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Solving Single Machine Total Weighted Tardiness Problem with Unequal Release Date Using Neurohybrid Particle Swarm Optimization Approach.

Cakar T, Koker R - Comput Intell Neurosci (2015)

Bottom Line: PSO searches for better solution than this solution.For each stage, local optimizers are used to perform exploitation to the best particle.All system is named as neurohybrid-PSO solution system.

View Article: PubMed Central - PubMed

Affiliation: Industrial Engineering Department, Engineering Faculty, Sakarya University, Esentepe Campus, 54187 Sakarya, Turkey.

ABSTRACT
A particle swarm optimization algorithm (PSO) has been used to solve the single machine total weighted tardiness problem (SMTWT) with unequal release date. To find the best solutions three different solution approaches have been used. To prepare subhybrid solution system, genetic algorithms (GA) and simulated annealing (SA) have been used. In the subhybrid system (GA and SA), GA obtains a solution in any stage, that solution is taken by SA and used as an initial solution. When SA finds better solution than this solution, it stops working and gives this solution to GA again. After GA finishes working the obtained solution is given to PSO. PSO searches for better solution than this solution. Later it again sends the obtained solution to GA. Three different solution systems worked together. Neurohybrid system uses PSO as the main optimizer and SA and GA have been used as local search tools. For each stage, local optimizers are used to perform exploitation to the best particle. In addition to local search tools, neurodominance rule (NDR) has been used to improve performance of last solution of hybrid-PSO system. NDR checked sequential jobs according to total weighted tardiness factor. All system is named as neurohybrid-PSO solution system.

No MeSH data available.


Flowchart and pseudocode of the simulating algorithm.
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fig1: Flowchart and pseudocode of the simulating algorithm.

Mentions: In Figure 1 the flowchart and pseudocode of SA algorithm have been given [30, 31]. As seen in the figure, the SA is starting with an initial solution (A), initial temperature (T), and an iteration number (C). The role of the temperature is to control the possibility of the acceptance of the disturbing solution. On the other hand, the reason of the usage of the iteration number is to decide the number of repetitions until a solution is found on a stable state under the temperature [32, 33]. The temperature may get the following implicit flexibility index meaning. At the beginning of the searches, in other words, at high temperature situation, some flexibility may be moved to a worse solution cases; however, less of this flexibility is existing in the searches done later, which means at lower temperature. Based on these T, C through a heuristic perturbation on the existing solutions, a new neighborhood solution (N) is generated. In case of improvement on the change of an objective function, the neighborhood solution (N) will be a good solution. Even if the change of an objective function is not improved, the neighborhood solution will be a new solution with a suitable probability based on e−D/T. This situation removes the possibility of finding a global optimum solution out of a local optimum. In case of no change after certain iterations, the algorithm is stopped. If there is still improvement on the new solution, the algorithm continues with a new temperature value.


Solving Single Machine Total Weighted Tardiness Problem with Unequal Release Date Using Neurohybrid Particle Swarm Optimization Approach.

Cakar T, Koker R - Comput Intell Neurosci (2015)

Flowchart and pseudocode of the simulating algorithm.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4493311&req=5

fig1: Flowchart and pseudocode of the simulating algorithm.
Mentions: In Figure 1 the flowchart and pseudocode of SA algorithm have been given [30, 31]. As seen in the figure, the SA is starting with an initial solution (A), initial temperature (T), and an iteration number (C). The role of the temperature is to control the possibility of the acceptance of the disturbing solution. On the other hand, the reason of the usage of the iteration number is to decide the number of repetitions until a solution is found on a stable state under the temperature [32, 33]. The temperature may get the following implicit flexibility index meaning. At the beginning of the searches, in other words, at high temperature situation, some flexibility may be moved to a worse solution cases; however, less of this flexibility is existing in the searches done later, which means at lower temperature. Based on these T, C through a heuristic perturbation on the existing solutions, a new neighborhood solution (N) is generated. In case of improvement on the change of an objective function, the neighborhood solution (N) will be a good solution. Even if the change of an objective function is not improved, the neighborhood solution will be a new solution with a suitable probability based on e−D/T. This situation removes the possibility of finding a global optimum solution out of a local optimum. In case of no change after certain iterations, the algorithm is stopped. If there is still improvement on the new solution, the algorithm continues with a new temperature value.

Bottom Line: PSO searches for better solution than this solution.For each stage, local optimizers are used to perform exploitation to the best particle.All system is named as neurohybrid-PSO solution system.

View Article: PubMed Central - PubMed

Affiliation: Industrial Engineering Department, Engineering Faculty, Sakarya University, Esentepe Campus, 54187 Sakarya, Turkey.

ABSTRACT
A particle swarm optimization algorithm (PSO) has been used to solve the single machine total weighted tardiness problem (SMTWT) with unequal release date. To find the best solutions three different solution approaches have been used. To prepare subhybrid solution system, genetic algorithms (GA) and simulated annealing (SA) have been used. In the subhybrid system (GA and SA), GA obtains a solution in any stage, that solution is taken by SA and used as an initial solution. When SA finds better solution than this solution, it stops working and gives this solution to GA again. After GA finishes working the obtained solution is given to PSO. PSO searches for better solution than this solution. Later it again sends the obtained solution to GA. Three different solution systems worked together. Neurohybrid system uses PSO as the main optimizer and SA and GA have been used as local search tools. For each stage, local optimizers are used to perform exploitation to the best particle. In addition to local search tools, neurodominance rule (NDR) has been used to improve performance of last solution of hybrid-PSO system. NDR checked sequential jobs according to total weighted tardiness factor. All system is named as neurohybrid-PSO solution system.

No MeSH data available.