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Project BNB-Grid : solving large scale optimization problems in a distributed environment. M. Posypkin (ISA RAS). GLOBAL OPTIMIZATION. Given f :. Find x 0 :. APPLICATIONS OF GLOBAL OPTIMIZATION. VLSI design Automated theorem proving Constructing optimal transport networks
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Project BNB-Grid: solving large scale optimization problems in a distributed environment M. Posypkin (ISA RAS)
GLOBAL OPTIMIZATION Given f: Findx0:
APPLICATIONS OF GLOBAL OPTIMIZATION • VLSI design • Automated theorem proving • Constructing optimal transport networks • Selecting a best investment package • Computational chemistry: finding molecular conformations OFTEN HARD TO SOLVE !
BRANCH-AND-BOUND METHOD BRANCHING BRANCHING TREE SUB-PROBLEM • DISCARDEDSUBPROBLEM: • NO SOLUTION • KNOWN OPTIMUM • OPTIMUM IS NOT BETTER THAN INCUMBENT (ALREADY FOUND)
BNB parallelization • HIGH COMPLEXITY • TREE-LIKE STRUCTURE SUITABLE FOR DECOMPOSITION SUITS FOR DISTRIBUTED COMPUTING
BNB-Grid: ARCHITECTURE CE-AGENT #1 CE-AGENT #2 IARnet CE-AGENT #3 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 AGENT FUNCTIONALITY COMPUTING ELEMENT AGENT MASTER AGENT
INSIDE A COMPUTING ELEMENT CE Agent BNB-Proxy BNB-Solver Interaction with BNB-Solver. A library for solving optimization problems on multiprocessor and uni-processor systems
FAULT-TOLERANCE inBNB-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
EXPERIMENTAL RESULTS: PLATFORM 1048x PowerPC 970 2,2 GHz, 2096 GB, Myrinet 256 x Itanium 2 1.6 GHz, 256 GB, Myrinet Workstation (ISA) 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):
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
КЛАССИЧЕСКИЕ МОДЕЛЬНЫЕ ЗАДАЧИ ОПТИМИЗАЦИИ • Задача коммивояжера • Задачи о покрытиях и разрезаниях графов • Задача о ранце (одномерная и многомерная) • Задачи транспортного типа • Поиск глобального экстремума функции многих переменных • … ДЛЯ РЕШЕНИЯ ТРЕБУЮТСЯ БОЛЬШИЕ ВЫЧИСЛИТЕЛЬНЫЕ РЕСУРСЫ