0
Research Papers

A Distributed Pool Architecture for Highly Constrained Optimization Problems in Complex Systems Design

[+] Author and Article Information
Vijitashwa Pandey

e-mail: pandey2@oakland.edu

Zissimos P. Mourelatos

e-mail: mourelat@oakland.edu
Mechanical Engineering Department,
Oakland University,
Rochester, MI 48309

A linear speed-up is achieved when the factor by which the solution time decreases is equal to the factor by which the number of processors increases.

Note that elitism can also be incorporated into the sequential GA to improve the objective function monotonically. It will, however, increase the solution time even more.

1Corresponding author.

Contributed by the Computers and Information Division of ASME for publication in the Journal of Computing and Information Science in Engineering. Manuscript received June 26, 2011; final manuscript received May 16, 2013; published online July 22, 2013. Editor: Bahram Ravani.

J. Comput. Inf. Sci. Eng 13(3), 031006 (Jul 22, 2013) (9 pages) Paper No: JCISE-11-1367; doi: 10.1115/1.4024713 History: Received June 26, 2011; Revised May 16, 2013

Optimal design of complex engineering systems is challenging because numerous design variables and constraints are present. Dynamic changes in design requirements and lack of complete knowledge of subsystem requirements add to the complexity. We propose an enhanced distributed pool architecture to aid distributed solving of design optimization problems. The approach not only saves solution time but is also resilient against failures of some processors. It is best suited to handle highly constrained design problems, with dynamically changing constraints, where finding even a feasible solution (FS) is challenging. In our work, this task is distributed among many processors. Constraints can be easily added or removed without having to restart the solution process. We demonstrate the efficacy of our method in terms of computational savings and resistance to partial failures of some processors, using two mixed integer nonlinear programming (MINLP)-class mechanical design optimization problems.

FIGURES IN THIS ARTICLE
<>
Copyright © 2013 by ASME
Your Session has timed out. Please sign back in to continue.

References

Roy, G., Lee, H., Welch, J., Zhao, Y., Pandey, V., and Thurston, D., 2009, “A Distributed Pool Architecture for Genetic Algorithms,” IEEE Conference on Evolutionary Computation, Trondheim, Norway.
Harrington, J. E., Hobbs, B. F., Pang, J. S., Liu, A., and Roch, G., 2005, “Collusive Game Solutions via Optimization,” Math. Program. Ser. B, 104, pp. 407–436. [CrossRef]
Facchinei, F., and Pang, J. S., 2003, Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols. I and II, Springer-Verlag, New York.
Forrester, A. I. J., Sobester, A., and Keane, A. J., 2008, Engineering Design via Surrogate Modelling a Practical Guide, John Wiley & Sons, New York.
Wujek, B., Renaud, J., and Batill, S., 1997, “A Concurrent Engineering Approach for Multidisciplinary Design in a Distributed Computing Environment,” Multidisciplinary Design Optimization: State of the Art, N.Alexandrov and M. Y.Hussaini, eds., SIAM, Philadelphia, PA.
Braun, R., 1996, “Collaborative Optimization: An Architecture for Large-Scale Distributed Design,” Ph.D. dissertation, Stanford University, Palo Alto, CA.
Kim, H. M., 2001, “Target Cascading in Optimal System Design,” Ph.D. dissertation, University of Michigan, Ann Arbor, Michigan.
Kroo, I., 2006, Distributed Multidisciplinary Design and Collaborative Optimization Multidisciplinary Design Consortium Workshop, Stanford University, CA. Available at: http://acdl.mit.edu/mdo/mdo_06/MDOarchitectures2.pdf
Sellar, R., Batill, S., and Renaud, J., 1996, “Response Surface Based, Concurrent Subspace Optimization for Multidisciplinary System Design,” 34th AIAA Aerospace Sciences Meeting, AIAA Paper No. 96-0714.
Wujek, B. A., Renaud, J. E., Batill, S. M., and Brockman, J. B., 1996, “Concurrent Subspace Optimization Using Design Variable Sharing in a Distributed Computing Environment,” Concurr. Eng., 4, pp. 361–377. [CrossRef]
Nayyer, S., 2005, “An Application of Parallel Computation to Collaborative Optimization,” M.S. thesis, Louisiana State University, Baton Rouge LA.
Liu, H., Chen, W., Kokkolaras, M., Papalambros, P. Y., and Kim, H. M., 2006, “Probabilistic Analytical Target Cascading—A Moment Matching Formulation for Multilevel Optimization Under Uncertainty,” ASME J. Mech. Des., 128(4), pp. 991–1000. [CrossRef]
Li, Y., Lu, Z., and Michalek, J., 2008, “Diagonal Quadratic Approximation for Parallelization of Analytical Target Cascading,” ASME J. Mech. Des., 130(5), p. 051402. [CrossRef]
Gurnani, A., and Lewis, K., 2008, “Collaborative, Decentralized Engineering Design at the Edge of Rationality,” ASME J. Mech. Des., 130(12), p. 121101. [CrossRef]
Herrmann, J., 2009, “Separating Design Optimization Problems for Bounded Rational Designers,” ASME International Design Engineering Technical Conferences, San Diego, CA.
Widger, J., and Grosu, D., 2009, “Parallel Computation of Nash Equilibria in N-Player Games,” International Conference on Computational Science and Engineering, Vancouver BC, Canada.
Hula, A., Jalali, K., Hamza, K., Skerlos, S. J., and Saitou, K., 2003, “Multi-Criteria Decision-Making for Optimization of Product Disassembly Under Multiple Situations,” Environ. Sci. Technol., 37(23), pp. 5303–5313. [CrossRef] [PubMed]
Deb, K., and Jain, S., 2003, “Multi-Speed Gearbox Design Using Multi-Objective Evolutionary Algorithms,” ASME J. Mech. Des., 125(3), pp. 609–619. [CrossRef]
Michalek, J. J., Papalambros, P. Y., and Skerlos, S. J., 2004, “A Study of Fuel Efficiency and Emission Policy Impact on Optimal Vehicle Design Decisions,” ASME J. Mech. Des., 126(6), pp. 1062–1070. [CrossRef]
Malkhi, D., Reiter, M., Wool, A., and Wright, R., 2001, “Probabilistic Quorum Systems,” Inf. Comput., 170(2), pp. 184–206. [CrossRef]
Lee, H., and Welch, J. L., 2005, “Randomized Registers and Iterative Algorithms,” Distrib. Comput., 17(3), pp. 209–221. [CrossRef]
Dorigo, M., and Gambardella, L. M., 1997, “Ant Colony System: A Cooperative Learning Approach to the Traveling Salesman Problem,” IEEE Trans. Evol. Comput., 1, pp. 53–66. [CrossRef]
Goldberg, D. E., 1989, Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley Publishing Company, pp. 197–199.
Colorni, A., Dorigo, M., and Maniezzo, V., 1992, “Distributed Optimization by Ant Colonies,” Proceedings of the First European Conference on Artificial Life, MIT Press, Cambridge, MA, pp. 134–142.
Whitley, D., 1994, “A Genetic Algorithm Tutorial,” Stat. Comput., 4, pp. 65–85. [CrossRef]
Carriero, N., and Gelernter, D., 1989, “Linda in Context,” Commun. ACM, 32(4), pp. 444–458. [CrossRef]
KreisselmeierG., and SteinhauserR., 1979, “Systematic Control Design by Optimizing a Vector Performance Index,” International Federation of Active Controls Symposium on Computer-Aided Design of Control Systems, Zurich, Switzerland.
Poon, N. M. K., and Martins, J. R., 2007, “An Adaptive Approach to Constraint Aggregation Using Adjoint Sensitivity Analysis,” J. Struct. Multidiscip. Optim., 34, pp. 61–73. [CrossRef]
Hager, W., and Phan, D., 2009, “An Ellipsoidal Branch and Bound Algorithm for Global Optimization,” SIAM J. Optim., 20(2), pp. 740–758. [CrossRef]
Dabbene, F., Gay, P., and Polyak, B. T., 2003, “Recursive Algorithms for Inner Ellipsoidal Approximation of Convex Polytopes,” Automatica, 39(10), pp. 1773–1781. [CrossRef]
Farhang-Mehr, A., and Azarm, S., 2003, “An Information-Theoretic Entropy Metric for Assessing Multi-Objective Optimization Solution Set Quality,” ASME J. Mech. Des., 125(4), pp. 655–663. [CrossRef]
Simpson, T., 1998, “A Concept Exploration Method for Product Family Design,” Ph.D. dissertation, Georgia Institute of Technology.

Figures

Grahic Jump Location
Fig. 1

A simplistic representation of a pool architecture

Grahic Jump Location
Fig. 2

Schematic of the constraint intersection method in finding the feasible set sequentially. The problem becomes exceedingly hard in higher dimensions.

Grahic Jump Location
Fig. 3

Schematic of the feasible solutions method. Note that for the same hypothetical problem of Fig. 2, the solutions do not provide a complete picture of the final feasible set.

Grahic Jump Location
Fig. 4

Convergence of the two architectures; “circles” and “crosses” represent the pool and sequential architectures, respectively. The first marker corresponds to the initial population (zeroth iteration). The pool architecture makes significant progress starting from the first generation.

Grahic Jump Location
Fig. 5

Fault-tolerance study of the pool architecture. Even after failure of six out of ten processors, there is no significant drop in convergence progress.

Grahic Jump Location
Fig. 6

Illustration of constraint addition. Adding constraints C5 and C6 at the fifth cycle (2.3 s) surprisingly improves the convergence.

Grahic Jump Location
Fig. 7

Convergence of the two architectures. Circles and crosses represent the pool and sequential architectures, respectively.

Grahic Jump Location
Fig. 8

Fault-tolerance study of the pool architecture for the gear-motor problem. Even after six out of ten processors fail, there is no significant drop in convergence progress.

Grahic Jump Location
Fig. 9

A simple speed reducer (adapted from Ref. [31]) The problem involves minimization of three objectives; volume (v), stress in shaft 1 (s1), and stress in shaft 2 (s2). The three objective functions are modified into a single objective function using the weighted sum approach. There are seven design variables; the gear face width (x1), the teeth module (x2), the number of teeth of pinion (x3), the distance between bearings 1 (x4), the distance between bearings 2 (x5), the diameter of shaft 1 (x6), and the diameter of shaft 2 (x7).

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In