Skip to main content
Top
Published in: Computational Mechanics 1/2014

01-01-2014 | Original Paper

An efficient dynamic load balancing algorithm

Author: Nikos D. Lagaros

Published in: Computational Mechanics | Issue 1/2014

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In engineering problems, randomness and uncertainties are inherent. Robust design procedures, formulated in the framework of multi-objective optimization, have been proposed in order to take into account sources of randomness and uncertainty. These design procedures require orders of magnitude more computational effort than conventional analysis or optimum design processes since a very large number of finite element analyses is required to be dealt. It is therefore an imperative need to exploit the capabilities of computing resources in order to deal with this kind of problems. In particular, parallel computing can be implemented at the level of metaheuristic optimization, by exploiting the physical parallelization feature of the nondominated sorting evolution strategies method, as well as at the level of repeated structural analyses required for assessing the behavioural constraints and for calculating the objective functions. In this study an efficient dynamic load balancing algorithm for optimum exploitation of available computing resources is proposed and, without loss of generality, is applied for computing the desired Pareto front. In such problems the computation of the complete Pareto front with feasible designs only, constitutes a very challenging task. The proposed algorithm achieves linear speedup factors and almost 100% speedup factor values with reference to the sequential procedure.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Tsompanakis Y, Lagaros ND, Papadrakakis M (eds) (2007) Structural optimization considering cncertainties. Taylor & Francis Tsompanakis Y, Lagaros ND, Papadrakakis M (eds) (2007) Structural optimization considering cncertainties. Taylor & Francis
2.
go back to reference Park GJ, Lee TH, Lee KH, Hwang KH (2006) Robust design: an overview. AIAA J 44(1):181–191CrossRef Park GJ, Lee TH, Lee KH, Hwang KH (2006) Robust design: an overview. AIAA J 44(1):181–191CrossRef
3.
4.
go back to reference Ritto TG, Soize C, Sampaio R (2010) Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model. Comput Mech 45:415–427CrossRefMATH Ritto TG, Soize C, Sampaio R (2010) Robust optimization of the rate of penetration of a drill-string using a stochastic nonlinear dynamical model. Comput Mech 45:415–427CrossRefMATH
5.
go back to reference Schevenels M, Lazarov BS, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput. Methods Appl Mech Eng 200(49–52):3613–3627CrossRefMATH Schevenels M, Lazarov BS, Sigmund O (2011) Robust topology optimization accounting for spatially varying manufacturing errors. Comput. Methods Appl Mech Eng 200(49–52):3613–3627CrossRefMATH
6.
go back to reference Youn BD, Choi KK, Du L, Gorsich D (2007) Integration of possibility-based optimization and robust design for epistemic uncertainty. J Mech Des Trans ASME 129(8):876–882CrossRef Youn BD, Choi KK, Du L, Gorsich D (2007) Integration of possibility-based optimization and robust design for epistemic uncertainty. J Mech Des Trans ASME 129(8):876–882CrossRef
7.
go back to reference Lagaros ND, Papadrakakis M (2007) Seismic design of RC structures: a critical assessment in the framework of multi-objective optimization. Earthq Eng Struct Dynam 36(12):1623–1639CrossRef Lagaros ND, Papadrakakis M (2007) Seismic design of RC structures: a critical assessment in the framework of multi-objective optimization. Earthq Eng Struct Dynam 36(12):1623–1639CrossRef
8.
go back to reference Farhat C, Roux F-X (1991) A method of finite element and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng 32:1205–1227CrossRefMATH Farhat C, Roux F-X (1991) A method of finite element and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng 32:1205–1227CrossRefMATH
9.
go back to reference Farhat C, Roux F-X (1994) Implicit parallel processing in structural mechanics. Comput Mech Adv 2:1–124MATHMathSciNet Farhat C, Roux F-X (1994) Implicit parallel processing in structural mechanics. Comput Mech Adv 2:1–124MATHMathSciNet
10.
go back to reference Charmpis DC, Papadrakakis M (2002) Enhancing the performance of the FETI method with preconditioning techniques implemented on clusters of networked computers. Comput Mech 30:12–28CrossRefMATH Charmpis DC, Papadrakakis M (2002) Enhancing the performance of the FETI method with preconditioning techniques implemented on clusters of networked computers. Comput Mech 30:12–28CrossRefMATH
11.
go back to reference EC3. Eurocode 3: Design of steel structures, Part 1.1: General Rules and Rules for Buildings. European Committee for Standardisation: Brussels, Belgium, The European Standard EN 1993-1-1 (2005) EC3. Eurocode 3: Design of steel structures, Part 1.1: General Rules and Rules for Buildings. European Committee for Standardisation: Brussels, Belgium, The European Standard EN 1993-1-1 (2005)
12.
go back to reference Lagaros ND, Plevris V, Papadrakakis M (2005) Multi-objective design optimization using cascade evolutionary computations. Comput Methods Appl Mech Eng 194(30–33):3496–3515CrossRefMATH Lagaros ND, Plevris V, Papadrakakis M (2005) Multi-objective design optimization using cascade evolutionary computations. Comput Methods Appl Mech Eng 194(30–33):3496–3515CrossRefMATH
13.
go back to reference Coello Coello CA (2000) An updated survey of GA-based multi-objective optimization techniques. ACM Comput Surv 32(2):109–143CrossRef Coello Coello CA (2000) An updated survey of GA-based multi-objective optimization techniques. ACM Comput Surv 32(2):109–143CrossRef
14.
go back to reference Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195CrossRef Zitzler E, Deb K, Thiele L (2000) Comparison of multiobjective evolutionary algorithms: empirical results. Evol Comput 8(2):173–195CrossRef
15.
go back to reference Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26(6):369–395CrossRefMATHMathSciNet Marler RT, Arora JS (2004) Survey of multi-objective optimization methods for engineering. Struct Multidiscip Optim 26(6):369–395CrossRefMATHMathSciNet
16.
go back to reference Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRef
17.
go back to reference Mitropoulou Ch, Fourkiotis Y, Lagaros ND, Karlaftis MG (2013) Metaheuristics in structural design optimization. In: Gandomi AH, Yang X-S, Talatahari S, Alavi AH (eds) Metaheuristic applications in structures and infrastructures. Elsevier, pp 79–102 Mitropoulou Ch, Fourkiotis Y, Lagaros ND, Karlaftis MG (2013) Metaheuristics in structural design optimization. In: Gandomi AH, Yang X-S, Talatahari S, Alavi AH (eds) Metaheuristic applications in structures and infrastructures. Elsevier, pp 79–102
18.
go back to reference Zitzler E, Laumanns M, Thiele L (2001) SPEA 2: improving the strength Pareto evolutionary algorithm. In: Giannakoglou K, Tsahalis D, Periaux J, Papailou P, Fogarty T (eds) EUROGEN 2001, evolutionary methods for design, optimization and control with applications to industrial problems. Greece, Athens, pp 95–100 Zitzler E, Laumanns M, Thiele L (2001) SPEA 2: improving the strength Pareto evolutionary algorithm. In: Giannakoglou K, Tsahalis D, Periaux J, Papailou P, Fogarty T (eds) EUROGEN 2001, evolutionary methods for design, optimization and control with applications to industrial problems. Greece, Athens, pp 95–100
19.
go back to reference Hansen N, Igel C, Roth S (2005) The multi-objective variable metric evolution strategy, Part 1, IR-INI 2005–04, ISSN 094302752 Hansen N, Igel C, Roth S (2005) The multi-objective variable metric evolution strategy, Part 1, IR-INI 2005–04, ISSN 094302752
20.
go back to reference Talbi El-G (2009) Metaheuristics: from design to implementation. Wiley, HobokenCrossRef Talbi El-G (2009) Metaheuristics: from design to implementation. Wiley, HobokenCrossRef
21.
go back to reference Lee J, Hajela P (1996) Parallel genetic algorithm implementation in multidisciplinary rotor blade design. J Aircr 33(5):962–969CrossRef Lee J, Hajela P (1996) Parallel genetic algorithm implementation in multidisciplinary rotor blade design. J Aircr 33(5):962–969CrossRef
22.
go back to reference Coello Coello CA, Van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, DordrechtCrossRefMATH Coello Coello CA, Van Veldhuizen DA, Lamont GB (2002) Evolutionary algorithms for solving multi-objective problems. Kluwer Academic Publishers, DordrechtCrossRefMATH
23.
go back to reference VanVeldhuizen DA, Zydallis JB, Lamont GB (2003) Considerations in engineering parallel multiobjective evolutionary algorithms. IEEE Trans Evol Comput 7(2):144–173CrossRef VanVeldhuizen DA, Zydallis JB, Lamont GB (2003) Considerations in engineering parallel multiobjective evolutionary algorithms. IEEE Trans Evol Comput 7(2):144–173CrossRef
24.
go back to reference de Toro Negro F, Ortega J, Ros E, Mota S, Paechter B, Martín JM (2004) PSFGA: Parallel processing and evolutionary computation for multiobjective optimisation. Parallel Comput 30(5–6):721–739CrossRef de Toro Negro F, Ortega J, Ros E, Mota S, Paechter B, Martín JM (2004) PSFGA: Parallel processing and evolutionary computation for multiobjective optimisation. Parallel Comput 30(5–6):721–739CrossRef
25.
go back to reference Wilson LA, Moore MD (2005) Cross-pollinating parallel genetic algorithms for multiobjective search and optimization. Int J Found Comput Sci 16(2):261–280CrossRef Wilson LA, Moore MD (2005) Cross-pollinating parallel genetic algorithms for multiobjective search and optimization. Int J Found Comput Sci 16(2):261–280CrossRef
26.
go back to reference Durillo JJ, Nebro AJ, Luna F, Alba E (2008) A study of master-slave approaches to parallelize NSGA-II, IPDPS Miami 2008—Proceedings of the \(22{{\rm nd}}\) IEEE International Parallel and Distributed Processing Symposium Durillo JJ, Nebro AJ, Luna F, Alba E (2008) A study of master-slave approaches to parallelize NSGA-II, IPDPS Miami 2008—Proceedings of the \(22{{\rm nd}}\) IEEE International Parallel and Distributed Processing Symposium
27.
go back to reference Kipouros T, Jaeggi DM, Dawes WN, Parks GT, Savill AM, Clarkson PJ (2008) Insight into high-quality aerodynamic design spaces through multi-objective optimization. Comput Model Eng Sci 37(1):1–44 Kipouros T, Jaeggi DM, Dawes WN, Parks GT, Savill AM, Clarkson PJ (2008) Insight into high-quality aerodynamic design spaces through multi-objective optimization. Comput Model Eng Sci 37(1):1–44
28.
go back to reference Bharti S, Frecker M, Lesieutre G (2009) Optimal morphing-wing design using parallel nondominated sorting genetic algorithm II. AIAA J 47(7):1627–1634CrossRef Bharti S, Frecker M, Lesieutre G (2009) Optimal morphing-wing design using parallel nondominated sorting genetic algorithm II. AIAA J 47(7):1627–1634CrossRef
29.
go back to reference Fan S-KS, Chang J-M (2009) A parallel particle swarm optimization algorithm for multi-objective optimization problems. Eng Optim 41(7):673–697CrossRefMathSciNet Fan S-KS, Chang J-M (2009) A parallel particle swarm optimization algorithm for multi-objective optimization problems. Eng Optim 41(7):673–697CrossRefMathSciNet
30.
go back to reference Nebro AJ, Durillo JJ (2010) A study of the parallelization of the multi-objective metaheuristic MOEA/D. Lecture Notes in Computer Science, vol 6073. LNCS, pp 303–317 Nebro AJ, Durillo JJ (2010) A study of the parallelization of the multi-objective metaheuristic MOEA/D. Lecture Notes in Computer Science, vol 6073. LNCS, pp 303–317
31.
go back to reference Zhou Y, Tan Y (2011) GPU-based parallel multi-objective particle swarm optimization. Int J Artif Intell 7(11):125–141 Zhou Y, Tan Y (2011) GPU-based parallel multi-objective particle swarm optimization. Int J Artif Intell 7(11):125–141
32.
go back to reference Mezmaz M, Melab N, Kessaci Y, Lee YC, Talbi E-G, Zomaya AY, Tuyttens D (2011) A parallel bi-objective hybrid metaheuristic for energy-aware scheduling for cloud computing systems. J Parallel Distrib Comput 71(11):1497–1508CrossRef Mezmaz M, Melab N, Kessaci Y, Lee YC, Talbi E-G, Zomaya AY, Tuyttens D (2011) A parallel bi-objective hybrid metaheuristic for energy-aware scheduling for cloud computing systems. J Parallel Distrib Comput 71(11):1497–1508CrossRef
33.
go back to reference Mezura-Montesa E, Coello Coello CA (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol Comput 1:173–194CrossRef Mezura-Montesa E, Coello Coello CA (2011) Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol Comput 1:173–194CrossRef
34.
go back to reference Arias-Montano A, Coello Coello CA (2012) Multiobjective evolutionary algorithms in aeronautical and aerospace engineering. IEEE Trans Evol Comput 16(50):662–694CrossRef Arias-Montano A, Coello Coello CA (2012) Multiobjective evolutionary algorithms in aeronautical and aerospace engineering. IEEE Trans Evol Comput 16(50):662–694CrossRef
35.
go back to reference Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338CrossRefMATH Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186(2–4):311–338CrossRefMATH
36.
go back to reference Kramer O, Schwefel H-P (2006) On three new approaches to handle constraints within evolution strategies. Natl Comput 5(4):363–385CrossRefMATHMathSciNet Kramer O, Schwefel H-P (2006) On three new approaches to handle constraints within evolution strategies. Natl Comput 5(4):363–385CrossRefMATHMathSciNet
37.
go back to reference LeTallec P (1994) Domain-decomposition methods in computational mechanics. Comput Mech Adv 1:121–220MathSciNet LeTallec P (1994) Domain-decomposition methods in computational mechanics. Comput Mech Adv 1:121–220MathSciNet
38.
go back to reference Papadrakakis M (ed) (1997) Parallel Solution Methods in Computational Mechanics. John Wiley & Sons, New York Papadrakakis M (ed) (1997) Parallel Solution Methods in Computational Mechanics. John Wiley & Sons, New York
39.
go back to reference Jönsthövel TB, van Gijzen MB, MacLachlan S, Vuik C, Scarpas A (2012) Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials. Comput Mech 50:321–333CrossRefMATHMathSciNet Jönsthövel TB, van Gijzen MB, MacLachlan S, Vuik C, Scarpas A (2012) Comparison of the deflated preconditioned conjugate gradient method and algebraic multigrid for composite materials. Comput Mech 50:321–333CrossRefMATHMathSciNet
40.
go back to reference Papadrakakis M, Lagaros ND, Fragakis Y (2003) Parallel computational strategies for structural optimization. Int J Numer Methods Eng 58(9):1347–1380CrossRefMATH Papadrakakis M, Lagaros ND, Fragakis Y (2003) Parallel computational strategies for structural optimization. Int J Numer Methods Eng 58(9):1347–1380CrossRefMATH
41.
go back to reference Papadrakakis M, Stavroulakis G, Karatarakis A (2011) A new era in scientific computing: domain decomposition methods in hybrid CPU-GPU architectures. Comput Methods Appl Mech Eng 200(13–16):1490–1508CrossRefMATHMathSciNet Papadrakakis M, Stavroulakis G, Karatarakis A (2011) A new era in scientific computing: domain decomposition methods in hybrid CPU-GPU architectures. Comput Methods Appl Mech Eng 200(13–16):1490–1508CrossRefMATHMathSciNet
42.
go back to reference Bhardwaj M, Day D, Farhat C, Lesoinne M, Pierson K, Rixen D (2000) Application of the FETI method to ASCI problems: scalability results on one-thousand processors and discussion of highly heterogeneous problems. Int J Numer Methods Eng 47:513–536CrossRefMATH Bhardwaj M, Day D, Farhat C, Lesoinne M, Pierson K, Rixen D (2000) Application of the FETI method to ASCI problems: scalability results on one-thousand processors and discussion of highly heterogeneous problems. Int J Numer Methods Eng 47:513–536CrossRefMATH
43.
go back to reference Papadrakakis M, Fragakis Y (2011) An integrated geometric-algebraic method for solving semi-definite problems in structural mechanics. Comput Methods Appl Mech Eng 190(49–50):6513–6532 Papadrakakis M, Fragakis Y (2011) An integrated geometric-algebraic method for solving semi-definite problems in structural mechanics. Comput Methods Appl Mech Eng 190(49–50):6513–6532
44.
go back to reference Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization, Natural Computing Series, Springer Price KV, Storn RM, Lampinen JA (2005) Differential evolution: a practical approach to global optimization, Natural Computing Series, Springer
45.
go back to reference Lagaros ND, Karlaftis MG (2011) A critical assessment of metaheuristics for scheduling emergency infrastructure inspections. Swarm Evol Comput 1(3):147–163CrossRef Lagaros ND, Karlaftis MG (2011) A critical assessment of metaheuristics for scheduling emergency infrastructure inspections. Swarm Evol Comput 1(3):147–163CrossRef
46.
go back to reference Lagaros ND, Papadrakakis M (2012) Applied soft computing for optimum design of structures. Struct Multidiscip Optim 45:787–799CrossRefMATH Lagaros ND, Papadrakakis M (2012) Applied soft computing for optimum design of structures. Struct Multidiscip Optim 45:787–799CrossRefMATH
47.
go back to reference Maaranen H, Miettinen K, Penttinen A (2007) On initial populations of a genetic algorithm for continuous optimization problems. J Glob Optim 37:405–436 Maaranen H, Miettinen K, Penttinen A (2007) On initial populations of a genetic algorithm for continuous optimization problems. J Glob Optim 37:405–436
48.
go back to reference Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4:284–294CrossRef Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4:284–294CrossRef
49.
go back to reference Ponsich A, Coello Coello CA (2011) Differential Evolution performances for the solution of mixed-integer constrained process engineering problems. Appl Soft Comput J 11(1):399–409CrossRef Ponsich A, Coello Coello CA (2011) Differential Evolution performances for the solution of mixed-integer constrained process engineering problems. Appl Soft Comput J 11(1):399–409CrossRef
50.
go back to reference Ellingwood BR, Galambos TV, MacGregor JG, Cornell CA (1980) Development of a probability-based load criterion for American National Standard A58. National Bureau of Standards, Washington Ellingwood BR, Galambos TV, MacGregor JG, Cornell CA (1980) Development of a probability-based load criterion for American National Standard A58. National Bureau of Standards, Washington
51.
go back to reference Sharp M, Farhat C (1994) TOPDOMDEC—a totally object oriented program for visualization, domain decomposition and parallel processing. User’s manual, PGSoft and University of Colorado, Boulder, USA Sharp M, Farhat C (1994) TOPDOMDEC—a totally object oriented program for visualization, domain decomposition and parallel processing. User’s manual, PGSoft and University of Colorado, Boulder, USA
Metadata
Title
An efficient dynamic load balancing algorithm
Author
Nikos D. Lagaros
Publication date
01-01-2014
Publisher
Springer Berlin Heidelberg
Published in
Computational Mechanics / Issue 1/2014
Print ISSN: 0178-7675
Electronic ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-013-0892-1

Other articles of this Issue 1/2014

Computational Mechanics 1/2014 Go to the issue