global, partitioned, and semi-partitioned scheduling models. Global scheduling allows jobs to migrate to any processor, while partitioned scheduling assigns each task to a dedicated processor. Semi-partitioned scheduling uses both partitioning and reservations to allow some migration. The document outlines advantages and disadvantages of each approach, and describes concepts like scheduling anomalies, bin-packing problems, demand-bound functions, and schedulability tests involved in multiprocessor real-time scheduling.
This document provides an overview of data structures and algorithms analysis. It discusses big-O notation and how it is used to analyze computational complexity and asymptotic complexity of algorithms. Various growth functions like O(n), O(n^2), O(log n) are explained. Experimental and theoretical analysis methods are described and limitations of experimental analysis are highlighted. Key aspects like analyzing loop executions and nested loops are covered. The document also provides examples of analyzing algorithms and comparing their efficiency using big-O notation.
Parallel Line and Machine Job Scheduling Using Genetic AlgorithmIRJET Journal
This document summarizes research on using a genetic algorithm to solve a parallel line and machine job scheduling problem. The objective is to minimize the makespan (completion time) of all jobs. A genetic algorithm is applied that represents possible job schedules as chromosomes. The fitness function evaluates schedules based on makespan. Genetic operators like crossover and mutation create new schedules from existing ones. The algorithm was tested on sample job data using a MATLAB program. Results showed the genetic algorithm approach can find optimal job allocations and schedules that minimize makespan for parallel line scheduling problems.
1. This document introduces parallel computing, which involves dividing large problems into smaller concurrent tasks that can be solved simultaneously using multiple processors to reduce computation time.
2. Parallel computing systems include single machines with multi-core CPUs and computer clusters consisting of multiple interconnected machines. Common parallel programming models involve message passing between distributed memory processors.
3. Performance of parallel programs is measured by metrics like speedup and efficiency. Factors like load balancing, serial fractions of problems, and parallel overhead affect how well a problem can scale with additional processors.
A Hybrid Evolutionary Optimization Model for Solving Job Shop Scheduling Prob...iosrjce
The heuristic optimization techniques were commonly used in solving several optimization
problems. The present work aims to develop a hybrid algorithm to solve the scheduling optimization problem of
JSSP. There are different variants of these algorithms that were addressed in several previous works. The
impacts of these two kinds (Genetic Algorithm (GA) and Simulated Annealing (SA) based optimization model)
of initial condition on the performance of these two algorithms were studied using the convergence curve and
the achieved makespan. Even though genetic algorithm performed better than other evolutionary algorithms, it
has some weakness. During running GA, sometimes, it will produce same result without any improvement. SA
has a mechanism to overcome from that situation. During SA, if same result will be repeated, then it is rapidly
changing the change in temperature variable and re-initiates another random search. By using this feature of
SA, it has been implemented a hybrid based evolutionary model for solving JSSP by improving GA.
Comparison has been made with the performance of the proposed SA-GA-Hybrid model with GA as well as SA.
This hybrid evolutionary optimization model combines genetic algorithm and simulated annealing to solve job shop scheduling problems. It initializes a population of solutions and then iterates through generations. In each generation, genetic operations like crossover and mutation are applied to perturb the solutions. The new solutions are evaluated and sorted by fitness. The best solution is then accepted or replaced using a simulated annealing mechanism that considers solution quality and temperature parameter. This allows acceptance of worse solutions to avoid local optima. The process repeats with temperature reduction until termination. The model is proposed to improve on genetic algorithm alone by incorporating simulated annealing's ability to escape local optima.
This document summarizes research on general profit scheduling on parallel processors. It discusses how profit functions can be parameterized to incorporate various metrics like weighted flow time. It presents solutions for special profit functions using dynamic programming formulations. The solutions are extended to handle multiple machines using a similar DP approach. Generalizations like jobs having different processing times on different machines and non-zero release times are also discussed. Reductions from general scheduling problems to geometric set cover problems are explained. Further work directions on improving approximations for these problems are mentioned.
Lecture 3 insertion sort and complexity analysisjayavignesh86
This document discusses algorithms and insertion sort. It begins by defining time complexity as the amount of computer time required by an algorithm to complete. Time complexity is measured by the number of basic operations like comparisons, not in physical time units. The document then discusses how to calculate time complexity by counting the number of times loops and statements are executed. It provides examples of calculating time complexities of O(n) for a simple for loop and O(n^2) for a nested for loop. Finally, it introduces insertion sort and divide-and-conquer algorithms.
The document shares hopes for the new year 2008, quoting a Bible verse about God meeting all needs. It expresses the hope that people focus on their relationship with God as the most important thing in life. It also hopes that people experience peace beginning with themselves and spreading out, and that faith, hope and love grow in their hearts each day with God's blessing on the coming year.
This document summarizes a paper on a multi-objective genetic algorithm for flowshop scheduling. [1] It discusses how large companies must deal with multiple scheduling objectives simultaneously. It then reviews a weighted multi-objective genetic algorithm that was presented in another paper to solve a 20 job, 10 machine flowshop scheduling problem by evaluating 48,600 solutions. The algorithm compares solution pairs to identify non-dominated solutions and select the best overall schedule. While classic scheduling methods are useful, heuristic algorithms like this multi-objective approach can better handle complex industrial scenarios. Scheduling remains an important tool for coordinating work and improving objectives in manufacturing companies.
Bicriteria in n x 2 flow shop scheduling problem under specified rental polic...Alexander Decker
This document presents an algorithm for solving a bicriteria scheduling problem involving n jobs and 2 machines in a flow shop configuration. The processing times and setup times are associated with probabilities. Jobs also have weights indicating their relative importance. The objectives are to minimize the total rental cost of the machines and the total elapsed time. An equivalent job block theorem and Johnson's algorithm are used. A computer program and numerical example are provided to illustrate the algorithm. The algorithm finds a sequence that minimizes rental cost while minimizing the total elapsed time.
11.bicriteria in nx0002www.iiste.org call for paper flow shop scheduling incl...Alexander Decker
This document discusses minimizing bicriteria (total rental cost and makespan) in an n x 2 flow shop scheduling problem where processing times and setup times are associated with probabilities and job blocks are considered. A heuristic algorithm is proposed to find optimal or near optimal job sequences. The algorithm calculates expected processing and setup times, expected flow times, and equivalent job blocks. It then aims to minimize machine rental costs while minimizing makespan by finding job sequences under the specified rental policy. A computer program and numerical example are provided to illustrate the algorithm.
The document discusses how students today are immersed in technology such as cell phones, MP3 players, laptops, and social media. It notes that 76% of secondary students have cell phones, with 30% having smartphones. It also discusses how students want to use their own technology for learning. The document provides examples of how some schools are integrating students' personal technology into the classroom, such as allowing cell phone use for assignments. It emphasizes that schools must prepare students for the technological workplace of the future.
This document discusses flow shop scheduling, which involves sequencing jobs through a set of machines or processes where each job must visit the machines in the same order. It defines flow shop scheduling and provides examples of its applications in industries that require a strict production order. The document then describes two common methods for flow shop scheduling - preemptive and non-preemptive - and provides an example to illustrate the difference. Finally, it discusses algorithms for solving flow shop scheduling problems, focusing on Johnson's algorithm, which provides an optimal solution for problems with two machines.
This document discusses job shop scheduling, which involves scheduling jobs at general purpose work stations. It describes factors like arrival patterns, number of machines, work sequences, and performance criteria. For arrival patterns, it notes static and dynamic types. For work sequences, it discusses fixed and random types. It provides examples of performance criteria like makespan and machine utilization. It also introduces Gantt charts for scheduling displays and discusses scenarios like scheduling n jobs on 1 machine, n jobs on a flow shop with 2 machines, and n jobs on m machines in general. Heuristics for the n jobs on m machines case include shortest processing time, earliest due date, and critical ratio rules.
This document discusses job shop scheduling, which involves scheduling jobs at general purpose work stations. It describes factors like arrival patterns, number of machines, work sequences, and performance criteria. Two common arrival patterns are static and dynamic. Work sequences can be fixed or random. Performance is often evaluated based on makespan (total time) and machine utilization. Gantt charts are used to graphically display schedules. Several scenarios for job shop scheduling are presented, including strategies for 1 machine, flow shops with 2 machines, and systems with multiple jobs and machines. Heuristics like shortest processing time are commonly used to generate schedules.
Application of branch and bound method for optimal two stage flow shop schedu...Alexander Decker
The document presents a study on solving a two-stage flow shop scheduling problem using the branch and bound method. It describes the problem of scheduling jobs on two machines (A and B) to minimize total elapsed time. An algorithm is provided using branch and bound to evaluate lower bounds at each node and branch to the lowest bound. A numerical example with 5 jobs is solved step-by-step and the optimal sequence is found to be 1-3-5-2-4 with a minimum elapsed time of 138 units.
11.application of branch and bound method for optimal two stage flow shop sch...Alexander Decker
This document summarizes a research paper that examines optimal scheduling for a two-stage flow shop problem using the branch and bound method. It presents the mathematical model and provides a numerical example to illustrate the algorithm. The paper studies a flow shop problem where equivalent jobs are defined for group jobs. The objective is to minimize total elapsed time. The branch and bound method is applied to obtain the optimal job sequence. A 5-job, 2-machine problem is used to demonstrate the step-by-step approach to determining the optimal schedule with minimum completion time of 138 units.
The International Journal of Engineering and Science (The IJES)theijes
This document summarizes a research paper on using work-stealing scheduling algorithms to effectively balance workloads across multiple processors in real-time systems. It discusses how work stealing allows tasks to be distributed from busy processors to idle ones, improving system throughput. The authors propose a priority-based approach where tasks are stolen following an earliest deadline first policy. Their EDF-HSB scheduling algorithm uses work stealing combined with periodic servers to ensure real-time tasks meet deadlines while also efficiently executing best-effort jobs opportunistically during idle periods. The system model and overall approach are described to integrate real-time and best-effort work using global scheduling with work stealing.
This document discusses different models for multiprocessor real-time scheduling, including identical, uniform, and unrelated processor models. It also covers global, partitioned, and semi-partitioned scheduling models. Global scheduling allows jobs to migrate to any processor, while partitioned scheduling assigns each task to a dedicated processor. Semi-partitioned scheduling uses both partitioning and reservations to allow some migration. The document outlines advantages and disadvantages of each approach, and describes concepts like scheduling anomalies, bin-packing problems, demand-bound functions, and schedulability tests involved in multiprocessor real-time scheduling.
This document provides an overview of data structures and algorithms analysis. It discusses big-O notation and how it is used to analyze computational complexity and asymptotic complexity of algorithms. Various growth functions like O(n), O(n^2), O(log n) are explained. Experimental and theoretical analysis methods are described and limitations of experimental analysis are highlighted. Key aspects like analyzing loop executions and nested loops are covered. The document also provides examples of analyzing algorithms and comparing their efficiency using big-O notation.
Parallel Line and Machine Job Scheduling Using Genetic AlgorithmIRJET Journal
This document summarizes research on using a genetic algorithm to solve a parallel line and machine job scheduling problem. The objective is to minimize the makespan (completion time) of all jobs. A genetic algorithm is applied that represents possible job schedules as chromosomes. The fitness function evaluates schedules based on makespan. Genetic operators like crossover and mutation create new schedules from existing ones. The algorithm was tested on sample job data using a MATLAB program. Results showed the genetic algorithm approach can find optimal job allocations and schedules that minimize makespan for parallel line scheduling problems.
1. This document introduces parallel computing, which involves dividing large problems into smaller concurrent tasks that can be solved simultaneously using multiple processors to reduce computation time.
2. Parallel computing systems include single machines with multi-core CPUs and computer clusters consisting of multiple interconnected machines. Common parallel programming models involve message passing between distributed memory processors.
3. Performance of parallel programs is measured by metrics like speedup and efficiency. Factors like load balancing, serial fractions of problems, and parallel overhead affect how well a problem can scale with additional processors.
A Hybrid Evolutionary Optimization Model for Solving Job Shop Scheduling Prob...iosrjce
The heuristic optimization techniques were commonly used in solving several optimization
problems. The present work aims to develop a hybrid algorithm to solve the scheduling optimization problem of
JSSP. There are different variants of these algorithms that were addressed in several previous works. The
impacts of these two kinds (Genetic Algorithm (GA) and Simulated Annealing (SA) based optimization model)
of initial condition on the performance of these two algorithms were studied using the convergence curve and
the achieved makespan. Even though genetic algorithm performed better than other evolutionary algorithms, it
has some weakness. During running GA, sometimes, it will produce same result without any improvement. SA
has a mechanism to overcome from that situation. During SA, if same result will be repeated, then it is rapidly
changing the change in temperature variable and re-initiates another random search. By using this feature of
SA, it has been implemented a hybrid based evolutionary model for solving JSSP by improving GA.
Comparison has been made with the performance of the proposed SA-GA-Hybrid model with GA as well as SA.
This hybrid evolutionary optimization model combines genetic algorithm and simulated annealing to solve job shop scheduling problems. It initializes a population of solutions and then iterates through generations. In each generation, genetic operations like crossover and mutation are applied to perturb the solutions. The new solutions are evaluated and sorted by fitness. The best solution is then accepted or replaced using a simulated annealing mechanism that considers solution quality and temperature parameter. This allows acceptance of worse solutions to avoid local optima. The process repeats with temperature reduction until termination. The model is proposed to improve on genetic algorithm alone by incorporating simulated annealing's ability to escape local optima.
This document summarizes research on general profit scheduling on parallel processors. It discusses how profit functions can be parameterized to incorporate various metrics like weighted flow time. It presents solutions for special profit functions using dynamic programming formulations. The solutions are extended to handle multiple machines using a similar DP approach. Generalizations like jobs having different processing times on different machines and non-zero release times are also discussed. Reductions from general scheduling problems to geometric set cover problems are explained. Further work directions on improving approximations for these problems are mentioned.
Lecture 3 insertion sort and complexity analysisjayavignesh86
This document discusses algorithms and insertion sort. It begins by defining time complexity as the amount of computer time required by an algorithm to complete. Time complexity is measured by the number of basic operations like comparisons, not in physical time units. The document then discusses how to calculate time complexity by counting the number of times loops and statements are executed. It provides examples of calculating time complexities of O(n) for a simple for loop and O(n^2) for a nested for loop. Finally, it introduces insertion sort and divide-and-conquer algorithms.
multiprocessor real_ time scheduling.pptnaghamallella
This document discusses different scheduling models for multiprocessor real-time systems, including global scheduling, partitioned scheduling, and semi-partitioned scheduling. Global scheduling uses a shared ready queue and allows tasks to migrate between processors, but can cause overhead from migration and scheduling anomalies. Partitioned scheduling assigns each task to a dedicated processor to avoid migration, but may underutilize processors. Semi-partitioned scheduling first partitions tasks then allows some to migrate to improve utilization.
Task allocation and scheduling inmultiprocessorsDon William
This document discusses task allocation and scheduling in a multi-processor environment. It describes generating synthetic tasks and assigning them priorities using static and dynamic scheduling algorithms like Rate Monotonic and Earliest Deadline First. It then covers allocating tasks to processors using algorithms like Next Fit and Bin Packing to optimize processor utilization. The goal is to schedule tasks dynamically in a multi-processor system to improve performance over uniprocessor scheduling.
The document discusses recursive functions and provides examples of recursive algorithms for calculating factorial, greatest common divisor (GCD), Fibonacci numbers, power functions, and solving the Towers of Hanoi problem. Recursive functions are functions that call themselves during their execution. They break down problems into subproblems of the same type until reaching a base case. This recursive breakdown allows problems to be solved in a top-down, step-by-step manner.
Optimal three stage flow shop scheduling in which processing time, set up tim...Alexander Decker
This document summarizes an algorithm for optimal three stage flow shop scheduling with processing times, set up times, and transportation times that have associated probabilities. Jobs are processed in two disjoint job blocks in a string. The algorithm introduces two fictional machines to reduce the problem to a standard form. It then calculates processing times for equivalent jobs and job blocks on the fictional machines. The jobs are then sequenced to minimize total elapsed time based on their processing times on the fictional machines.
11.optimal three stage flow shop scheduling in which processing time, set up ...Alexander Decker
This document summarizes an algorithm for optimal three stage flow shop scheduling with processing times, set up times, and transportation times that have associated probabilities. Jobs are processed in two disjoint job blocks in a string. The algorithm introduces two fictional machines to reduce the problem to a standard form. It then calculates processing times for equivalent jobs and job blocks on the fictional machines. The jobs are then sequenced to minimize total elapsed time based on their processing times on the fictional machines.
11.optimal three stage flow shop scheduling in which processing time, set up ...
R0260950100
1. International Journal Of Computational Engineering Research (ijceronline.com) Vol. 2 Issue. 6
An Improved Heuristic for Permutation Flow Shop Scheduling
(NEH ALGORITHM)
1
Ekta Singhal, 2Shalu Singh, 3Aneesh Dayma
(Department of Software Engineering),
3
(Department of Computer Science), Suresh Gyan Vihar University,Jaipur
Abstract- Flowshop Scheduling is used to determine the It is in the set of NP (nondeterministic polynomial
optimal sequence of n jobs to be processed on m machines time) problems: Any given solution to L can be verified
in the same order. Permutation Flowshop Scheduling quickly (in polynomial time).
Problems (PFSP) require same job sequence on all the It is also in the set of NP-hard problems: Any NP
machines with the constraint that machines can only process problem can be converted into L by a transformation of the
one job at a time and jobs can be processed by only one inputs in polynomial time. Although any given solution to
machine at a time. No machine is allowed to remain idle such a problem can be verified quickly, there is no known
when a job is ready for processing. Such problems are NP- efficient way to locate a solution in the first place; indeed,
Complete and hence optimal solutions are not guaranteed the most notable characteristic of NP-complete problems is
but heuristics have been shown to produce good working that no fast solution to them is known. That is, the time
solutions. required to solve the problem using any currently known
NEH (Nawaz, Enscore, Ham) Algorithm is an algorithm increases very quickly as the size of the problem
efficient algorithm that works by minimizing the makespan grows.
for Permutation Flowshop Scheduling Problems PFSP. The 1.1.5 Makespan
proposed algorithm is obtained by modifying the NEH Makespan is the completion time of last job on last
algorithm and produces improved quality solutions with machine.
algorithmic complexity same as the original algorithm. 1.1.6 Constructive Heuristics
In constructive heuristics once a decision is taken it cannot
Keywords: Flowshop Scheduling, heuristics, makespan be changed for improvement[10].
I. Introduction 1.1.7 Improvement Heuristics
1.1 Important Definitions Pawel J. Kalczynski, Jerzy Kamburowski [3] used
1.1.1 Heuristics improvement heuristics, we start with an initial sequence
Heuristic refers to experience-based techniques for problem and attempt to improve it as we proceed.
solving, learning, and discovery. Heuristic methods are used
to speed up the process of finding a good enough solution, 1.2 Problem Definition
where an exhaustive search is impractical[6]. The permutation flow shop problem requires to find the
order in which n jobs are to be processed on m consecutive
1.1.2 Flowshop Scheduling machines. The jobs are processed in the order machine 1,
Flowshop Scheduling determines an optimum sequence of n machine 2, . . . machine m.
jobs to be processed on m machines in the same order i.e. Machines can only process one job at a time and jobs can
every job must be processed on machines 1,2,...,m in this be processed by only one machine at a time without
same order[10]. preemption.
No job can jump over any other job, meaning that the order
1.1.3 Permutation Flowshop Scheduling in which jobs are processed in machine 1 is maintained
Permutation Flowshop Scheduling is a special case of FSPs throughout the system. Moreover, no machine is allowed to
where same job sequence is followed in all machines i.e. remain idle when a job is ready for processing. All jobs and
processing order of the jobs on the machines is the same for machines are available at time 0.
every machine.
II. OBJECTIVE
1.1.4 NP-Complete For each job two parameters are computed:
A problem L is NP-complete if it has two properties: tp (i, j) processing time of job j on machine i
tc (i, j) completion time of job j on machine i
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The completion time of all jobs is can be computed as:
Machin Machin Machin Machin Machin
tc (M1, J1) = tp (M1, J1) e1 e2 e3 e4 e5
tc (Mi, J1) = tc (Mi-1, J1) + tp (Mi, J1)
tc (M1, Jj) = tc (M1, Jj-1) + tp (M1, Jj) Job 1 5 9 8 10 1
tc (Mi, Jj) = max {tc (Mi-1, Jj), tc (Mi, Jj-1)} + tp (Mi, Jj) (J1)
The objective is to find an n-job sequence so as to minimize Job 2 9 3 10 1 8
the makespan i.e. tc (Mm, Jn). (J2)
III. Neh Algorithm (Nawaz Enscore Ham) Job 3 9 4 5 8 6
It is a constructive heuristic. (J3)
Step 1: Sort the n jobs in non-increasing order of their total
processing times Job 4 4 8 8 7 2
(J4)
Step 2: Take the first two jobs and schedule them in order to
minimise the partial makespan as if there were only these Job 5 3 5 6 3 7
two jobs (J5)
Step 3: For k= 3 to n do Step 4
Total processing times of jobs
Job 1= 5+9+8+10+1= 33
Step 4: Insert the kth job at the place, which minimises the
Job 2= 9+3+10+1+8= 31
partial makespan among the k possible ones.
Job 3= 9+4+5+8+6= 32
Job 4= 4+8+8+7+2= 29
IV. Improved Heuristic Job 5= 3+5+6+3+7= 24
Step 1: Sort the n jobs in non-increasing order of their total
processing times Sorting in non-increasing order of total processing times
J1, J3, J2, J4, J5
Step 2: Take the first four jobs from the sorted list and form
4! = 24 partial sequences (each of length 4). The best k (k is NEH Algorithm
a parameter of the algorithm) out of these 24 partial
sequences are selected for further processing. The relative
positions of jobs in any partial sequence is not altered in any
later (larger) sequence
Step 3: Set z = 5
Step 4: The zth job on the sorted list is inserted at each of
the z positions in each of the k (z − 1)-job partial sequences,
resulting in (z × k) z-job partial sequences
Step 5: The best k out of the z × k sequences are selected for Fig: 1
further processing
Step 6: Increment z by 1
Step 7: If z > n, accept the best of the k n-job sequences as
the final solution and stop.
Otherwise go to step 4.
V. Comparision (EXAMPLE)
Comparison (Example) Fig: 2
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Fig: 14
Fig: 10 Sequence:
J5- J4-J3-J1-J2
Makespan: 58
Sequence: J4-
J5- J3-J1-J2 Makespan: 58
Sequence: J4-
J3- J5-J1-J2
Makespan: 59
Sequence: J4-J3-J1-J5-J2 Makespan: 63
Sequence: J4-J3-J1-J2-J5 Makespan: 61
Fig: 11 Thus, the best sequence is J5-J4-J3-J2-J1 and J4-J5-J3-J1-
J2 with makespan of 58.
VI. Improved Heuristic
Taking first four jobs from the sorted order to form 24
partial sequences.
Sequence: J1-J2-J3-J4 Makespan: 59
Sequence: J1-J4-J2-J3 Makespan: 59
Sequence: J1-J3-J2-J4 Makespan: 57
Sequence: J1-J4-J3-J2 Makespan: 61
Sequence: J3-J1-J2-J4 Makespan: 58
Fig: 12 Sequence: J3-J4-J1-J2 Makespan: 57
Sequence: J2-J1-J3-J4 Makespan: 58
Sequence: J2-J4-J1-J3 Makespan: 62
Sequence: J2-J3-J1-J4 Makespan: 58
Sequence: J2-J4-J3-J1 Makespan: 56
Sequence: J3-J2-J1-J4 Makespan: 58
Sequence: J3-J4-J2-J1 Makespan: 58
Sequence: J1-J2-J4-J3 Makespan: 61
Sequence: J4-J1-J2-J3 Makespan: 58
Sequence: J1-J3-J4-J2 Makespan: 58
Sequence: J4-J1-J3-J2 Makespan: 63
Sequence: J3-J1-J4-J2 Makespan: 58
Fig: 13 Sequence: J4-J3-J1-J2 Makespan: 54
Sequence: J2-J1-J4-J3 Makespan: 62
Sequence: J4-J2-J1-J3 Makespan: 63
Sequence: J3-J2-J4-J1 Makespan: 58
Sequence: J4-J3-J2-J1 Makespan: 55
Sequence: J4-J2-J3-J1 Makespan: 55
Sequence: J2-J3-J4-J1 Makespan: 57
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The parameter of the algorithm k is taken as 7. J4-J5-J3-J1-J2
Selecting the best 7 sequences for further processing.
J5-J4-J3-J2-J1
J4-J3-J1-J2
Sequence: J5-J4-J3-J1-J2 Makespan: 58 J5-J4-J2-J3-J1
Sequence: J4-J5-J3-J1-J2 Makespan: 58
Sequence: J4-J3-J5-J1-J2 Makespan: 59 with makespan of 58.
Sequence: J4-J3-J1-J5-J2 Makespan: 63
Sequence: J4-J3-J1-J2-J5 Makespan: 61
VII. Complexity
J4-J3-J2-J1 Complexity of NEH Algorithm
Sequence: J5-J4-J3-J2-J1 Makespan: 58 The total number of enumerations in Neh is given by
Sequence: J4-J5-J3-J2-J1 Makespan: 60 n(n+1)/2
Sequence: J4-J3-J5-J2-J1 Makespan: 60 which clearly states that the complexity of this algorithm is
Sequence: J4-J3-J2-J5-J1 Makespan: 60 Θ(n^2).
Sequence: J4-J3-J2-J1-J5 Makespan: 64
Complexity of improved heuristic
J4-J2-J3-J1 The total number of enumerations in case of the improved
Sequence: J5-J4-J2-J3-J1 Makespan: 58 heuristic is given by[18]
Sequence: J4-J5-J2-J3-J1 Makespan: 60 4! + ∑, (z=5 to n) k * z
Sequence: J4-J2-J5-J3-J1 Makespan: 60 = 4! + k * ∑, (z=5 to n) z
Sequence: J4-J2-J3-J5-J1 Makespan: 60 Where, k denotes the algorithm parameter,
Sequence: J4-J2-J3-J1-J5 Makespan: 64 And n is the number of jobs.
Hence, the algorithmic complexity of this approach is
J2-J4-J3-J1 Θ(n^2).
Sequence: J5-J2-J4-J3-J1 Makespan: 60
Sequence: J2-J5-J4-J3-J1 Makespan: 62 VIII. Conclusions
Sequence: J2-J4-J5-J3-J1 Makespan: 60 The improved heuristic proposed for PFSP yields better
Sequence: J2-J4-J3-J5-J1 Makespan: 60 result than original NEH algorithm while maintaining the
Sequence: J2-J4-J3-J1-J5 Makespan: 65 same algorithmic complexity.
As shown using an example, the improved heuristic
J2-J3-J4-J1 generates more number of minimum makespan sequences as
Sequence: J5-J2-J3-J4-J1 Makespan: 62 compared to the NEH algorithm and hence we have more
Sequence: J2-J5-J3-J4-J1 Makespan: 61 options of job sequences that can be implemented for
Sequence: J2-J3-J5-J4-J1 Makespan: 63 greater production.
Sequence: J2-J3-J4-J5-J1 Makespan: 63 Experimental studies show that the improved heuristic for
Sequence: J2-J3-J4-J1-J5 Makespan: 67 PFSP results in sequences with lower makespan as
compared to those obtained from NEH algorithm in case of
J1-J3-J2-J4 medium sized (n=12 – 30) and large sized (n>70) problems.
Sequence: J5-J1-J3-J2-J4 Makespan: 59
Sequence: J1-J5-J3-J2-J4 Makespan: 60
IX. Future Scope
Sequence: J1-J3-J5-J2-J4 Makespan: 63
NEH is considered to be the best known heuristic for
Sequence: J1-J3-J2-J5-J4 Makespan: 63
PFSPs. But the proposed heuristic has been proved to
Sequence: J1-J3-J2-J4-J5 Makespan: 63
outperform NEH.
Hence, this heuristic has a great scope in industry where n
J3-J4-J1-J2
jobs are required to be scheduled on m machines for greater
Sequence: J5-J3-J4-J1-J2 Makespan: 60
production, efficient planning of resources and maintaining
Sequence: J3-J5-J4-J1-J2 Makespan: 62
proper control over the industry.
Sequence: J3-J4-J5-J1-J2 Makespan: 62
Sequence: J3-J4-J1-J5-J2 Makespan: 66
Sequence: J3-J4-J1-J2-J5 Makespan: 64
Thus, the best sequences are
J5-J4-J3-J1-J2
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