1. Constraint-based heuristics for amphibious embarkation planning
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Constraint-based heuristics for amphibious embarkation planning
Paul A. Chircop & Timothy J. Surendonk
D1. Mathematical modelling for defence applications
MODSIM 2015

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Introduction
Amphibious operations:
Transportation of army units (e.g. vehicles) from the sea to the land.
Optimally embark units onto a ship’s deck:
Amphibious embarkation problem:
Represented as a packing problem.
Units modelled by rectangular items with width, length and mass.
A CH-47D Chinook conducts load lifting trials with HMAS Canberra in Jervis Bay.
images.navy.gov.au

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Packing Problem
Input:
A rectangular deck (with/without obstacles).
A list of rectangular items (dimensions, mass).
Objective:
Maximize the total area of packed items.
Constraints:
Items cannot overlap each other or the deck boundary.
No stacking and no rotation of items.
Items cannot overlap obstacles (if present).
Priority ordering (optional).
Mass balance + threshold (optional).

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Illustration

5. Modelling / Solution Approach
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Modelling / Solution Approach
Constraint Programming (CP):
Expressive modelling power.
Domain filtering, logical constraint propagation, branch-and-bound search.
Constraint Optimization Packing Tool:
Java-based software package.
ILOG CP Solver (IBM) as CP engine.

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Why COmPacT?
Flexibility:
Choice of CP engine (commercial/open source).
Customized heuristics.
User Interaction for manual control:
Automated and manual packing.
Time-out functionality for iterative packing
Run from a warmstart.

7. GUI / Test Rig CP search engine information.
Builds a tree of feasible packing solutions.
Allows user to click-drag-and-lock items (manual mode).
Allows for buffers (borders) on individual items.
Sets movement constraints on individual items.
Implements sequential packing heuristics.

8. Binary Decision Variables
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Binary Decision Variables

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Relative positions
(x1, y1) w1
(x3, y3) w3
(x2, y2) l1 w2 l3 l2

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Constraint Model
Objective
Deck Boundary
Bounds
Packing Feasibility
Symmetry Breaking
Obstacles
Variables
Mass Balance

11. Example – Solver Only (I)
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Example – Solver Only (I)
Obstacle
Obstacle
15.8 m
Obstacle
93.5 m

12. Example – Solver Only (II)
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Example – Solver Only (II)
3,003 variables.
17,774 constraints.
Optimal solution found in 0.68 seconds.

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Heuristics
Aggregation:
Joining (adjacent) like items together before throwing to the solver.
Limited by priority ordering.
Sequential Packing:
Iterates through a series of warmstart solutions.
Local movement (constrain position).
Pack by priority or by size.

14. Aggregation Illustration (I)
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Aggregation Illustration (I)
Combine identical items adjacent in priority list.
Carried out along the length axis or width axis.

15. Aggregation Illustration (II)
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Aggregation Illustration (II)

16. Example – Aggregation + Solver
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Example – Aggregation + Solver
21.0 m
Obstacles
94.5 m

17. Solution – Aggregation x 3
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Solution – Aggregation x 3

18. Aggregation Heuristic Performance
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Aggregation Heuristic Performance

19. Sequential Packing Illustration (I)
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Sequential Packing Illustration (I)

20. Sequential Packing Illustration (II)
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Sequential Packing Illustration (II)

21. Sequential Packing Illustration (III)
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Sequential Packing Illustration (III)

22. Sequential Packing Illustration (IV)
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Sequential Packing Illustration (IV)

23. Sequential Packing Illustration (V)
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Sequential Packing Illustration (V)

24. Example – Sequential Packing by Size
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Example – Sequential Packing by Size
15.8 m
Obstacles
93.5 m

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Solution

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Solution

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Solution

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Solution

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Solution

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Solution

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Solution

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Solution

33. Example – Sequential Packing by Priority
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Example – Sequential Packing by Priority
Priority Ordering
15.8 m
93.5 m

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Solution

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Solution

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Solution

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Solution

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Solution

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Solution

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Solution

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Solution

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Summary / Future Work
Constraint programming approach:
CP solver + customized heuristics.
Improvement on extant in-house techniques:
Simulated annealing + compaction heuristics.
Future work:
Benchmarking performance:
Broader spectrum of test problems.

43. Questions UNCLASSIFIED – Approved For Public Release
Paul Chircop & Timothy Surendonk
Joint and Operations Analysis Division
Defence Science & Technology Group