75th MORSS CD Cover Page UNCLASSIFIED DISCLOSURE FORM CD Presentation

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1 75th MORSS CD Cover Page UNCLASSIFIED DISCLOSURE FORM CD Preentation 712CD For office ue only June 2007, at US Naval Academy, Annapoli, MD Pleae complete thi form 712CD a your cover page to your electronic briefing ubmiion to the MORSS CD. Do not fax to the MORS office. Author Requet (To be completed by applicant) - The following author() requet authority to dicloe the following preentation in the MORSS Final Report, for incluion on the MORSS CD and/or poting on the MORS web ite. Name of Principal Author and all other author(): Jean-Paul Waton, David Strip, David L. Woodruff Principal Author Organization and addre: Sandia National Laboratorie, P.O. Box 5800, MS 1318, Albuquerque, NM Phone: Fax: jwaton@andia.gov Original title on 712 A/B: Simultaneou Conumable, Reource, and Spare Optimization for Future Combat Sytem Logitic Revied title: Preented in (input and Bold one): (WG_19/21, CG, Special Seion, Poter, Demo, or Tutorial): Slide 1 Thi preentation i believed to be: UNCLASSIFIED AND APPROVED FOR PUBLIC RELEASE

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3 Simultaneou Conumable, Reource, and Spare Optimization for Future Combat Sytem Logitic Dr. Jean-Paul Waton 1 Dr. David R. Strip 2 Profeor David L. Woodruff 3 jwaton@andia.gov 1 drtrip@andia.gov 2 Sandia National Laboratorie Albuquerque, NM USA dlwoodruff@ucdavi.edu 3 Univerity of California, Davi Davi, CA USA Sandia i a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United State Department of Energy National Nuclear Security Adminitration under contract DE-AC04-94AL85000.

4 Talk Overview Motivation The Sytem-of-Sytem Analyi Toolkit (SoSAT) Hybrid Simulation and Optimization Strategie Randomized Greedy Search Generating Solution for Individual Scenario Progreive Hedging Aggregating Solution Acro Multiple Scenario Concluion In-Progre and Future Reearch Direction Slide 3

5 Motivation Logitic optimization in the context of Future Combat Sytem poe many difficult challenge for the algorithm deigner Same goe for SBCT, HBCT, IBCT, Feature #1: Simultaneou conideration of pare, reource, and commoditie Apect are typically treated independently, and combined a poteriori Yield ub-optimal olution due to lack of eparability Yield infeaible olution due to log footprint contraint Feature #2: Short time-cale Ground combat operation are a tranient phenomenon Day to week-long miion = > marginal analyi olution are untable Feature #3: Non-parametric failure ditribution Damage incurred due to force-on-force action i non-parametric Extant logitic optimization algorithm aume parametric ditribution Slide 4

6 SoSAT: The Sytem-of-Sytem Analyi Toolkit (1) Slide 5

7 SoSAT: The Sytem-of-Sytem Analyi Toolkit (2) Obervation Logitic olution are increaingly being developed in the context of imulation, a oppoed to analytic, model Sandia SoSAT tool for Future Combat Sytem logitic modeling Time-tepped, PC-baed, high-reolution logitic imulator What operation can SoSAT model? Logitic / reliability for brigade-level ground combat ytem FBCT, SBCT, HBCT, IBCT Thouand of platform, each with ten to hundred of part 15 minute time-tep Stochatic model of combat damage via CASTFOREM run Dynamic buine rule, platform inter-dependencie What analytic capabilitie doe SoSAT provide? Track operational availability, lethality, mobility, etc., over time On platform/quad/platoon/etc. level Quantifie variability and related tatitic over N trial What-if aement of tructure / platform modification Slide 6

8 Integrating Simulation and Optimization Model Computing Platform: K-node Beowulf cluter Analyze Simulation K independent trial of flooded imulation Failure equence Progreive Hedging Optimization given K failure equence K independent trial of nominal imulation Inventory, reource, and commodity level adjutment Slide 7 Ae Solution Refine Solution Inventory, reource, and commodity level Bottleneck information Repeat until target availabilitie are met

9 Generating Solution for Individual Scenario (1) Output from a ingle flooded imulation run yield Failure equence for each part on each platform Run-out time for each commodity on each platform Analyi of imulation model yield Impact of not having a pare part, commodity, or reource E.g., lack of a tread down M1A2 mobility and availability Optimization objective Determine a minimal-cot olution that will achieve target performance metric (e.g., 95% availability) given a particular failure equence Obervation Approach aume independence of failure => olution i conervative E.g., lack of a tread on day N might delay engine failure on day N+2 Aggreive performance target => conervatim i not ignificant E.g., delay are not long given requirement of 95% availability Aume precience; olution doe not generalize! Slide 8

10 Generating Solution for Individual Scenario (2) Short time horizon facilitate very high-peed imulation Few number of failure during training miion Moderate number of failure during combat miion Developed a dicrete-event urrogate of SoSAT Input: Failure equence under flooded SoSAT imulation Input: Propoed pare, reource, and commodity level Output: Performance metric for the provided olution given the particular failure equence (i.e., cenario) Execution time: Milliecond Domain-pecific heuritic are ued to obtain an initial olution Highly ub-optimal, typically infeaible Marginal analyi i ued to iteratively adjut pare / reource / commodity level ROI i quantified (exactly) uing the urrogate imulator Executed until feaibility w.r.t. footprint and performance i achieved Optimality gap ha been aeed off-line uing a Mixed-Integer Program Within at wort 5% of optimality, more likely 1-2% Slide 9

11 The Single-Scenario Solution Approach: Dicuion Thi approach i a dramatic hift from traditional marginal analyi Why bother? Offer everal advantage over marginal analyi and other approache Paradigm implification; focu i on individual cenario Natural to imultaneouly conider pare, reource, and commoditie Non-parametric; can handle any form of failure type Far eaier to impoe buine rule and ide contraint Meet performance target not jut in expectation Expreion and atifaction of complex performance metric But with the baggage of Increaed computational cot (more later) Exact olution, retrictive aumption => heuritic olution, few aumption Far le developed problem domain theory Slide 10

12 Progreive Hedging: Overview We now have olution to N independent cenario So what? We aren t precient The next tage i intelligent olution blending No individual olution yield good performance in all cenario Taking the maximum olution yield infeaibilitie, unacceptable cot An effective alternative: Progreive Hedging (PH) A horizontal cenario decompoition technique Stochatic (mixed-integer) programming Contrat with vertical or tage-baed decompoition technique Rockafellar and Wet (1991) In general, multi-tage (deciion making with recoure) Not ued yet, but an intereting future avenue General obervation Logitic optimization problem can be canonically expreed a Stochatic Mixed-Integer Program Slide 11

13 Progreive Hedging: High-Level Architecture Sole parameter: ρ PH Iteration 0: Generate Solution For Individual Scenario min c x Initialize Scenario Weight Vector w = ρ( x x) Done Global Convergence Criterion Achieved? Fix Variable That Have Converged ( ( x x) ε ) ( cx cx) ε )? d max q PH Iteration k: Generate Solution For Individual Weighted Scenario min c x + w x + ρ / 2 x x 2 Update W w = w + ρ( x x) Slide 12

14 Progreive Hedging: Dicuion Convergence proof for PH Global optimum in the cae of convex problem (SLP) Local optimum in the cae of non-convex problem (SMIP) Selection of good value for the ρ parameter i an art Magnitude dictate convergence peed Intuitively hould be cot-proportional Mathematically-motivated heuritic (Waton, Woodruff, and Strip) Goal i to trade off optimality for convergence peed Other algorithmic engineering technique Fix lag (fix variable if they have tabilized over lat N iteration) Cycle detection and cycle breaking Acceleration once termination criteria i nearly achieved Progreive Hedging i trivially and efficiently parallelized Individual cenario olve are independent Barrier ynchronization to compute/update weight and olution tatitic Slide 13

15 Progreive Hedging: Reult Unclaified, real-world-inpired tet problem 100 platform, 50 part per platform One-week urge 30 cenario Optimization objective 95% operational availability in all cenario All cenario are feaible Solution obtained via PH in ~500 aggregate minute of run-time Parallelization on Beowulf cluter yield 25 minute wall-clock time Within 5% of optimality (determined via expenive MIP olve) Scalability to FCS-ized problem i under way Undertanding algorithm behavior a a function of proportion of pare, reource, and conumable level Slide 14

16 Concluion Logitic optimization for the Future Combat Sytem raie everal key and novel algorithmic challenge Simultaneou pare, reource, and commoditie Non-parametric analyi Short time horizon Simulation-baed optimization can be leveraged to yield olution to individual miion cenario Progreive hedging can effectively blend individual olution into a conitent global olution New approach offer advantage over traditional logitic optimization approache, but imultaneouly incur unique cot Much work remain in thi area Potential to ignite novel, intereting algorithmic work Slide 15

17 In-Progre and Future Reearch Direction Outlier-Aware optimization Empirically, there are many cenario for which feaible olution are extremely expenive New deign objective: Generate the minimal-cot logitic olution that atifie the performance target in 95% of the miion cenario Robut optimization To what olution component i performance mot enitive? How can generate le enitive olution? What i the trade-off between cot and robutne? Run-time reduction in Progreive Hedging Even better ρ election method Improved convergence accelerator Slide 16

18 Quetion? Thank! Progreive Hedging Innovation for a Stochatic Spare Part Support Enterprie Problem (Waton, Woodruff, Strip) Submitted Slide 17