Presentation is loading. Please wait.

Presentation is loading. Please wait.

Focus on Parallel Combinatorial Optimization

Published byStuart Tucker Modified over 5 years ago

Similar presentations

Presentation on theme: "Focus on Parallel Combinatorial Optimization"— Presentation transcript:

1 Focus on Parallel Combinatorial Optimization
Claude Tadonki MINES ParisTech – PSL Research University Centre de Recherche Informatique Monthly CRI Seminar MINES ParisTech - CRI January 21, 2019, Fontainebleau (France)

2 Focus on Parallel Combinatorial Optimization
Performance Overview of Supercomputers November 2018 ranking 71% 75% 74% 61% 77% Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

3 Focus on Parallel Combinatorial Optimization
Combinatorial Optimization Illustration NP-complete Problem + Subtour breaking constraints Method (Super)Computer TSP heroes: Applegate, Bixby, Chvatal, and Cook Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

4 Focus on Parallel Combinatorial Optimization
Branch-and-Bound Practical instances of discrete (pure or mixed) optimization problems are better solved though a skillfull combination of continuous optimization techniques and branch&bound-like mechanisms. For a pure discrete problem, a relaxation is used. For a mixed formulation, a decomposition approach can be considered. In number of cases, the objective function is (or becomes) non differentiable . We then need a good non differentiable optimization method and solver. Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

5 Focus on Parallel Combinatorial Optimization
Potential Sources of Scalability Issue Load imbalance The real volume of a branch is know after its exploration and cannot be predicted Synchronization There is a strong need of synchronization for the management of the common pool of working items like the gradients and lower/upper bounds. Concurrent and irregular memory accesses From the structural nature of the branch-and-bound, we should expect a significant memory penalty, which will be exacerbated on NUMA architectures. Heavy data exchanges Lot of occurrences of data exchange are expected for the coordination of the process beside ordinary reasons. Resources sharing and weak scalability of node problems Solving the node problems might suffer from weak scalability depending on the Implementation and the required resources are taken from the whole machine. Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

6 We now focus on directive-based parallelization of
Parallelizing common paradigms involved on node problems We now focus on directive-based parallelization of Dynamic Programming and Greedy Algorithms Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

7 Focus on Parallel Combinatorial Optimization
Dynamic Programming Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

8 Focus on Parallel Combinatorial Optimization
Shortest Paths A direct parallelization of a the update is valid because The only dependencies are with the pivot (row and column) The pivot (row and column) is invariant at the corresponding step Pivots sharing is a good point especially with a efficient SM cache protocol Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

9 Focus on Parallel Combinatorial Optimization
Dominated Graph Flooding A direct parallelization of a the update is valid because There is no dependence inside a step The only dependencies are from one step to the next (k axis) & no in-place Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

10 Focus on Parallel Combinatorial Optimization
Dominated Graph Flooding Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

11 Focus on Parallel Combinatorial Optimization
0-1 Knapsack Problem Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

12 Focus on Parallel Combinatorial Optimization
0-1 Knapsack Problem All dependencies are of the form The computation along i-axis can be freely parallelized The one-step lifetime of V(i, :) suggests a V(i mod2, :) array compression Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

13 Focus on Parallel Combinatorial Optimization
0-1 Knapsack Problem Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

14 Focus on Parallel Combinatorial Optimization
Longest Common Subsequence (LCS) The Longest Common Subsequence (LCS) problem is to find the (length of the) longest common contiguous subsequence given two finite sequences. The dependence does not allow a direct parallelization A loop skewing transformation where the computation is done along the hyperplane makes a direct parallelization possible Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

15 Focus on Parallel Combinatorial Optimization
Longest Common Subsequence (LCS) Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

16 Focus on Parallel Combinatorial Optimization
Performance evaluation Intel® Xeon® Processor E v4 Released in April 2016 Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

17 Focus on Parallel Combinatorial Optimization
Greedy Algorithms Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

18 Focus on Parallel Combinatorial Optimization
END END & QUESTIONS Focus on Parallel Combinatorial Optimization Monthly CRI Seminar, Mines ParisTech - CRI January 21, 2019, Fontainebleau (France)

Download ppt "Focus on Parallel Combinatorial Optimization"

Similar presentations

Accelerator-based Implementation of the Harris Algorithm International Conference on Image and Signal Processing 2012 (ICISP 2012) June 28-30, Agadir,

Accelerator-based Implementation of the Harris Algorithm International Conference on Image and Signal Processing 2012 (ICISP 2012) June 28-30, Agadir,
Branch prediction Titov Alexander MDSP November, 2009.

Branch prediction Titov Alexander MDSP November, 2009.
Parallel Jacobi Algorithm Steven Dong Applied Mathematics.

Parallel Jacobi Algorithm Steven Dong Applied Mathematics.
1 Finite Constraint Domains. 2 u Constraint satisfaction problems (CSP) u A backtracking solver u Node and arc consistency u Bounds consistency u Generalized.

1 Finite Constraint Domains. 2 u Constraint satisfaction problems (CSP) u A backtracking solver u Node and arc consistency u Bounds consistency u Generalized.
Dendrogram-based Algorithm Weighted Graphs Flooding Algorithm – Implementation - Parallelization Claude Tadonki and Fernand Meyer Centre de Recherche en.

Dendrogram-based Algorithm Weighted Graphs Flooding Algorithm – Implementation - Parallelization Claude Tadonki and Fernand Meyer Centre de Recherche en.
Algorithms + L. Grewe.

Algorithms + L. Grewe.
Introductory Lecture. What is Discrete Mathematics? Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous)

Introductory Lecture. What is Discrete Mathematics? Discrete mathematics is the part of mathematics devoted to the study of discrete (as opposed to continuous)
11Sahalu JunaiduICS 573: High Performance Computing5.1 Analytical Modeling of Parallel Programs Sources of Overhead in Parallel Programs Performance Metrics.

11Sahalu JunaiduICS 573: High Performance Computing5.1 Analytical Modeling of Parallel Programs Sources of Overhead in Parallel Programs Performance Metrics.
Branch and bound Pasi Fränti 30.9.2014. Explore all alternatives Solution constructed by stepwise choices Decision tree Guarantees optimal solution Exponential.

Branch and bound Pasi Fränti Explore all alternatives Solution constructed by stepwise choices Decision tree Guarantees optimal solution Exponential.
Chapter 7 Dynamic Programming 7.

Chapter 7 Dynamic Programming 7.
High Performance Computing 1 Parallelization Strategies and Load Balancing Some material borrowed from lectures of J. Demmel, UC Berkeley.

High Performance Computing 1 Parallelization Strategies and Load Balancing Some material borrowed from lectures of J. Demmel, UC Berkeley.
Solving the Protein Threading Problem in Parallel Nocola Yanev, Rumen Andonov Indrajit Bhattacharya CMSC 838T Presentation.

Solving the Protein Threading Problem in Parallel Nocola Yanev, Rumen Andonov Indrajit Bhattacharya CMSC 838T Presentation.
Metaheuristics The idea: search the solution space directly. No math models, only a set of algorithmic steps, iterative method. Find a feasible solution.

Metaheuristics The idea: search the solution space directly. No math models, only a set of algorithmic steps, iterative method. Find a feasible solution.
Domain decomposition in parallel computing Ashok Srinivasan www.cs.fsu.edu/~asriniva Florida State University COT 5410 – Spring 2004.

Domain decomposition in parallel computing Ashok Srinivasan Florida State University COT 5410 – Spring 2004.
Decentralised Coordination of Mobile Sensors School of Electronics and Computer Science University of Southampton Ruben Stranders,

Decentralised Coordination of Mobile Sensors School of Electronics and Computer Science University of Southampton Ruben Stranders,
Distributed Asynchronous Bellman-Ford Algorithm

Distributed Asynchronous Bellman-Ford Algorithm
Parallel Programming Models Jihad El-Sana These slides are based on the book: Introduction to Parallel Computing, Blaise Barney, Lawrence Livermore National.

Parallel Programming Models Jihad El-Sana These slides are based on the book: Introduction to Parallel Computing, Blaise Barney, Lawrence Livermore National.
Claude Tadonki Mines ParisTech – CRI – Mathématiques et Systèmes Laboratoire de l’Accélérateur Linéaire/IN2P3/CNRS France 2nd.

Claude Tadonki Mines ParisTech – CRI – Mathématiques et Systèmes Laboratoire de l’Accélérateur Linéaire/IN2P3/CNRS France 2nd.
Automatic LQCD Code Generation Quatrièmes Rencontres de la Communauté Française de Compilation December 5-7, 2011 Saint-Hippolyte (France) Claude Tadonki.

Automatic LQCD Code Generation Quatrièmes Rencontres de la Communauté Française de Compilation December 5-7, 2011 Saint-Hippolyte (France) Claude Tadonki.
Graph Algorithms. Definitions and Representation An undirected graph G is a pair (V,E), where V is a finite set of points called vertices and E is a finite.

Graph Algorithms. Definitions and Representation An undirected graph G is a pair (V,E), where V is a finite set of points called vertices and E is a finite.

Similar presentations

Ads by Google