Accelerating Simulated Annealing for the Permanent and Combinatorial Counting Problems

2008 ◽  
Vol 37 (5) ◽  
pp. 1429-1454 ◽  
Author(s):  
Ivona Bezáková ◽  
Daniel Štefankovič ◽  
Vijay V. Vazirani ◽  
Eric Vigoda
Keyword(s):  
Simulated Annealing ◽  
Counting Problems ◽  
Combinatorial Counting

scholarly journals Square root singularities of infinite systems of functional equations

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Johannes F. Morgenbesser
Keyword(s):  
Functional Equations ◽  
Nonlinear Function ◽  
Square Root ◽  
Counting Problems ◽  
Taylor Coefficients ◽  
Infinite Systems ◽  
Finite Dimensional ◽  
International Audience ◽  
Finite Dimensional Case ◽  
Combinatorial Counting

International audience Infinite systems of equations appear naturally in combinatorial counting problems. Formally, we consider functional equations of the form $\mathbf{y} (x)=F(x,\mathbf{y} (x))$, where $F(x,\mathbf{y} ):\mathbb{C} \times \ell^p \to \ell^p$ is a positive and nonlinear function, and analyze the behavior of the solution $\mathbf{y} (x)$ at the boundary of the domain of convergence. In contrast to the finite dimensional case different types of singularities are possible. We show that if the Jacobian operator of the function $F$ is compact, then the occurring singularities are of square root type, as it is in the finite dimensional setting. This leads to asymptotic expansions of the Taylor coefficients of $\mathbf{y} (x)$.

Penjadwalan Produksi Menggunakan Metode Simulated Annealing pada Unit Produksi Daun Pintu di PT. ML

2019 ◽  
Vol 2 (2) ◽  
Author(s):  
Rosnani Ginting ◽  
Chairul Rahmadsyah Manik
Keyword(s):  
Simulated Annealing ◽  
Problem Solving ◽  
Production Scheduling ◽  
Production Control ◽  
Delivery Time ◽  
Production Schedule ◽  
A Company ◽  
Predetermined Time ◽  
Factory Floor

Penjadwalan merupakan aspek yang sangat penting karena didalamnya terdapat elemen perencanaan dan pengendalian produksi bagi suatu perusahaan yang dapat mengirim barang sesuai dengan waktu yang telah ditentukan, untuk memperoleh waktu total penyelesaian yang minimum. Masalah utama yang dihadapi oleh PT. ML adalah keterlambatan penyelesaian order yang mempengaruhi delivery time ke tangan costumer karena pelaksanaan penjadwalan produksi dilantai pabrik belum menghasilkan makespan yang sesuai dengan order yang ada. Oleh kaena itu dituntut untuk mencari solusi pemecahan masalah optimal dalam penentuan jadwal produksi untuk meminimisasi total waktu penyelessaian (makespan) semua order. Dalam penelitian ini, penjadwalan menggunakan metode Simulated Annealing (SA) diharapkan dapat menghasilkan waktu total penyelesaian lebih cepat dari penjadwalan yang ada pada perusahaan.   Scheduling is a very important aspect because in it there are elements of planning and production control for a company that can send goods in accordance with a predetermined time, to obtain a minimum total time of completion. The main problem faced by PT. ML is the delay in completing orders that affect delivery time to customer because the implementation of production scheduling on the factory floor has not produced the makespan that matches the existing order. Therefore, it is required to find optimal problem solving solutions in determining the production schedule to minimize the total time of elimination (makespan) of all orders. In this study, scheduling using the Simulated Annealing (SA) method is expected to produce a total time of completion faster than the existing scheduling in the company.

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