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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.

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Figures

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Fig. 1

A simplistic representation of a pool architecture

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Fig. 2

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

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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.

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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.

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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.

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Fig. 6

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

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Fig. 7

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

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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.

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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).

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