Smart Design for Assembly using the Simulated Annealing Approach

1
Smart Design for Assembly using the Simulated
Annealing Approach

• Hao Shen, Aleksandar Subic
• School of Aerospace, Mechanical Manufacturing
  Engineering
• RMIT University, Australia
• 02.07.2007

2
Scope of Presentation

• In this presentation we look at a combinatorial
  optimization problem in application to a layout
  of mechatronic devices. The presentation scope
  includes
• Introduction to space optimization for an
  assembly.
• Simulated annealing (SA) algorithm.
• Three-dimensional design layout optimization.
• 3.1 Problem formulation and solution strategy
• 3.2 Overlap detection and evaluation
• 3.3 Spatial constraint and annealing violation
• Software implementation and embedment
• Smart design for assembly
• Conclusions

3
1. Introduction

• Space optimization for an assembly of components
  in complex electric-mechanical systems is a
  challenging structural design task. Experience
  and common sense have been usual engineering
  tools in the optimization process.

4
Although CAD environment helps designers to
achieve compact designs to a certain degree, it
is still time consuming and the solution is less
than optimal.
5

• Modeling and simulation techniques allow flexible
  and optimal handling of a complex n dimensional
  design space.
• Simulated Annealing mimics the physical annealing
  process and is successfully used to obtain an
  intelligent solution for a variety of
  combinatorial optimization problems.

6
Thus it becomes essential to create an
intelligent design environment which gives the
benefit of SA optimization in loop with
comprehensive CAD models, such as Solid
Works.The process can be formulated as the
problem of finding among a potentially very
large number of solutions a layout solution
with lowest energy or cost function.

C opt min C
(i), i ?R
7

• This work presents the concept of space
  optimization methodology for mechatronic devices
  within a 3D envelope.This optimized
  solution is then fully designed in Solid Works
  CAD environment using the identified envelope as
  the design space.
  

8
2. Simulated Annealing Algorithm

• Simulated Annealing is a kind of hill-climbing
  search for finding a good solution.
• It searches in the neighborhood of the best
  solution found to date, and jumps to a new
  solution whenever found the best to date.

9
Within the algorithm, an initial design state
is chosen and the value of the cost function for
that state is evaluated. A step is taken to a new
state by applying a move, or operator, from an
available move set.
Probability accept e ?C/T
(1)Where ?C is the change in cost function due
to the move and T is the current temperature.
10

• Applications of SA algorithms require
  specifications of three distinct items
• (1) a concise problem representation
• consists of configuration representation
  and cost function
• (2) a transition mechanism
• generates a new configuration from a
  current one
• (3) a cooling schedule.
• used to control the temperature in the
  algorithm

11
3. Three-Dimensional Design Layout Optimization

• The undertaken work is a new trial of using SA
  technique embedded in SolidWorks environment to
  optimize complex mechatronic assemblies.

12
3.1 Problem Formulation and Solution Strategy

• In this work, the 3D layout problem can be
  described as packing a batch of components of
  different sizes into an envelope. The packing
  tasks are characterized by the following four
  objectives
• Fitting the components into the specified
  envelope
• Observing topological connections or assembly
  relationships between components
• Avoiding any overlap between components and
  the envelope protrusion
• Achieving high packing density, or minimizing
  the overall space of the envelope.

13

• The strategy is to move components around
  within a pre-defined space and analyze each move
  on its effectives towards minimizing a combined
  cost function.
• The cost function includes design goals such as
  minimizing the packing density, the relationships
  between components, and the penalty terms, that
  evaluate the amount of components overlaps,
  envelope penetrations and spatial constraint
  violations.

14
3.2 Overlap Detection and Evaluation

• At each iteration in the optimization process,
  the annealing algorithm perturbs (moves) the
  position of components and requires overlap
  detection and evaluation.
• The easiest way to detect an overlap between two
  components is to detect its projections in each
  2-D plane (x-y, y-z, or z-x plane).
• If there is no overlap between their projections
  in any 2-D plane, then there is no overlap
  between these two components.

15

• The following three figures illustrate the
  concept of decomposition levels of a component in
  2-D plane.
• Figure 1 First level of decomposition of 2-D
  model

16

• The following two figures illustrate the
  principle of resolution levels of an overlap in
  2-D plane.
• Figure 4 Detected overlap at a low level
  of resolution Figure 5 Detected no
  overlap at a higher level of resolution
• A multi-resolution detection scheme could be
  adapted to obtain reasonable running time.

17
3.3 Spatial Constraint and Annealing Violation

• There are special relationships between
  particular components or housing constraints, it
  is necessary to constrain components with respect
  to the envelope and each other.

18

• For those particular components with
  restrictions in a given direction (a particular
  absolute position or orientation with respect to
  a linear combination of global coordinate axes),
• it is simple to place the component in a
  feasible initial position and its moves are
  restricted in such a way that it cannot be moved
  to an non-feasible point or be rotated along an
  non-feasible axis.

19

• Similarly, for those components with particular
  restrictions to the global coordinate axes.
• The constraints may be violated under the
  assumption that allows the annealing to pass
  through non feasible layouts and lead to
  feasible layouts.
• In this work, two types of such constraints would
  be adopted with the employment of violation
  process, which is constrained by centers or by
  extents.

20

• Constrained by center is to restrict the position
  of component based upon its origin of coordinate
  system (Figure 6).
• Figure 6 Spatial constraints by centre

B
A
21

• Constrained by extent is to restrict the position
  of all points of the component rather than only
  its origin (Figure 7).
• Figure 7 Spatial constraints by extents

B
A
22
4. Software Implementation and Embedment

• The developed optimization algorithm / procedure
  was programmed in Visual C and was embedded
  into SolidWorks so that the designer can
  concurrently recall the optimization software
  while developing.

23

• The implementation flow chart can be illustrated
  as following.

24
5. Smart Design for Assembly

• Once the CAD system embedded with intelligence,
  designer could concurrently recall the software
  while developing, to simultaneously run more than
  one optimization processes.
• Allows the designer to develop different
  configurations of assembly and compare its
  packing performances before selecting a detail
  design.
• Enables the designer to link pre-processed
  modules or subassemblies into a new envelope to
  provide integrative tailored modeling solutions
  for even much more complex assembly space in a
  systematic manner.
• Particularly achieves minimized assembly space
  for complex electric-mechanical devices

25
Figure 9 Concurrently recall the optimization
software while drafting in Solidworks
26
Figure 10 Recalled GUI of the optimization
software
27
(a)
(b) Figure 11 Comparison
of different pre-processed assembly solutions
28
6. Conclusions

• This work presented a novel space optimization
  algorithm for design of mechatronic assemblies
  based on Simulated Annealing technique.
• This algorithm / procedure can be used as an
  optimization tool to intelligently minimize the
  housing space for such devices where a large
  number of different sections and components are
  interfaced in the assembly.
• As an intelligent design tool, SA algorithm /
  procedure can be used for the optimal design of a
  wide range of portable devices and also other
  compact equipment which require high density
  packing performance.
• An interesting future work would be to test the
  algorithm in application to other complex
  problems and to improve the detection of overlap
  in order to minimize the computational time.

29
Thanks and questions