This document summarizes an ant colony optimization algorithm for solving job shop scheduling problems. It describes how ant colony optimization is inspired by the behavior of real ants finding shortest paths between their nest and food sources. The algorithm models artificial ants probabilistically constructing solutions to the job shop scheduling problem. The ants are guided by pheromone trails and heuristic information associated with edges in a graph representation of the problem. The pheromone trails, representing learned desirability of choices, are updated based on the quality of the solutions constructed by the ants. The algorithm aims to find high-quality solutions with relatively few evaluations of the objective function for minimizing makespan in job shop scheduling problems.
MULTIPROCESSOR SCHEDULING AND PERFORMANCE EVALUATION USING ELITIST NON DOMINA...ijcsa
Task scheduling plays an important part in the improvement of parallel and distributed systems. The problem of task scheduling has been shown to be NP hard. The time consuming is more to solve the problem in deterministic techniques. There are algorithms developed to schedule tasks for distributed environment, which focus on single objective. The problem becomes more complex, while considering biobjective.This paper presents bi-objective independent task scheduling algorithm using elitist Nondominated
sorting genetic algorithm (NSGA-II) to minimize the makespan and flowtime. This algorithm generates pareto global optimal solutions for this bi-objective task scheduling problem. NSGA-II is implemented by using the set of benchmark instances. The experimental result shows NSGA-II generates efficient optimal schedules.
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
applications.
Efficient dispatching rules based on data mining for the single machine sched...csandit
In manufacturing the solutions found for scheduling
problems and the human expert’s
experience are very important. They can be transfor
med using Artificial Intelligence techniques
into knowledge and this knowledge could be used to
solve new scheduling problems. In this
paper we use Decision Trees for the generation of n
ew Dispatching Rules for a Single Machine
shop solved using a Genetic Algorithm. Two heuristi
cs are proposed to use the new Dispatching
Rules and a comparative study with other Dispatchin
g Rules from the literature is presented.
EFFICIENT USE OF HYBRID ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM COMBINED WITH N...csandit
This research study proposes a novel method for automatic fault prediction from foundry data
introducing the so-called Meta Prediction Function (MPF). Kernel Principal Component
Analysis (KPCA) is used for dimension reduction. Different algorithms are used for building the
MPF such as Multiple Linear Regression (MLR), Adaptive Neuro Fuzzy Inference System
(ANFIS), Support Vector Machine (SVM) and Neural Network (NN). We used classical
machine learning methods such as ANFIS, SVM and NN for comparison with our proposed
MPF. Our empirical results show that the MPF consistently outperform the classical methods.
MULTIPROCESSOR SCHEDULING AND PERFORMANCE EVALUATION USING ELITIST NON DOMINA...ijcsa
Task scheduling plays an important part in the improvement of parallel and distributed systems. The problem of task scheduling has been shown to be NP hard. The time consuming is more to solve the problem in deterministic techniques. There are algorithms developed to schedule tasks for distributed environment, which focus on single objective. The problem becomes more complex, while considering biobjective.This paper presents bi-objective independent task scheduling algorithm using elitist Nondominated
sorting genetic algorithm (NSGA-II) to minimize the makespan and flowtime. This algorithm generates pareto global optimal solutions for this bi-objective task scheduling problem. NSGA-II is implemented by using the set of benchmark instances. The experimental result shows NSGA-II generates efficient optimal schedules.
Multi objective predictive control a solution using metaheuristicsijcsit
The application of multi objective model predictive control approaches is significantly limited with
computation time associated with optimization algorithms. Metaheuristics are general purpose heuristics
that have been successfully used in solving difficult optimization problems in a reasonable computation
time. In this work , we use and compare two multi objective metaheuristics, Multi-Objective Particle
swarm Optimization, MOPSO, and Multi-Objective Gravitational Search Algorithm, MOGSA, to generate
a set of approximately Pareto-optimal solutions in a single run. Two examples are studied, a nonlinear
system consisting of two mobile robots tracking trajectories and avoiding obstacles and a linear multi
variable system. The computation times and the quality of the solution in terms of the smoothness of the
control signals and precision of tracking show that MOPSO can be an alternative for real time
applications.
Efficient dispatching rules based on data mining for the single machine sched...csandit
In manufacturing the solutions found for scheduling
problems and the human expert’s
experience are very important. They can be transfor
med using Artificial Intelligence techniques
into knowledge and this knowledge could be used to
solve new scheduling problems. In this
paper we use Decision Trees for the generation of n
ew Dispatching Rules for a Single Machine
shop solved using a Genetic Algorithm. Two heuristi
cs are proposed to use the new Dispatching
Rules and a comparative study with other Dispatchin
g Rules from the literature is presented.
EFFICIENT USE OF HYBRID ADAPTIVE NEURO-FUZZY INFERENCE SYSTEM COMBINED WITH N...csandit
This research study proposes a novel method for automatic fault prediction from foundry data
introducing the so-called Meta Prediction Function (MPF). Kernel Principal Component
Analysis (KPCA) is used for dimension reduction. Different algorithms are used for building the
MPF such as Multiple Linear Regression (MLR), Adaptive Neuro Fuzzy Inference System
(ANFIS), Support Vector Machine (SVM) and Neural Network (NN). We used classical
machine learning methods such as ANFIS, SVM and NN for comparison with our proposed
MPF. Our empirical results show that the MPF consistently outperform the classical methods.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Scheduling By Using Fuzzy Logic in ManufacturingIJERA Editor
This paper represents the scheduling process in furniture manufacturing unit. It gives the fuzzy logic application in flexible manufacturing system. Flexible manufacturing systems are production system in furniture manufacturing unit. FMS consist of same multipurpose numerically controlled machines. Here in this project the scheduling has been done in FMS by using fuzzy logic tool in Matlab software. The fuzzy logic based scheduling model in this paper will deals with the job and best alternative route selection with multi-criteria of machine. Here two criteria for job and sequencing and routing with rules. This model is applicable to the scheduling of any manufacturing industry.
Multi-way Array Decomposition on Acoustic Source Separation for Fault Diagnos...IJECEIAES
In this study, we propose a multi-way array decomposition approach to solve the complexity of approximate joint diagonalization process for fault diagnosis of a motor-pump system. Sources used in this study came from drive end-motor, nondrive end-motor, drive end pump, and nondrive end pump. An approximate joint diagonalization is a common approach to resolving an underdetermined cases in blind source separation. However, it has quite heavy computation and requires more complexity. In this study, we use an acoustic emission to detect faults based on multi-way array decomposition approach. Based on the obtained results, the difference types of machinery fault such as misalignment and outer bearing fault can be detected by vibration spectrum and estimated acoustic spectrum. The performance of proposed method is evaluated using MSE and LSD. Based on the results of the separation, the estimated signal of the nondrive end pump is the closest to the baseline signal compared to other signals with LSD is 1.914 and MSE is 0.0707. The instantaneous frequency of the estimated source signal will also be compared with the vibration signal in frequency spectrum to test the effectiveness of the proposed method.
MARKOV CHAIN AND ADAPTIVE PARAMETER SELECTION ON PARTICLE SWARM OPTIMIZERijsc
Particle Swarm Optimizer (PSO) is such a complex stochastic process so that analysis on the stochastic
behavior of the PSO is not easy. The choosing of parameters plays an important role since it is critical in
the performance of PSO. As far as our investigation is concerned, most of the relevant researches are
based on computer simulations and few of them are based on theoretical approach. In this paper,
theoretical approach is used to investigate the behavior of PSO. Firstly, a state of PSO is defined in this
paper, which contains all the information needed for the future evolution. Then the memory-less property of
the state defined in this paper is investigated and proved. Secondly, by using the concept of the state and
suitably dividing the whole process of PSO into countable number of stages (levels), a stationary Markov
chain is established. Finally, according to the property of a stationary Markov chain, an adaptive method
for parameter selection is proposed.
Performance is a process of assessment of the algorithm. Speed and security is the performance to be achieved in determining which algorithm is better to use. In determining the optimum route, there are two algorithms that can be used for comparison. The Genetic and Primary algorithms are two very popular algorithms for determining the optimum route on the graph. Prim can minimize circuit to avoid connected loop. Prim will determine the best route based on active vertex. This algorithm is especially useful when applied in a minimum spanning tree case. Genetics works with probability properties. Genetics cannot determine which route has the maximum value. However, genetics can determine the overall optimum route based on appropriate parameters. Each algorithm can be used for the case of the shortest path, minimum spanning tree or traveling salesman problem. The Prim algorithm is superior to the speed of Genetics. The strength of the Genetic algorithm lies in the number of generations and population generated as well as the selection, crossover and mutation processes as the resultant support. The disadvantage of the Genetic algorithm is spending to much time to get the desired result. Overall, the Prim algorithm has better performance than Genetic especially for a large number of vertices.
Performance analysis of real-time and general-purpose operating systems for p...IJECEIAES
In general, modern operating systems can be divided into two essential parts, real-time operating systems (RTOS) and general-purpose operating systems (GPOS). The main difference between GPOS and RTOS is the system is time-critical or not. It means that; in GPOS, a high-priority thread cannot preempt a kernel call. But, in RTOS, a low-priority task is preempted by a high-priority task if necessary, even if it’s executing a kernel call. Most Linux distributions can be used as both GPOS and RTOS with kernel modifications. In this study, two Linux distributions, Ubuntu and Pardus, were analyzed and their performances were compared both as GPOS and RTOS for path planning of the multi-robot systems. Robot groups with different numbers of members were used to perform the path tracking tasks using both Ubuntu and Pardus as GPOS and RTOS. In this way, both the performance of two different Linux distributions in robotic applications were observed and compared in two forms, GPOS, and RTOS.
APPLYING DYNAMIC MODEL FOR MULTIPLE MANOEUVRING TARGET TRACKING USING PARTICL...IJITCA Journal
In this paper, we applied a dynamic model for manoeuvring targets in SIR particle filter algorithm for improving tracking accuracy of multiple manoeuvring targets. In our proposed approach, a color distribution model is used to detect changes of target's model . Our proposed approach controls
deformation of target's model. If deformation of target's model is larger than a predetermined threshold,then the model will be updated. Global Nearest Neighbor (GNN) algorithm is used as data association algorithm. We named our proposed method as Deformation Detection Particle Filter (DDPF) . DDPF
approach is compared with basic SIR-PF algorithm on real airshow videos. Comparisons results show that, the basic SIR-PF algorithm is not able to track the manoeuvring targets when the rotation or scaling is occurred in target' s model. However, DDPF approach updates target's model when the rotation or
scaling is occurred. Thus, the proposed approach is able to track the manoeuvring targets more efficiently
and accurately.
Face recognition based on curvelets, invariant moments features and SVMTELKOMNIKA JOURNAL
Recent studies highlighted on face recognition methods. In this paper, a new algorithm is proposed for face recognition by combining Fast Discrete Curvelet Transform (FDCvT) and Invariant Moments with Support vector machine (SVM), which improves rate of face recognition in various situations. The reason of using this approach depends on two things. first, Curvelet transform which is a multi-resolution method, that can efficiently represent image edge discontinuities; Second, the Invariant Moments analysis which is a statistical method that meets with the translation, rotation and scale invariance in the image. Furthermore, SVM is employed to classify the face image based on the extracted features. This process is applied on each of ORL and Yale databases to evaluate the performance of the suggested method. Experimentally, the proposed method results show that our system can compose efficient and reasonable face recognition feature, and obtain useful recognition accuracy, which is able to face and side-face states detection of persons to decrease fault rate of production.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
An Efficient Heuristic Algorithm for Flexible Job Shop Scheduling with Mainte...mathsjournal
This paper deals with the flexible job shop scheduling problem with the preventive maintenance constraints where the objectives are to minimize the overall completion time (makespan), the total workload of machines and the workload of the most loaded machine. A fast heuristic algorithm based on a constructive procedure is developed to solve the problem in very short time. The algorithm is tested on the benchmark instances from the literature in order to evaluate its performance. Computational results show that, the proposed heuristic method is computationally efficient and promising for practical problems.
AN EFFICIENT HEURISTIC ALGORITHM FOR FLEXIBLE JOB SHOP SCHEDULING WITH MAINTE...mathsjournal
This paper deals with the flexible job shop scheduling problem with the preventive maintenance constraints where the objectives are to minimize the overall completion time (makespan), the total workload of machines and
the workload of the most loaded machine. A fast heuristic algorithm based on a constructive procedure is developed to solve the problem in very short time. The algorithm is tested on the benchmark instances from the
literature in order to evaluate its performance. Computational results show that, the proposed heuristic method is computationally efficient and promising for practical problems.
Hybrid Genetic Algorithm with Multiparents Crossover for Job Shop Scheduling ...CHUNG SIN ONG
The job shop scheduling problem (JSSP) is one of the well-known hard combinatorial scheduling problems. This paper proposes a hybrid genetic algorithm withmultiparents crossover for JSSP.Themultiparents crossover operator known as extended precedence preservative crossover (EPPX) is able to recombine more than two parents to generate a single new offspring distinguished from common crossover operators that recombine only two parents. This algorithm also embeds a schedule generation procedure to generate full-active schedule that satisfies precedence constraints in order to reduce the search space. Once a schedule is obtained, a neighborhood search is applied to exploit the search space for better solutions and to enhance the GA. This hybrid genetic algorithm is simulated on a set of benchmarks from the literatures and the results are compared with other approaches to ensure the sustainability of this algorithm in solving JSSP. The results suggest that the implementation of multiparents crossover produces competitive results.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Scheduling By Using Fuzzy Logic in ManufacturingIJERA Editor
This paper represents the scheduling process in furniture manufacturing unit. It gives the fuzzy logic application in flexible manufacturing system. Flexible manufacturing systems are production system in furniture manufacturing unit. FMS consist of same multipurpose numerically controlled machines. Here in this project the scheduling has been done in FMS by using fuzzy logic tool in Matlab software. The fuzzy logic based scheduling model in this paper will deals with the job and best alternative route selection with multi-criteria of machine. Here two criteria for job and sequencing and routing with rules. This model is applicable to the scheduling of any manufacturing industry.
Multi-way Array Decomposition on Acoustic Source Separation for Fault Diagnos...IJECEIAES
In this study, we propose a multi-way array decomposition approach to solve the complexity of approximate joint diagonalization process for fault diagnosis of a motor-pump system. Sources used in this study came from drive end-motor, nondrive end-motor, drive end pump, and nondrive end pump. An approximate joint diagonalization is a common approach to resolving an underdetermined cases in blind source separation. However, it has quite heavy computation and requires more complexity. In this study, we use an acoustic emission to detect faults based on multi-way array decomposition approach. Based on the obtained results, the difference types of machinery fault such as misalignment and outer bearing fault can be detected by vibration spectrum and estimated acoustic spectrum. The performance of proposed method is evaluated using MSE and LSD. Based on the results of the separation, the estimated signal of the nondrive end pump is the closest to the baseline signal compared to other signals with LSD is 1.914 and MSE is 0.0707. The instantaneous frequency of the estimated source signal will also be compared with the vibration signal in frequency spectrum to test the effectiveness of the proposed method.
MARKOV CHAIN AND ADAPTIVE PARAMETER SELECTION ON PARTICLE SWARM OPTIMIZERijsc
Particle Swarm Optimizer (PSO) is such a complex stochastic process so that analysis on the stochastic
behavior of the PSO is not easy. The choosing of parameters plays an important role since it is critical in
the performance of PSO. As far as our investigation is concerned, most of the relevant researches are
based on computer simulations and few of them are based on theoretical approach. In this paper,
theoretical approach is used to investigate the behavior of PSO. Firstly, a state of PSO is defined in this
paper, which contains all the information needed for the future evolution. Then the memory-less property of
the state defined in this paper is investigated and proved. Secondly, by using the concept of the state and
suitably dividing the whole process of PSO into countable number of stages (levels), a stationary Markov
chain is established. Finally, according to the property of a stationary Markov chain, an adaptive method
for parameter selection is proposed.
Performance is a process of assessment of the algorithm. Speed and security is the performance to be achieved in determining which algorithm is better to use. In determining the optimum route, there are two algorithms that can be used for comparison. The Genetic and Primary algorithms are two very popular algorithms for determining the optimum route on the graph. Prim can minimize circuit to avoid connected loop. Prim will determine the best route based on active vertex. This algorithm is especially useful when applied in a minimum spanning tree case. Genetics works with probability properties. Genetics cannot determine which route has the maximum value. However, genetics can determine the overall optimum route based on appropriate parameters. Each algorithm can be used for the case of the shortest path, minimum spanning tree or traveling salesman problem. The Prim algorithm is superior to the speed of Genetics. The strength of the Genetic algorithm lies in the number of generations and population generated as well as the selection, crossover and mutation processes as the resultant support. The disadvantage of the Genetic algorithm is spending to much time to get the desired result. Overall, the Prim algorithm has better performance than Genetic especially for a large number of vertices.
Performance analysis of real-time and general-purpose operating systems for p...IJECEIAES
In general, modern operating systems can be divided into two essential parts, real-time operating systems (RTOS) and general-purpose operating systems (GPOS). The main difference between GPOS and RTOS is the system is time-critical or not. It means that; in GPOS, a high-priority thread cannot preempt a kernel call. But, in RTOS, a low-priority task is preempted by a high-priority task if necessary, even if it’s executing a kernel call. Most Linux distributions can be used as both GPOS and RTOS with kernel modifications. In this study, two Linux distributions, Ubuntu and Pardus, were analyzed and their performances were compared both as GPOS and RTOS for path planning of the multi-robot systems. Robot groups with different numbers of members were used to perform the path tracking tasks using both Ubuntu and Pardus as GPOS and RTOS. In this way, both the performance of two different Linux distributions in robotic applications were observed and compared in two forms, GPOS, and RTOS.
APPLYING DYNAMIC MODEL FOR MULTIPLE MANOEUVRING TARGET TRACKING USING PARTICL...IJITCA Journal
In this paper, we applied a dynamic model for manoeuvring targets in SIR particle filter algorithm for improving tracking accuracy of multiple manoeuvring targets. In our proposed approach, a color distribution model is used to detect changes of target's model . Our proposed approach controls
deformation of target's model. If deformation of target's model is larger than a predetermined threshold,then the model will be updated. Global Nearest Neighbor (GNN) algorithm is used as data association algorithm. We named our proposed method as Deformation Detection Particle Filter (DDPF) . DDPF
approach is compared with basic SIR-PF algorithm on real airshow videos. Comparisons results show that, the basic SIR-PF algorithm is not able to track the manoeuvring targets when the rotation or scaling is occurred in target' s model. However, DDPF approach updates target's model when the rotation or
scaling is occurred. Thus, the proposed approach is able to track the manoeuvring targets more efficiently
and accurately.
Face recognition based on curvelets, invariant moments features and SVMTELKOMNIKA JOURNAL
Recent studies highlighted on face recognition methods. In this paper, a new algorithm is proposed for face recognition by combining Fast Discrete Curvelet Transform (FDCvT) and Invariant Moments with Support vector machine (SVM), which improves rate of face recognition in various situations. The reason of using this approach depends on two things. first, Curvelet transform which is a multi-resolution method, that can efficiently represent image edge discontinuities; Second, the Invariant Moments analysis which is a statistical method that meets with the translation, rotation and scale invariance in the image. Furthermore, SVM is employed to classify the face image based on the extracted features. This process is applied on each of ORL and Yale databases to evaluate the performance of the suggested method. Experimentally, the proposed method results show that our system can compose efficient and reasonable face recognition feature, and obtain useful recognition accuracy, which is able to face and side-face states detection of persons to decrease fault rate of production.
IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com
An Efficient Heuristic Algorithm for Flexible Job Shop Scheduling with Mainte...mathsjournal
This paper deals with the flexible job shop scheduling problem with the preventive maintenance constraints where the objectives are to minimize the overall completion time (makespan), the total workload of machines and the workload of the most loaded machine. A fast heuristic algorithm based on a constructive procedure is developed to solve the problem in very short time. The algorithm is tested on the benchmark instances from the literature in order to evaluate its performance. Computational results show that, the proposed heuristic method is computationally efficient and promising for practical problems.
AN EFFICIENT HEURISTIC ALGORITHM FOR FLEXIBLE JOB SHOP SCHEDULING WITH MAINTE...mathsjournal
This paper deals with the flexible job shop scheduling problem with the preventive maintenance constraints where the objectives are to minimize the overall completion time (makespan), the total workload of machines and
the workload of the most loaded machine. A fast heuristic algorithm based on a constructive procedure is developed to solve the problem in very short time. The algorithm is tested on the benchmark instances from the
literature in order to evaluate its performance. Computational results show that, the proposed heuristic method is computationally efficient and promising for practical problems.
Hybrid Genetic Algorithm with Multiparents Crossover for Job Shop Scheduling ...CHUNG SIN ONG
The job shop scheduling problem (JSSP) is one of the well-known hard combinatorial scheduling problems. This paper proposes a hybrid genetic algorithm withmultiparents crossover for JSSP.Themultiparents crossover operator known as extended precedence preservative crossover (EPPX) is able to recombine more than two parents to generate a single new offspring distinguished from common crossover operators that recombine only two parents. This algorithm also embeds a schedule generation procedure to generate full-active schedule that satisfies precedence constraints in order to reduce the search space. Once a schedule is obtained, a neighborhood search is applied to exploit the search space for better solutions and to enhance the GA. This hybrid genetic algorithm is simulated on a set of benchmarks from the literatures and the results are compared with other approaches to ensure the sustainability of this algorithm in solving JSSP. The results suggest that the implementation of multiparents crossover produces competitive results.
Presenting a new Ant Colony Optimization Algorithm (ACO) for Efficient Job Sc...Editor IJCATR
Grid computing utilizes the distributed heterogeneous resources in order to support complicated computing problems. Job
scheduling in computing grid is a very important problem. To utilize grids efficiently, we need a good job scheduling algorithm to assign
jobs to resources in grids.
In the natural environment, the ants have a tremendous ability to team up to find an optimal path to food resources. An ant algorithm
simulates the behavior of ants. In this paper, a new Ant Colony Optimization (ACO) algorithm is proposed for job scheduling in the
Grid environment. The main contribution of this paper is to minimize the makespan of a given set of jobs. Compared with the other job
scheduling algorithms, the proposed algorithm can outperform them according to the experimental results.
In this paper, a modified invasive weed optimization (IWO) algorithm is presented for
optimization of multiobjective flexible job shop scheduling problems (FJSSPs) with the criteria
to minimize the maximum completion time (makespan), the total workload of machines and the
workload of the critical machine. IWO is a bio-inspired metaheuristic that mimics the
ecological behaviour of weeds in colonizing and finding suitable place for growth and
reproduction. IWO is developed to solve continuous optimization problems that’s why the
heuristic rule the Smallest Position Value (SPV) is used to convert the continuous position
values to the discrete job sequences. The computational experiments show that the proposed
algorithm is highly competitive to the state-of-the-art methods in the literature since it is able to
find the optimal and best-known solutions on the instances studied.
Artificial Neural Networks can achieve high degree of computation rates by
employing a massive number of simple processing elements with a high degree of
connectivity between elements. In this paper an attempt is made to present a Constraint
Satisfaction Adaptive Neural Network (CSANN) to solve the generalized job-shop
scheduling problem and it shows how to map a difficult constraint satisfaction job-shop
scheduling problem onto a simple neural net, where the number of neural processors equals
the number of operations, and the number of interconnections grows linearly with the total
number of operations. The proposed neural network can be easily constructed and can adjust
its weights of connections based on the sequence and resource constraints of the job-shop
scheduling problem during its processing. Simulation studies have shown that the proposed
neural network produces better solutions to job-shop scheduling problem.
Modified artificial immune system for single row facility layout problemIAEME Publication
One of the main optimization algorithms currently available in the research field is an Artificial Immune System where abundant applications are using this algorithm for clustering and patter recognition processes. These algorithms are providing more effective optimized results in multi-model optimization problems than Genetic Algorithm.
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.
An efficient simulated annealing algorithm for a No-Wait Two Stage Flexible F...ijait
In this paper, no wait two stage flexible flow shop scheduling problem (FFSSP) is solved using two metaheuristic algorithms. This problem with minimum makespan performance measure is NP-Hard. The proposed algorithms are Simulated Annealing and Genetic Algorithm. The results are analyzed in terms of Relative Percentage Deviation of Makespan. The performance of the proposed algorithms are studied and compared with that of MDA algorithm. For this propose a number of problems in different sizes are solved. The results of the studies proposes the effective algorithm. This is followed by describing the
outline of the study, concluding remarks and suggesting potential areas for further researches
An efficient simulated annealing algorithm for a No-Wait Two Stage Flexible F...ijait
In this paper, no wait two stage flexible flow shop scheduling problem (FFSSP) is solved using two metaheuristic algorithms. This problem with minimum makespan performance measure is NP-Hard. The proposed algorithms are Simulated Annealing and Genetic Algorithm. The results are analyzed in terms of Relative Percentage Deviation of Makespan. The performance of the proposed algorithms are studied and compared with that of MDA algorithm. For this propose a number of problems in different sizes are solved. The results of the studies proposes the effective algorithm. This is followed by describing the outline of the study, concluding remarks and suggesting potential areas for further researches
Proposing a New Job Scheduling Algorithm in Grid Environment Using a Combinat...Editor IJCATR
Scheduling jobs to resources in grid computing is complicated due to the distributed and heterogeneous nature of the resources.
The purpose of job scheduling in grid environment is to achieve high system throughput and minimize the execution time of applications.
The complexity of scheduling problem increases with the size of the grid and becomes highly difficult to solve effectively.
To obtain a good and efficient method to solve scheduling problems in grid, a new area of research is implemented. In this paper, a job
scheduling algorithm is proposed to assign jobs to available resources in grid environment. The proposed algorithm is based on Ant
Colony Optimization (ACO) algorithm. This algorithm is combined with one of the best scheduling algorithm, Suffrage. This paper uses
the result of Suffrage in proposed ACO algorithm. The main contribution of this work is to minimize the makespan of a given set of
jobs. The experimental results show that the proposed algorithm can lead to significant performance in grid environment.
In industries, the completion time of job problems in the manufacturing unit has risen significantly. In several types of current study, the job's completion time, or makespan, is reduced by taking straight paths, which is time-consuming. In this paper, we used an Improved Ant Colony Optimization and Tabu Search (ACOTS) algorithm to solve this problem by precisely defining the fault occurrence location in order to rollback. We have used a short-term memory-based rollback recovery strategy to minimise the job's completion time by rolling back to its own short-term memory. The recent movements in Tabu quest are visited using short term memory. As compared to the ACO algorithm, our proposed ACOTS-Cmax solution is more efficient and takes less time to complete.
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
Why You Should Replace Windows 11 with Nitrux Linux 3.5.0 for enhanced perfor...SOFTTECHHUB
The choice of an operating system plays a pivotal role in shaping our computing experience. For decades, Microsoft's Windows has dominated the market, offering a familiar and widely adopted platform for personal and professional use. However, as technological advancements continue to push the boundaries of innovation, alternative operating systems have emerged, challenging the status quo and offering users a fresh perspective on computing.
One such alternative that has garnered significant attention and acclaim is Nitrux Linux 3.5.0, a sleek, powerful, and user-friendly Linux distribution that promises to redefine the way we interact with our devices. With its focus on performance, security, and customization, Nitrux Linux presents a compelling case for those seeking to break free from the constraints of proprietary software and embrace the freedom and flexibility of open-source computing.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Climate Impact of Software Testing at Nordic Testing DaysKari Kakkonen
My slides at Nordic Testing Days 6.6.2024
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AN ANT COLONY OPTIMIZATION ALGORITHM FOR JOB SHOP SCHEDULING PROBLEM
1. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
DOI : 10.5121/ijaia.2013.4406 53
AN ANT COLONY OPTIMIZATION ALGORITHM FOR
JOB SHOP SCHEDULING PROBLEM
Edson Flórez1
, Wilfredo Gómez2
and MSc. Lola Bautista3
Universidad Industrial de Santander, Bucaramanga, Colombia
1
Systems Engineering Student
edson.florez@correo.uis.edu.co
2
Systems Engineer, member of the Research Group in Biomedical Engineering
wilfredo.gomez@correo.uis edu.co
3
Director of the Research Group in Biomedical Engineering
lxbautis@uis.edu.co
ABSTRACT
The nature has inspired several metaheuristics, outstanding among these is Ant Colony Optimization
(ACO), which have proved to be very effective and efficient in problems of high complexity (NP-hard) in
combinatorial optimization. This paper describes the implementation of an ACO model algorithm known as
Elitist Ant System (EAS), applied to a combinatorial optimization problem called Job Shop Scheduling
Problem (JSSP). We propose a method that seeks to reduce delays designating the operation immediately
available, but considering the operations that lack little to be available and have a greater amount of
pheromone. The performance of the algorithm was evaluated for problems of JSSP reference, comparing
the quality of the solutions obtained regarding the best known solution of the most effective methods. The
solutions were of good quality and obtained with a remarkable efficiency by having to make a very low
number of objective function evaluations.
KEYWORDS
Metaheuristics, Ant Colony Optimization, Swarm intelligence, Combinatorial Optimization, Job Shop
Scheduling Problem.
1. INTRODUCTION
ACO is a metaheuristic that brings together concepts from fields such as Artificial Intelligence
and Biology, inspired in the collective behavior of ants. These social insects form colonies of
ants, which are self-organizing systems and decentralized which are considered as a Swarm
Intelligence [12]. Thanks to that intelligence emerging from simple relationships between ants, a
colony can solve complex problems in their environment, such as the problem of finding the
shortest path between the colony and the food, which can be used to find the best solution for
combinatorial optimization problems.
In this paper, we apply the collective intelligence of many simple agents to the problem of Job
Shop Scheduling [22], which consists of finding an optimal plan that minimizes the makespan,
which is the time required to perform a finite number of tasks in a finite number of machines [13].
Each task is a sequence of operations, each one with a determined machine and processing time.
Feasible solutions must comply with the restrictions that apply to the problem of Job Shop
Scheduling, as respecting the precedence between operations determining the technological
2. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
54
sequence without interrupting any operations until completion [21]. The operations conform the
graph nodes that represent the problem, united by edges in which ants are moving. Each
individual only has local information of the system that shares through a hormone called
pheromone.
The update of the pheromone trail deposited on the edges can be done globally or locally. Ants
build roads that represent feasible solutions, guided by the pheromone trails and the heuristic
information of each edge [1]. For this reason the ant population performs a stochastic search,
selecting the next node to visit only based on information available locally, used on a
probabilistic approach where initially the ant decisions are completely random in the absence of
pheromone trails.
In the literature, several algorithms have been proposed following the ACO probabilistic
technique for finding approximate solutions to complex optimization problems. The first ACO
algorithm was Ant System (AS), proposed by Marco Dorigo in 1991 [26], and completed with the
contributions of Maniezzo and Colorni [1]. New developments gave better results, like Ant
Colony System (ACS) [2], the Max-Min Ant System (MMAS) [7], the Rank-based Ant System
(ASrank) [8], among others. This article presents a variant of Elitist Ant System, also proposed by
Dorigo as an improvement to SH [1], applied in JSSP instances widely used known as LA
instances, that were raised by Lawrence [11].
2. JSSP PROBLEM FORMULATION
The JSSP or resource planning problem (or jobs) consists in "accommodate resources over time
to perform a set of jobs" [6], building plan or execution sequence of jobs j in a set of m machines
[13], where an operation is every job that is processed in each machine (Operation(j, m)) and is
assigned a specific processing time.
This problem is presented in multiple human activities, taking applications to tasks such as
scheduling for packet delivery (eg airway), computer networks (networking), computers
(multitasking and multiprocessing), project management (agenda or plan), production and
administrative processes (eg assembly lines, etc.) [20].
JSSP must comply with certain restrictions in the execution of jobs and the goal is to complete
them in the shortest possible time. This time to optimize is known as makespan (CMAX) or
Maximum Workflow which forms the objective function to minimize given as
, where is the job completion time. It is a combinatorial
optimization problem because the number of candidate solutions is combinatorial in size with
variables of discrete nature, therefore the representation of the solutions are permutations over the
operations of each job, making it impossible to determine all possible solutions in a reasonable
time.
2.1. Computational complexity of JSSP
In 1976 Michael Garey [17] provided evidence that this problem is NP-hard for m> 2, ie cannot
be quickly found (polynomial-time) an optimal solution for JSSP with more than two machines.
Along with David Johnson in 1979, they finished demonstrating that JSSP is NP-hard [18], unless
in Computational Complexity Theory is proved that P = NP, if so, any problem that can be
checked quickly by a computer, it could also be quickly resolved by that computer.
The NP-hard complexity of JSSP lies in the vast number of possible combinations that arise
because each sequence of operations on a machine can be permuted independently of the
3. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
55
sequence of operations on another machine, so with a few jobs and machines can have
possible solutions which corresponds to the search space (S) of the problem.
2.2. Formal definition of Job Shop Scheduling Problem
Having [5]:
: Set of n jobs to be processed.
: Set of m machines or resources.
: Operation of the job that must be processed in the machine by .
: Uninterrupted period of processing time for each operation.
Objective function: Minimize
Subject to:
Start times restriction for each operation
Precedence constraint if preceding
Disjunctive restriction if preceding ,
in another case.
Where: , with .
The previous set of constraints of the JSSP is explained of this way [21]:
Start restriction: The time when an operation starts are not specified, so work can start at any
point in time as long as the required machine is available.
Restriction of precedence: Each job must go through a particular sequence of operations that is
predefined, so that operations cannot begin until the end of its predecessor, preventing the
processing of two operations of the same job simultaneously.
Restrictions disjunctive: A machine can process only one job at a time. Each operation must be
fully processed on a single machine and cannot be interrupted even if there are jobs waiting for
that machine to be available, for instance, no work may be processed more than once on the same
machine.
In addition to the above restrictions, we have determined that all operations have the same
priority of processing, and all machines are the same and can be idle at any time. The fulfillment
of these restrictions can be seen clearly by a Gantt chart (Figure 1), which shows an instance of
JSSP (Table 1) matrix defined by [15], in which it has an additional column to indicate that each
row of the matrix corresponds to a job (J1, J2 and J3).
Table 1. An instance of JSSP 3×3
Job (J) Machine (time)
Sequence: S1 S2 S3
J1 3 (4) 2 (3) 1 (3)
J2 2 (1) 3 (2) 1 (4)
J3 2 (3) 1 (2) 3 (3)
4. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
56
Figure 1. Gantt diagram of a 3×3 instance of JSSP
The JSSP is usually represented as a disjunctive graph G = (V, C ∪ D) [14], where V is
the set of nodes (Figure 2) representing the Operations (job, machine) with the exception
of starting node (I) and ending nodes (F) of the graph, C is a set of directed graphs (→)
linking operations corresponding to the same job (technological sequence), and D is a set
of undirected graphs connecting operations running on a same machine. In addition
the processing time of each operation is placed in the upper part of node.
Figure 2. Graph of a 3×3 instance of JSSP
The problem of Job Shop Scheduling has been tackled with methods that can only solve
instances of a limited number of operations, because they perform exhaustive searches to
find the exact solution, as Branch and Bound (B&B) proposed in 1960 [23], can solve
only up to 15 x 14, ie up to 220 operations [24]. So it must use approximate methods
(Table 2 [9]) like simulated annealing (SA), Tabu Search (TS) [10], Iterative Local
Search (ILS), GRASP, ACO, Evolutionary Algorithms (EA) as Artificial Immune System
(AIS) and Cultural algorithm (CULT), etc.
5. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
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Table 2. The main features of metaheuristics
Metaheuristic Features
SA
Acceptance criteria
Cooling Time
TS
Choosing neighbor (tabu list)
Suction Criterion
EC
Recombination
Mutation
Selection
ILS
Local search
Initial movement
Acceptance criteria
ACO
Construction probabilistic
Update pheromone
GRASP
Local Search
Restricted Candidate List (RCL)
3. ANT COLONY OPTIMIZATION
This bioinspired algorithm is based on a population of ants that perform a cooperative search. In
an experiment of the self-organization of Argentine ants made in 1989 [12], we observed the
feeding behavior of a colony of ants, that were able to find the shorter branches of a bridge
between the nest and the food (Figure 3), through the pheromone trail they leave behind when
moving.
Figure 3. Picture of a colony of ants that find the shortest path to the food [12]
The ants initially move randomly in search of food and along the way back to the colony the
pheromone is deposited. If another ant finds this trail, probably it will follow it increasing the
amount of pheromone, which further stimulates other ants to follow this path (Figure 4). But over
time the pheromone trail starts to evaporate and reduces its attractiveness, making more attractive
6. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
58
only the most used trajectories, causing convergence to an optimal solution that is the only path
that eventually most ants will follow. By the long road less pheromone accumulates because of
the low passing frequency of the ants when they spend more time completing their road.
Figure 4. A. ants in a pheromone trail between nest and food; B. an obstacle interrupts the trail; C. ants find
two paths to go around the obstacle; D. a new pheromone trail is formed along the shorter path [19]
In the ACO algorithms family, ant’s behavior is simulated with a virtual agent that has the
capacity to explore a limited search space and obtain information about the surrounding
environment. The artificial ant (k) moves from one node to another (from source node i to
destination node j), building step by step solution to be written to the Tabuk memory (that stores
information about the nodes sequence or route taken until time t), that ends when it reaches one of
the accepting states defined by the objective of the problem.
Thus, the ants can construct approximate solutions to complex problems such as sequencing,
assigning, planning or programming. Each edge of the graph has two types of associated
information that guide the movement of the ant [4] and whose values are modified by ants at each
iteration:
ηij Heuristic information that measures the heuristics preference of moving from node i to node j,
when touring the edge aij. Ants do not change this information during the execution of the
algorithm.
τij Information of artificial pheromone trails, that measures the "desirability learned" of the i to j
movement. This information is modified during the execution of the algorithm depending on the
solutions found by the ants to reflect the experience gained by these agents.
Pseudocode of the ACO metaheuristic [3]:
ACO procedure
Set parameters,Initialize the pheromone trails
scheduled activities
Construction of solutions by ants
Server of actions (Optional)
Updating pheromone
End-Scheduled activities
End-procedure
The metaheuristic consists of a parameter initialization step and three algorithmic procedures
whose activation is regulated by the builder Scheduled activities, in which is repeated until a
7. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
59
termination condition is met, such as reaching a maximum number of iterations or a maximum
CPU time. The three algorithmic procedures submitted to the Scheduled activities consist of [25]:
Construction of solutions by ants is the probabilistic construction of solutions by all the ants in a
colony, which visit the adjacent states of the considered problem. The ants can move by applying
a stochastic decision policy using information from the pheromone trails and the heuristic
information, with which ants incrementally construct a solution to the problem.
Server of actions are centralized actions that modify the behavior of the algorithm and cannot be
developed by ants individually. The most common is the local optimization or improvement of
the solutions with the application of a local search algorithm. The locally optimized solutions are
then used to set the values of the pheromone to update.
Updating pheromone is the process that updates the pheromone trails on each aij edge, called
posteriori online update or offline because it is performed at the end of a road. The amount of
pheromone that deposits each ant at the edges depends on the total length of the path (equation 3).
It also can perform a step by step online update of the pheromone trails, that is a local update or
in "real time" of the pheromone, performed when an ant moves from node i to node j. The
pheromone trail value is reduced by a constant evaporation of pheromone, which prevents
premature convergence of the algorithm by discarding the less frequented corners.
4. ELITIST ANT SYSTEM (EAS)
This version of the ACO implements a simple change to the Ant System that improves the results,
simply reinforcing the pheromone trail of the best path that is found in each iteration. At the
edges of the best generated solution by an ant, more pheromone is deposited through all the other
ants.
In this algorithm artificial ants perform a probabilistic construction of solutions in each cycle, for
which they require represent the problem by means of a graph in which the ants move along each
edge from one node to another to build roads that represent solutions from a randomly chosen
initial node, the following choice is the next node in this path is done according to the state
transition rule (equation 1).
Equation 1
Where α and β parameters determine the influence of the values of the pheromone information
and from the heuristic information ( ) respectively, over the decision of each ant (k). It seeks
that the edges with large amount of pheromone to be the most visible, having a higher transition
probability to the edges of the other nodes of the set of achievable operations. To have a balanced
algorithm (with an appropriate adjustment), α and β parameters must have appropriate values,
avoiding close to zero values, because if α = 0, only the heuristic information would indicate that
possible elements of the solution will have a higher probability of being selected, which
corresponds to a stochastic greedy algorithm (greedy), and if β = 0, will only be relevant the
amount of pheromone. In both cases the ants might get stuck in a local optimum, generating the
same solution in each iteration, without opportunities to find a better solution which could be the
8. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
60
global optimum solution. These parameters are normally set to integer values between 1 and 5,
but in this case we will relate them as follows with .
The amount of pheromone present at each edge of the road in the generation is given by
the equation 2.
Equation 2
Where is the contribution of the ant to the total pheromone of the generation and is
the evaporation rate of the pheromone. The reason for including the evaporation rate is that old
pheromone should not have much influence on future decisions of the ants. The amount of
pheromone that each ant is contributing depends on the quality of the solution obtained which is
inversely proportional to the cost of the solution of the objective function (equation 3).
Equation 3
Where is a constant and is the length of the makespan of the solution obtained by the ant.
To accelerate the convergence of the algorithm, increasing the visibility of the pheromone trail on
all edges of the shortest path, passing all elitists ants (e) of the system. Therefore, the equation 3
for the best path built in each cycle is replaced by the equation 2.
Equation 4
5. EAS IMPLEMENTATION FOR JSSP
The rapid convergence of this algorithm can reduce the scanning capability since the ants soon
will end in a single way, which can be a local optimum. To compensate this, is allowed to include
in the set of achievable operations (point 3.3 of pseudocode), operations that makes the machines
wait (on pause) some units of time to begin execution because the corresponding job is still active
on another machine. But this operation that delay or retards the onset of the machines will only be
selected if the edge that reaches the node, has enough pheromone to make the probability to be
greater than the operations that have immediately available jobs. That will only be given with
large amounts of pheromone, because having idle machines is not adequate and is penalized
lowering the visibility of the operation.
This method further explores the search space in order to obtain many solutions, from which it
can be obtained solutions that exceed the local optima found in the first iterations. These optimal
are the ones limiting the search, stopping it on solutions distant up to a 5% the global optimum.
The initial diversity of the algorithm is the one that ensures that the ants move towards the search
space where the path corresponding to the overall optimal solution is found. The following is the
pseudocode implemented to solve the JSSP:
9. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
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Pseudocode Description:
1. The best results were obtained with the parameters initialized in ,
the number of cycles (or iterations) is fixed at 1000 and the amount of ants (K) is calculated
according to the number of jobs, which is the amount elements that the J set has, thereby:
Equation 5
2. The pheromone trail of all edges is started in a small positive constant.
3. The Probabilistic Construction Phase of solutions begins by K ants.
3.1 The first operation is selected randomly between nodes initially visited according to the
constraints of the problem.
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3.2 The selection of the decidability rule is done randomly, with equal probability between the
rule with the shortest processing time SPT (Shortest Processing Time) or the rule with the longest
processing time LPT (Longest Processing Time) of the operations [30].
3.3 While tabúk memory has not finished filling, it means that the ant has not completed the plan
generation therefore it continuous traveling the graph until completing the total operations
( ). The tabuk list restricts the choice of operations to prevent a return to recently
visited nodes. In the set of visited operations are included operations that generate a delay in the
machines less or equal to five time units. To maintain the balance affected by the delay generated,
visibility of the node is reduced on a percentage point per unit of time lost.
3.4 Once each ant has built a solution, the pheromone actualization process is started, reviewing
the traveled path to add the appropriate amount of pheromone according to equation 3 or 4, to the
pheromone accumulator of the current cycle. If the makespan of the solution is expensive, less
importance is given to the way, thus depositing few pheromone on edges.
3.5 Update pheromone trails of the visited edges using a process known as posteriori online
update, which is a global update performed offline, that is, after the execution of each cycle of the
algorithm. It is deposited in the pheromone trails of each of the edges of the graph, what the ants
have been added in the respective pheromone accumulator. Then the actual pheromone
accumulator is restarted at zero for not to redeposit this pheromone in the next cycle.
3.6 The best quality plan of the current cycle is saved with its respective makespan.
3.7 Memory (tabuk) is erased on each ant to start building new plans in the next cycle.
4. Shows the best plan of all cycles performed by the algorithm.
6. ANALYSIS AND COMPARISON OF RESULTS
Results shown in Table 3 were obtained in 30 executions of the algorithm (1000 iterations) for
each of the 40 JSSP instances raised by Lawrence [11], that are of different sizes and difficulty,
and because of its wide use, we can compare the results with other techniques that generate the
best known solution (BKS) taken from [13] and [27] The table shows, the name of the instance of
Lawrence, its size and BKS, the best makespan found and their percentage relative error respect
al BKS, the makespan average, standard deviation, and finally the average number of evaluations
of the objective function.
Table 3. Experimental results
Instance Size BKS
Best
Cmax
Relative
Error (%)
Cmax
Average
Standard
deviation
#Eval.
Average
LA01 10 x 5 666 666 0 667.8 2.3 2375
LA02 10 x 5 655 669 2.13 689.7 6.2 2809
LA03 10 x 5 597 623 4.36 644.8 8.0 2230
LA04 10 x 5 590 611 3.56 617.7 5.0 2257
LA05 10 x 5 593 593 0 593.0 0.0 101
LA06 15 x 5 926 926 0 926.0 0.0 531
LA07 15 x 5 890 890 0 898.2 5.6 3443
LA08 15 x 5 863 863 0 863.1 0.4 2251
LA09 15 x 5 951 951 0 951.0 0.0 391
LA10 15 x 5 958 958 0 958.0 0.0 637
LA11 20 x 5 1222 1222 0 1222.0 0.0 1504
11. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
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LA12 20 x 5 1039 1039 0 1039.0 0.0 1752
LA13 20 x 5 1150 1150 0 1150.0 0.2 2952
LA14 20 x 5 1292 1292 0 1292.0 0.0 471
LA15 20 x 5 1207 1212 0.41 1245.6 9.9 3836
LA16 10 x 10 945 1005 6.35 1020.1 10.1 2700
LA17 10 x 10 784 812 3.57 836.1 10.9 2401
LA18 10 x 10 848 885 4.36 904.8 9.8 2946
LA19 10 x 10 842 875 3.92 881.7 4.7 2394
LA20 10 x 10 902 912 1.11 936.8 9.6 2496
LA21 15 x 10 1046 1107 5.38 1162.3 16.4 3658
LA22 15 x 10 927 1018 9.82 1050.2 14.2 2938
LA23 15 x 10 1032 1051 1.84 1069.2 10.0 3826
LA24 15 x 10 935 1011 8.13 1033.5 8.3 3097
LA25 15 x 10 977 1062 8.7 1093.3 14.1 3632
LA26 20 x 10 1218 1296 6.4 1339.6 16.2 5955
LA27 20 x 10 1235 1362 10.28 1379.8 9.6 4450
LA28 20 x 10 1216 1330 9.38 1363.8 13.9 3938
LA29 20 x 10 1157 1339 15.73 1374.4 11.9 4532
LA30 20 x 10 1355 1410 4.06 1443.2 15.0 5186
LA31 30 x 10 1784 1798 0.78 1825.8 12.5 7098
LA32 30 x 10 1850 1868 0.97 1906.0 20.7 8016
LA33 30 x 10 1719 1731 0.7 1771.0 15.1 5796
LA34 30 x 10 1721 1788 3.89 1823.9 13.9 6811
LA35 30 x 10 1888 1913 1.32 1974.1 22.8 7357
LA36 15 x 15 1268 1396 10.09 1430.4 18.5 3405
LA37 15 x 15 1397 1517 8.59 1544.2 12.7 2142
LA38 15 x 15 1196 1315 9.95 1343.8 10.1 4051
LA39 15 x 15 1233 1304 5.76 1359.5 16.2 3266
LA40 15 x 15 1222 1307 6.96 1323.7 9.2 2655
Average: 3.96 9.09 3307.15
Although the efficacy of the algorithm to find the optimum isn't high, reaching the BKS in 27.5%
of the LA instances, the average relative error in the 40 instances is only 4%, which is a good
approximation to the optimal of JSSP. And the highlight is the low average number of objective
function evaluations, which is much lower compared to the methods that obtained the BKS (Table
4). The AIS on average takes 52 times more evaluations our algorithm and Cultural algorithm
(CULT) has 137 times more evaluations. Compared with Tabu Search (TS) the number of
evaluations is only three times lower, because it is not included the number of evaluations
performed by the INSA algorithm that gives the TS base solution [28]. So we can state that our
algorithm has a high computational efficiency, reducing costs in time and memory, something
very important in this type of problems where getting an "economic" solution is as important as
the quality of it. Furthermore, EAS is an algorithm stable because its standard deviation is very
low.
The following table compares the average number of objective function evaluations made by
EAS, with those made by TS, AIS and CULT [29]:
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Table 4. Number of evaluations of objective function
Algorithm N° of Average evaluations
EAS 3307
AIS 175058
CULT 454525
TS 11108
Table 3 shows that on the problems of size 10 x 5 did not have trouble finding the BKS, with the
exception of the instance LA04 until LA02l, where the best obtained result is close to the BKS
(less than 5%). Also for instances of size 15 x 5 and 20 x 5, with the exception of the LA15 that
only moves away from BKS in 5 units of time. In the other instances (size 10 x 10, 15 x 10, 20 x
10, 30 x 10 and 15 x 15), which have 5 or 10 machines more than the previous, complexity is
quite high because of the considerable number of operations to be performed, this means lower
quality solutions obtained. For example, to instances of size 30 x 10, 300 operations must be
performed, and the total number of possible combinations is (30!)10
, that is approximately 2.65 x
1042
. However, the algorithm achieves to present high quality solutions on instances of 30 x 10
(Figure 5). In general, 65% of executed instances approaches less than 5% of BKS and 47.5%
deviate by less than 3% of the BKS.
Figure 5. Relative Error average by instance size
7. CONCLUSIONS
The Ant Colony Optimization is a technique of swarm intelligence, which is applied for
combinatorial optimization problems as JSSP. The algorithm implemented, Elitist Ant System,
has proven to be competitive by find good quality solutions to JSSP in a low number of objective
function evaluations, although requires improvements to obtain the best known solution in all LA
instances. Therefore, ACO is a metaheuristic that has the potential to obtain efficiently solutions
of scheduling problems, with minimal cost of time and computational resources.
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REFERENCES
[1] M. Dorigo, V. Maniezzo, and V.M. Colorni, “The Ant System: Optimization by a colony of
cooperating agents,” IEEE: Transactions on Systems, Man, and Cybernetics, Part B, vol. 26, no. 1,
pp. 29-41, 1996.
[2] M. Dorigo and L.M. Gambardella, “Ant Colony System: A cooperative learning approach to the
Traveling Salesman Problem,” IEEE: Transactions on Evolutionary Computation, vol. 1, no. 1, pp.
53-66, 1997.
[3] M. Dorigo and K. Socha, “An introduction to Ant Colony Optimization,” Technicalreport N° 10 of the
Institut de RecherchesInterdisciplinaires et de Développements en IntelligenceArtificielle (IRIDIA),
Université Libre de Bruxelles, Belgium, 2006.
[4] S. Alonso, O. Cordón, I. Fernández, and F. Herrera F,“La metaheurística de Optimización basada en
Colonias de Hormigas: Modelos y nuevos enfoques,” Trabajo realizado en el marco del proyecto
Mejora de Metaheurísticas mediante Hibridación y sus Aplicaciones, de la Universidad de Granada,
España, 2004.
[5] V. Peña and L. Zumelzu, Estado del arte del Job Shop Scheduling Problem, Departamento de
Informática, Universidad Técnica Federico Santa María Valparaíso, Chile, 2006.
[6] J. Blazewicz, K. H. Ecker, G. Schmidt, and J. Weglarz. Scheduling in Computer and Manufacturing
System. Springer, 1994.
[7] T. Stützle and H.H. Hoos, “MAX-MIN Ant System”. Future Generation Computer Systems,vol. 16, no.
8, pp. 889-914, 2000.
[8] B. Bullnheimer, R.F. Hartl, and C. Strauss, “A New Rank-Based version of the Ant System: A
computational study,” Central European Journal for Operations Research and Economics,vol. 7, no.
1, pp. 25-38, 1999.
[9] C. Blum and A. Roli, “Metaheuristics in combinatorial optimization: Overview and conceptual
comparison,” ACM Computing Surveys, vol. 35, no. 3, pp. 268-308, 2003.
[10] M. Ben-Daya and M.Al-Fawzan, A tabu search approach for the flow shop scheduling problem.
InEuropean Journal of Operational Research, vol. 109, pp. 88-95, 1998.
[11] S. Lawrence, ”Resource constrained project scheduling: an experimental investigation of heuristic
scheduling techniques”,In Graduate School of Industrial Administration, Carnegie Mellon University,
Pittsburgh, Pennsylvania, 1984.
[12] S. Goss, S. Aron, J. Deneubourg,and J. Pasteels,“Self-organized shortcuts in the Argentine
ant,”Naturwissenschaften,vol. 76, no.12, pp. 579-581, 1989.
[13] D. Applegate and W. Cook, “A computational study of the job-shop scheduling problem,” In ORSA
Journal on Computing, vol. 3, No. 2, pp. 149–156, 1991.
[14] R. J. M. Vaessens, E. H. L. Aarts, and J. K. Lenstra,“Job Shop Scheduling by Local Search,”
INFORMS J. Comput., vol. 8, no. 3, pp. 302–317, 1996.
[15] M. Ventresca and B. M. Ombuki, “Ant Colony Optimization for Job Shop Scheduling Problem,”
Tech. Rep. N° CS-04-04, Department of Computer Science, Brock University, 2004.
[16] O. Cordon, Sistemas Complejos, Algoritmos Evolutivos y Bioinspirados. Universidad de Granada,
España, 2005.
[17] M. R. Garey, “The complexity of Flowshop and Job Shop Scheduling,” Mathematics of Operations
Research, vol. 1, no. 2, pp. 117–129, 1976.
[18] M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-
Completeness, 1979.
[19] M. Perretto and S. Lopes, Reconstruction of phylogenetic trees using the ant colony optimization
paradigm. Genetics and Molecular Research, 4(3), pp. 581-589, 2005.
[20] V. A. Peña, Cadena de Suministros: sus niveles e importancia. Modelado de Procesos de Negocios,
2006.
[21] A. Manne, “On the Job-Shop Scheduling Problem”, Operations Research, vol. 8, no. 2, pp. 219-223,
1960.
[22] J. L. Denebourg, J. M. Pasteels, and J.C. Verhaeghe, “Probabilistic behaviour in ants: a strategy of
errors?”, Journal of Theoretical Biology, no. 105, 1983.
[23] A. H. Land and A. G. Doig, “An automatic method of solving discrete programming problems”.
Econometrica, vol. 28, no 3, pp. 497–520, 1960.
[24] T. Yamada and R. Nakano. Job-shop scheduling. In P. J. Fleming A. M. S. Zalzala, editor, Genetic
Algorithms in Engineering Systems, chapter 7, pp. 134–160. IET, 1999.
14. International Journal of Artificial Intelligence & Applications (IJAIA), Vol. 4, No. 4, July 2013
66
[25] M. Dorigo and T. Stützle, Ant Colony Optimization. Cambridge, Massachusetts, USA: The MIT
Press, 2004.
[26] M. Dorigo, Optimization, Learning and Natural Algorithms. Ph.D.Thesis, Politecnico di Milano, Italy,
1992.
[27] C. Coello Coello, D. Cortez Rivera, and N. Cruz Cortez, “Use of an artificial immune system for job
shop scheduling,” in Artificial Immune Systems,” Proceedings of ICARIS, Lecture Notes in
Computer Science vol. 2787, pp. 1–10, 2003.
[28] E. Nowicki and C. Smutnicki, “A fast taboo search algorithm for the job shop problem,” Management
Science, vol. 42, no. 6, pp. 797–813, 1996.
E. Téllez, Uso de una Colonia de Hormigas para resolver Problemas de programación de Horarios,
2007.
A. Colorni, M. Dorigo, V. Maniezzo and M. Trubian. Ant system for job-shop scheduling. Belgian
Journal of Operations Research, Statistics and Computer Science, 34(1), pp. 39-53, 1994.
AUTHORS
Edson Flórez was born at San Gil (Colombia) in 1991, is currently an engineer student at
School of Engineering and Computing Systems of the Universidad Industrial de Santander.
His research areas are on Swarm Intelligence algorithms, Operations Research and
Distributed systems.
Wilfredo Gómez was born at Bucaramanga(Colombia) in 1984, is currently an Magister
candidate in system engineering at School of Engineering and Computing Systems of
the Universidad Industrial de Santander. His research areas are on Bioinspired
Computation, Operations Research and Education.
Lola Bautista is MSc. in Computer Engineering University of Puerto Rico she is currently
the Director of the Research Group in Biomedical Engineering. His research areas are on
Software Design in Cardiology and Electrocardiography, Digital Signal Processing and
Graphics, Data Mining.