Project BNB-Grid: solving large scale optimization problems in a distributed environment Good afternoon, I’m Mikhail Posypkin from Institute for System Analysis. My talk is entitled … It is wellknown that Grid is a perfect platform for processing huge experimental data, Monte-Carlo simulation and many other fields. In this talk I’ll try to show that Grid may also be used for solving hard computational problems like global optimization. M. Posypkin (ISA RAS)
GLOBAL OPTIMIZATION Given f : Find x0: The global optimization problem is generally stated as follows: given a function f find its global minimum (or maximum) over the domain of definition.
APPLICATIONS OF GLOBAL OPTIMIZATION VLSI design Automated theorem proving Constructing optimal transport networks Selecting a best investment package Computational chemistry: finding molecular conformations Lots of problems in practice may be reduced to global optimization problems. The most famous are design automation automated theorem proving optimizing transport networks some problems from economics and computational chemistry. It is worth noting that optimization problems are often hard to solve and require lots of computational resources. OFTEN HARD TO SOLVE !
BRANCH-AND-BOUND METHOD BRANCHING BRANCHING TREE SUB-PROBLEM DISCARDED SUBPROBLEM: NO SOLUTION KNOWN OPTIMUM OPTIMUM IS NOT BETTER THAN INCUMBENT (ALREADY FOUND) The branch-and-bound is a primary method for solving optimization problems. This method is based on a iterative decomposition of a search space. The decomposition is organized as a tree with the root in the initial problem. On the first step the initial problem is split on two sub-problems. On the subsequent steps the sub-problems created earlier are decomposed. After the sub-problem is created one of its feasible solutions can be found by some heuristic procedure. The sub-problems are discarded if at least one of the following conditions holds.
BNB parallelization HIGH COMPLEXITY TREE-LIKE STRUCTURE SUITABLE FOR DECOMPOSITION The tree like structure of the Branch-and bound method perfectly suits for implementation in parallel and distributed environments. Indeed different branches of the search tree can be processed almost independently and hence that can be executed by different computing nodes. SUITS FOR DISTRIBUTED COMPUTING
DISTRIBUTED ENVIRONMENT We will consider the distributed system which unlike a parallel system consists of heterogeneous geographically distributed computing elements. Where computing nodes are ranged from workstations to supercomputers.
BNB-Grid: ARCHITECTURE CE-AGENT #1 CE-AGENT #2 IARnet Our BNB-Grid implements branch-and-bound method in a distributed environment. Nodes interaction is organized via IARnet. Each CE is represented by an IARnet agent. There is also a master agent which manages computations and gives a control to the user. There are two kinds of agents here: computing element agent and master agent. CE-AGENT #3 MASTER AGENT
COMPUTING ELEMENT AGENT AGENT FUNCTIONALITY COMPUTING ELEMENT AGENT MASTER AGENT Start solver Interact with the CE batch system Load initial data Monitor computing element Send and receive sub-problems Manage distributed application Manage load balancing Monitor and visualize computational process
INSIDE A COMPUTING ELEMENT CE Agent BNB-Proxy BNB-Solver Each computing element runs an instance of BNB-Solver library which. The BNB-Solver library also developed by us is aimed at solving optimization problems on a uni- and multi-processor systems. It is implemented in accordance with technology available for a given architecture. For multiprocessor systems it is usually MPI. Large publicly available supercomputers are normally well protected and the direct communication between CE-Agent and BNB-Solver is problematic. For this reason we introduce a special proxy process which usually runs on front-end node of a supercomputers and supports interaction between BNB-Solver and CE-Agent. Interaction with BNB-Solver. A library for solving optimization problems on multiprocessor and uni-processor systems
FAULT-TOLERANCE in BNB-Grid Dynamically changing computing space: nodes may leave or join at run-time BNB-Grid backs up sub-problems and resubmits them In the case of the node failure Because of a lack of time I only list main features of BNB-Grid system.
EXPERIMENTAL RESULTS: PLATFORM 1048 x PowerPC 970 2,2 GHz, 2096 GB, Myrinet 256 x Itanium 2 1.6 GHz, 256 GB, Myrinet Workstation (ISA) Computational experiments were run on a system consisting of a central workstation at Institute for systems analysis of Russian academy of sciences and two HPC clusters: MVS 15000BM and MVS 6000IM located at Joint Supercomputer Center and Computational Center of Russian academy of sciences respectively. Both clusters contain CPU nodes of approximately same performances on the considered kind of problems. МВС 15000 BM (JSCC) МВС 6000 IM (CC)
EXPERIMENTAL RESULTS: KNAPSACK PROBLEM We are given n items with weights wi and profits pi and a knapsack with capacity C. The objective: select a subset of items such that the total profit is maximized and the total weight does not exceed C:
EXPERIMENTAL RESULTS: DATA The hard knapsack instance (introduced by Finkelshtejn): 8 CPU on MVS 15000 BM 5.57 min 8CPU on MVS 6000 IM 6.04 min 8CPU on MVS 15000 BM + 8 CPU on MVS 6000 IM 3.15 min The following knapsack problem instance was selected for experiments: This problem is known as a hard one: the number of vertices in the search tree is 601080389. Three configurations were tried. The average running times obtained from several runs are given in the table.
CONCLUSIONS Usage a number of supercomputers in BNB-Grid does increase performance for large scale optimization problems IARnet framework makes development of complex distributed applications rather simple
THANK YOU!
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