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Constraint-based heuristics for amphibious embarkation planning

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Presentation on theme: "Constraint-based heuristics for amphibious embarkation planning"— Presentation transcript:

1 Constraint-based heuristics for amphibious embarkation planning
UNCLASSIFIED – Approved For Public Release 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
UNCLASSIFIED – Approved For Public Release 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
UNCLASSIFIED – Approved For Public Release 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)
UNCLASSIFIED – Approved For Public Release Example – Solver Only (I) Obstacle Obstacle 15.8 m Obstacle 93.5 m

12 Example – Solver Only (II)
UNCLASSIFIED – Approved For Public Release 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)
UNCLASSIFIED – Approved For Public Release Aggregation Illustration (I) Combine identical items adjacent in priority list. Carried out along the length axis or width axis.

15 Aggregation Illustration (II)
UNCLASSIFIED – Approved For Public Release Aggregation Illustration (II)

16 Example – Aggregation + Solver
UNCLASSIFIED – Approved For Public Release Example – Aggregation + Solver 21.0 m Obstacles 94.5 m

17 Solution – Aggregation x 3
UNCLASSIFIED – Approved For Public Release Solution – Aggregation x 3

18 Aggregation Heuristic Performance
UNCLASSIFIED – Approved For Public Release Aggregation Heuristic Performance

19 Sequential Packing Illustration (I)
UNCLASSIFIED – Approved For Public Release Sequential Packing Illustration (I)

20 Sequential Packing Illustration (II)
UNCLASSIFIED – Approved For Public Release Sequential Packing Illustration (II)

21 Sequential Packing Illustration (III)
UNCLASSIFIED – Approved For Public Release Sequential Packing Illustration (III)

22 Sequential Packing Illustration (IV)
UNCLASSIFIED – Approved For Public Release Sequential Packing Illustration (IV)

23 Sequential Packing Illustration (V)
UNCLASSIFIED – Approved For Public Release Sequential Packing Illustration (V)

24 Example – Sequential Packing by Size
UNCLASSIFIED – Approved For Public Release 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
UNCLASSIFIED – Approved For Public Release 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


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