1 / 11

Implementation of Parallel Simulated Annealing

Implementation of Parallel Simulated Annealing. Simulated Annealing. A popular heuristic search algorithm to solve NP complete problems Applications: VLSI Routing, placement Named after glass making procedure

valentine-gaines
Télécharger la présentation

Implementation of Parallel Simulated Annealing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Implementation of Parallel Simulated Annealing

  2. Simulated Annealing • A popular heuristic search algorithm to solve NP complete problems • Applications: VLSI Routing, placement • Named after glass making procedure • The fundamental idea is to allow moves resulting in solutions of worse quality than the current solution (uphill moves) in order to escape from local minima.

  3. Simulated annealing algorithm • The algorithm starts by generating an initial solution and by initializing the temperature parameter T. • A solution s1 from the neighborhood N(s) is accepted as new solution depending on f(s), f(s1) and T. • s1 replaces s if f(s1) < f(s) or, in case f(s1) >= f(s), with a probability which is a function of T and f(s1) – f(s). • The probability is generally computed following the Boltzmann distribution e-(f(s1) - f(s))/T.

  4. SA algorithm

  5. TSP • Problem: Given a list of cities and their pair wise distances, the task is to find a shortest possible tour that visits each city exactly once. • N! possible paths for N city trip • Complexity: NP Complete

  6. Solving TSP with simulated annealing • Lemma1: any tour can be obtained from any other tour by a sequence of 2-neighbourhood changes • Lemma2: Any neighborhood can be generated at random by generating 2 uniform numbers for i and j ALGORITHM: • s_0 = generate random initial solution • t_0 = initial temperature • Repeat • select s in N(s_0) (i.e., select i and j) • cost = d(v_i, v_j) + d(v_i+1, v_j+1) - d(v_i, v_i+1) - d(v_j+1, v_j) • if cost > 0 then s_0 = s • else generate random x in (0, 1); if x < exp(-cost/t) then s_0 = s • t = t / (1 + b t) • until stopping condition

  7. Parallel Simulated annealing • Run SA algorithm on N nodes with different initial solution • Exchange the partial results among the nodes after a fixed no of iterations • Select the best partial results and continue SA on each node. • Repeat this process

  8. Parallel algorithm • Control node: • Worker node:

  9. Work in progress • Written working code for simulated annealing • Few parts of the control node and worker node are done. • Still have to debug and get parallel simulated annealing working • Do a comparative runtime comparison

  10. Expected results • Runtime should be roughly same for serial and parallel algorithm • Parallel algorithm is expected to yield a robust solution.

  11. References • Parallel Simulated Annealing Algorithms by D. JANAKI RAM,1 T. H. SREENIVAS, AND K. GANAPATHY SUBRAMANIAM JOURNAL OF PARALLEL AND DISTRIBUTED COMPUTING 37, 207–212 (1996)‏ • Parallel Simulated Annealing by Mixing of States King-Wai Chu,¤ Yuefan Deng,¤ and John Reinitzy Journal of Computational Physics 148, 646–662 (1999)‏ • http://www.cs.duke.edu/brd/Teaching/Previous/AI/Lectures/l4.html • Greening, Daniel R., Parallel simulated annealing techniques, PhysicaD 42 (1990), 293–306. • VLSI CAD Algorithms ECE 6095

More Related