THE TYCHE AND SAFE MODELS: COMPARING TWO MILITARY FORCE STRUCTURE ANALYSIS SIMULATIONS

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1 THE TYCHE AND SAFE MODELS: COMPARING TWO MILITARY FORCE STRUCTURE ANALYSIS SIMULATIONS Cheryl Eiler and Slawomir Weolkowki Daniel T. Wojtazek Centre for Operational Reearch and Analyi Atomic Energy of Canada Ltd. Defence Reearch and Development Canada Chalk River Laboratorie 101 Colonel By Drive, Ottawa, ON K1A 0K2 Canada 1 Plant Road, Chalk River, ON K0J 1J0 Canada cheryl.eiler@drdc-rddc.gc.ca wojtazd@aecl.ca .weolkowki@ieee.org KEYWORDS Force Structure Analyi, Fleet mix analyi, Capability- Baed Planning, Dicrete Event Simulation, Multi- Objective Optimization, Scheduling. ABSTRACT In the pat, everal force tructure analye have been conducted for the Canadian Armed Force uing moderate fidelity (e.g., Tyche) and low-fidelity (e.g. Stochatic Fleet Etimation or SaFE) imulation model within optimization framework. Monte Carlo dicrete event imulation like Tyche are computationally expenive and can only be ued in optimization that require few force tructure evaluation. The SaFE model act a a imple urrogate model that can be utilized by more global optimization technique. SaFE, originally developed to tudy air mobility fleet, wa adapted to accommodate a larger et of capabilitie and more cheduling heuritic o that the performance of many force tructure can be quickly aeed while minimizing a et of objective. The amount of time required to find the SaFE optimal force tructure i ignificantly le than uing Tyche. Thi indicate that SaFE could be an important tool for dicovering paretooptimal force tructure (within the pace of all poible mixe) that would repreent practical lower bound on the force tructure requirement for accomplihing expected future cenario. The purpoe of thi paper i to compare and contrat the ue of Tyche and SaFE through imulation optimization on a given dataet. INTRODUCTION Determining the bet future military force tructure, compried of a et of aet, to accomplih a et of defence and ecurity tak i a challenging undertaking. The et of tak mut be thoroughly invetigated; requirement, frequencie, and duration for each tak require definition. Potential aet mut be identified and their abilitie to meet tak requirement aeed. Beide the neceity for accurate data from which to model, the force tructure problem i further complicated by the deep uncertainty (Bui et al. 2009) inherent in modelling future environment. Thu, a force tructure mut be capable of addreing many poible combination of future operational tak. Furthermore, aet are large capital invetment; accordingly, the goal i not only to find the appropriate force tructure ize and mix with repect to the devied future cenario, but alo the mot capable tructure at the lowet cot (Wojtazek and Weolkowki 2012). Since large capital procurement project undergo ignificant internal and external crutiny, it i incumbent upon deciion-maker to balance many conflicting objective, jutifying invetment with anticipated need. Due to the non-linear nature of the performance objective function, a well a the length of computational time required to evaluate individual force tructure, it i often not realitic to find a globally optimal tructure in the time normally given to complete uch tudie. The computational complexity i exacerbated when earching for the pareto-optimal et of tructure with repect to multiple objective (Wojtazek and Weolkowki 2013). It i, therefore, critical that methodologie for quickly identifying optimal future force tructure be invetigated. Two optimization-imulation approache to force tructure analyi ued within the Defence Reearch and Development Canada Centre for Operational Reearch and Analyi (DRDC CORA) are examined. The firt approach ue a computationally intenive, Monte Carlo dicrete event imulation model known a Tyche (Eiler and Allen 2012) within a direct earch optimization framework. The model take a top-down approach to tet force tructure, mimicing the deciion of a military cheduler by aigning aet within a given force tructure to cenario a they arie. A ingle imulation run often require hour to complete, and an optimization earch can take week or month on today dektop computer; neceitating an optimization procedure that require relatively few tep to converge to the optimal force tructure compoition. An alternative to the moderate-fidelity approach baed on Tyche i the low-fidelity approach of DRDC CORA Stochatic Fleet Etimation (SaFE) model (Wojtazek and Weolkowki 2013). SaFE i alo a Monte-Carlo baed imulation, which generate average yearly requirement from a dataet with frequency, duration, and capacity requirement for tak (cenario Proceeding 28th European Conference on Modelling and Simulation ECMS Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Catellani (Editor) ISBN: / ISBN: (CD)

2 without a tochatic location element) and aet. However, the total force tructure requirement are etimated from the bottom up, through a fixed matching of aet to cenario, and no attempt i made to account for cheduling contraint (e.g., tart and end date). Given SaFE relatively quick run time (approximately one milliecond on the ame data run through Tyche), optimization i carried out over the olution pace of all poible tak to aet aignment, not jut all of the force tructure compoition. Both model will be decribed ubequently in further detail. The optimization reult of the Tyche and SaFE model will be compared, and their role for military force tructure analyi contrated. THE TYCHE MODEL Tyche chedule the deployment of aet within a force tructure to addre a et of miion (Eiler and Allen 2012). Figure 1 illutrate the implementation of the Tyche model. On the top right, a fixed et of demand i created: miion to which a military force tructure hould endeavour to repond. Thee miion are created a cenario, and may be broken down into one or more phae. Each phae may be random or cheduled, with it own frequency, duration (and aociated probability ditribution) and poible theatre location, a well a a et of capability demand. they are baed. To run a Tyche imulation, one force tructure i elected to tet a capability upply from the et of aet againt demand requeted from the given cenario. Demand i contructed tochatically from the cenario for frequency, tart date, and duration in the chedule. Scenario can be randomly generated uing a Poion proce or cheduled at known interval; duration are generated uing uniform or triangular ditribution. Aet within a force tructure are then aigned to the chedule chronologically utilizing the policy to meet a ingle requirement by electing from a lit of available aet baed on information that i known and actionable at the moment a miion occur (Wu et al. 2009). The available aet within the force tructure are aeed a numerical core for the capability ued in the cenario and optional penaltie for exce capability upply, timeline into theatre, and cheduling conflict. The coring algorithm (Eiler and Allen 2012) factor in the quality, quantity, and ubjective weighting of importance of capabilitie matched between the upply and demand for a pecific combination of aet. The combination of aet with the highet core i then aigned to the cenario in the operational chedule. Thi proce i repeated for all imulation iteration in a Monte Carlo approach (Robert and Caella 2004), and force tructure performance i evaluated baed on how well and how often the cenario capability requirement are met. Thi i done in the form of tatitic gathered from the collection of operational chedule on unmet capability demand per cenario, and by factoring in the frequency of cenario occurrence and political impact of failure to meet uch requirement, to form a metric of political rik. Performance Metric The average yearly political rik R for a et of cenario i defined a R (1) f I P Figure 1: Tyche Model Tyche can model a number of aet type, each upplying different capabilitie. Force tructure are contructed out of thee aet type by pecifying a quantity for each type and a phyical location where where the rik for a given cenario i defined a the product of the annual frequency of occurrence f, the political impact I of cenario failure, and the percentage of time the capability upply deployed by the cheduler i inadequate P. The firt factor i aeed by averaging the number of time the cenario occur yearly acro all chedule. The econd factor, impact core, i provided by ubject matter expert (SME) into the calculation. Each cenario i aigned to an impact category with an aociated impact core. The third factor in the rik calculation i defined a a weighted calculation of the percentage of time that capability requirement are not met at variou level for the cenario (Eiler and Allen 2012).

3 Optimization Framework Tyche wa deigned a a tool to evaluate and compare individual force tructure. There i no optimization built in to drive the earch for better force tructure compoition. However, Tyche can be ued inide an optimization framework, provided that the algorithm doe not require a ignificant number of force tructure evaluation due to the computational cot aociated with each imulation run. An optimization i conducted within the olution pace of all poible force tructure compoition, with Tyche evaluating the performance of each feaible tructure. A force tructure analyi tudy conducted internally by DRDC CORA ued the Hooke-Jeeve algorithm (Hooke and Jeeve 1961), modified to combine a local exploratory earch with a global pattern earch, to perform the optimization procedure. Starting from an initial force tructure compoition, the exploratory earch make cumulative incremental change to each aet type to determine if the objective value improved. The bet combination of local improvement i ued to drive the pattern earch for larger tep ize. Although thi algorithm can eaily get trapped in local optima, it ha two major advantage for application with Tyche. Firt, it require few function evaluation, which are computationally cotly. Second, it i imple enough not to require automation, given that manual input i required to et up force tructure within Tyche. Two primary objective were defined to determine optimal force tructure: minimizing total force tructure rik and ize. Due to the dicrete political impact categorie, the rik minimization wa then defined in two way, each ued to drive eparate optimization. The firt optimization minimized total rik and tructure ize, where a change in force tructure wa retained if the total rik decreae wa deemed tatitically ignificant. Noting that the tandard error SE wa etimated uing the ample variance of the rik ditribution divided by the quare root of the number of chedule realization and, auming that the ditribution can be normally approximated, the tatitical ignificance wa calculated in pairwie comparion where the ±2 SE interval did not overlap (Payton et al. 2003). A econd optimization minimized rik per impact category until a threhold of acceptable rik (a defined by military SME) wa reached. That i, a change in force tructure wa retained if the rik in any impact categorie howed a tatitically ignificantly decreae. Again, the number of aet in the force tructure wa minimized by rejecting change (i.e., with aet addition) that howed no tatitically ignificant improvement. The earch wa terminated once the rik in each impact category met the given threhold within the bound of the tatitical ignificance. The procedure i illutrated by the following peudo code on the force tructure of compoition x, a vector count of each aet type, α a the pattern earch acceleration factor and a the pattern earch tep vector: procedure modifiedhj( x,, ) with DO WHILE termination criterion not met // Exploratory earch tep ize, initially a vector of zero for total number of aet type FOR i = 1 to number of aet type xi x i i Evaluate imulation at x R x ) 2SE R( x) SE IF ( R ( x ) 2 R ( x ) i i ENDIF NEXT // Pattern earch DO WHILE x x x x Evaluate imulation at R x ) 2SE x IF R( x) SE ENDIF LOOP LOOP ( R ( x ) 2 R ( x ) 0.5, a acceleration factor, where all i value mut be integer and MIN ( ) 1 A ubequent a greedy earch i then applied to trim the olution. Trimming i carried out only if the modified Hooke-Jeeve algorithm i ucceful at either minimiing the total rik to zero or the rik per category under the pecified threhold. Thi trimming tep i neceary ince the pattern earch can add everal aet from different type at the ame time, leading to a larger tructure than neceary to achieve the pecified objective. The trim procedure i illutrated by the following peudo code on the force tructure of compoition x : i procedure Trim( x ) DO WHILE termination criterion met FOR i = 1 to number of aet type x i x i 1 Evaluate imulation at x IF termination criterion NOT met xi x i ENDIF NEXT Evaluate imulation at x

4 DO WHILE termination criterion NOT met FOR all reduction to x Select i with the maximum reduction of R( x ) and revere change by LOOP LOOP x i x i 1 NEXT Evaluate imulation at x The total time for each aet type i then averaged over all iteration to form the average annual demand. The number of aet required in the force tructure to atify thi average level of demand i computed imply a the whole number of aet that can provide uch time (for example, 2.6 year of average annual demand require 3 aet within the force tructure). The ample variance of thee duration i alo computed to determine how much the demand varie acro all of the cenario. The reult of the optimization of the Tyche run will be dicued in comparion with the reult of the SaFE imulation optimization (a conducted on the ame input data et) after a decription of the SaFE model and it optimization framework i given. THE SAFE MODEL Like Tyche, SaFE i alo a capability-baed model that ue a Monte-Carlo approach to determine poible force tructure baed on the tak that mut be performed. It ue a dataet of tak frequency, aet- and tak-pecific duration, and capability (in the cae of air mobility (Wojtazek and Weolkowki 2013), thee were paenger and freight capacitie) requirement to derive demand over a tochatically generated number of tak. The force tructure i built from the bottom up, where it compoition i computed uch that there are ufficient aet to accomplih an average et of tak. Since aet are matched to tak via capabilitie, there can be many aignment combination. Force tructure generated by SaFE are input into an (uually multiobjective) optimization procedure o that aet can be traded off againt each other baed on common capability. Given that SaFE i a bottom-up tak-driven model, if in one olution the number of aet of a particular type increae (in comparion to another olution), then the number of aet of a different type which ha imilar capability will uually decreae. To illutrate the difference between SaFE and Tyche, conider Figure 2. Intead of building a force tructure out of a variety of aet type at a number of bae to tet during a imulation, SaFE exhautively matche each tak to a pecific aet or group of aet. Thi aet to tak aignment i done in a capability-baed manner ahead of the optimization proper in order to limit the olution pace to all feaible aet aignment. Each individual aet to tak aignment i known a a configuration. On the top right of Figure 2, demand i generated tochatically from a et of tak, uing frequencie and duration derived from triangular ditribution. Aetpecific duration ditribution (uniform) are alo defined for completion of each tak, and computed baed on the configuration in ue. For each iteration, the total demand can be calculated a time required for each aet type. Figure 2: SaFE Model Eentially, SaFE aume a much implified world where only total time on tak for each aet type i needed to compute force tructure requirement. It doe not take into conideration event cheduling, uch a tak tart and end time, tak cancellation or prioritization, or other aignment contraint. SaFE yield the bet poible repreentation of tak requirement and, thu, underetimate realitic tak requirement to produce a lower bound on a required force tructure. Due to thi implification, SaFE can be ued in an optimization framework to generate and evaluate force tructure much more quickly than even the mot efficient Monte Carlo dicrete event imulation. Thi improved peed i vital when earching for optimal tructure, a proce that require many force tructure to be evaluated. For analye where higher fidelity i required, the SaFE model could be exploited a a preproceing tool. It may reduce the problem pace by eliminating large number

5 of inefficient option and, thu, reduce the cot of uing higher fidelity tool uch a Tyche. Adaptation to New Data In Figure 2, there are everal object indicated with dahed line, uch a bae, theatre, and cenario. Thee are common concept between Tyche and SaFE; however, SaFE doe not provide direct upport for uch data entry. To accommodate thee concept, the following adaptation were made: Multiple bae: aet of the ame type defined at different location and with different tranit time to theatre (a aet-pecific tak completion duration). Scenario with a probability of occurring at more than one theatre and/or more than one phae per cenario: handled through data manipulation to obtain a uitable equivalent of multiple tak in SaFE. Aet aignment dependent upon availability at the time a cenario arie in the imulation: Tyche would end the ame unique et of aet to a cenario every time if there were no limit on the number of aet available, but to enable the SaFE model to ue an optimization mechanim for configuration generation, poible aet to tak aignment are calculated a thoe that provide all the capabilitie at the required level while alo providing a minimum of exce capability. The effect of aet type that act a force multiplier: captured by modelling a ingle additional aet type with enhanced capabilitie. Performance Metric The objective of the optimization i to earch for force tructure that are capable of fulfilling the average requirement and are minimal with repect to ize, cenario duration, and rik of failure. The force tructure ize objective (E ize ) i an evaluation of the number of aet reulting from the choen configuration and identifie tructure which require minimal reource but are till capable of accomplihing the average cenario. The ize objective i defined a E ize F am a w F m (3) the ummation of the number (F) in each aet type (a) plu a mall weighted (w=0.01) total to account for the number of a ingle type of relatively low-value force multiplier aet (m). The cenario duration objective function evaluate the average time it take to accomplih a cenario. The duration objective (E time ) i defined a E, where ( ) max d ( a) time a (4) where d (a) i the time it take one aet of type a to accomplih it portion of all intance of cenario, and δ() i the maximum time it would take any of the aigned aet to complete the cenario (thu the duration of the aet that travel furthet to the theatre i the one that define the duration for the whole configuration). Thi aume that all aet travel at the ame peed, and that all aet mut arrive at the theatre before the cenario can commence. The force tructure ize and cenario duration objective are evaluated uing the average duration output from SaFE. However, the requirement of any iteration may vary from that of the average iteration. To mitigate the effect of thi uncertainty, a rik-baed objective i ued, which i an evaluation of the ability of a configuration to accomplih all iteration. The rik objective (E rik ) i computed by E 1 ( a) rik a (5) a the probability that at leat one aet will not be able to accomplih it requirement. The probability that an aet will be able to fulfill it requirement i given a π(a) (Willick et al. 2010). Optimization Framework A ingle imulation run in SaFE i conducted for a given aet to tak aignment configuration over 10 4 iteration (typically) of one year in duration each. An average force tructure can then be calculated to meet the average et of demand over all iteration. The pace of all poible configuration i very large (Wojtazek and Weolkowki 2013) ignificantly larger than the force tructure compoition olution pace. Since thi large configuration pace cannot be exhautively earched in a practical amount of time, a metaheuritic i required. Given that multiple objective are conidered, a multiobjective optimization algorithm need to be ued to provide a et of non-dominated olution with repect to thee objective. Among the multi-objective algorithm that exit (Deb 2005), a well-tudied one that ha been utilized previouly with Safe i the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II). NSGA-II i an elitit evolutionary algorithm that group individual olution into non-dominated front, and ue a crowding-ditance operator to preerve diverity of olution (Deb et al. 2002). Each olution comprie a configuration of aet to tak aignment, and a bae ditribution for each aet. The NGSA-II peudo code i not provided here, a it i adequately given in a variety of reference, including (Deb et al. 2002). RESULTS The tudy dataet included 164 cenario and 28 theatre. There were 14 aet type modeled, each at two

6 poible bae. The reult of the aet to tak aignment algorithm generate 7.4 x poible configuration over all cenario. The NSGA II wa run 50 time with individual (configuration) for generation each with a mutation rate of 20%. Multiple run were ued to enure the repeatability of the reult obtained with repect to quality. The quality of the reult wa aeed uing a hyper-volume meaure (Fleicher 2003). The nondominated front of the lat generation over each run were combined into a ingle et of individual, and then the non-dominated orting algorithm wa performed on thi et to give the combined non-dominated front over the olution from the 50 run. The hyper-volume of the lat generation of each run wa then computed and compared to the hyper-volume of the combined nondominated front. The hyper-volume average and tandard deviation over all the run correponded to 96%±3% with repect to the combined bet nondominated front. Therefore, the quality of the reult from each run can be conidered to be imilar to the other, and, therefore, analyi in the remainder of thi ection i carried out on the reult of one of the run. Figure 3 how a plot of E time veru E ize for the 81 configuration in the non-dominated front, with the colour of each point repreenting the value of E rik. Thi figure how the trade-off between the ize of the force tructure and the rik of not being able to fulfill all of the demand in an iteration. When looking at configuration with the ame value of E ize, configuration with lower E time have higher E rik, thu demontrating that there i a rik of not being able to aign aet from the cloet bae to theatre. The lowet value of E rik over the non-dominated configuration i 0.27, indicating that the duration of aet ue in an iteration may deviate ignificantly from the average. Recall that E rik doe not take into account the timing of cenario within an iteration and the requirement that cenario mut be performed within time window. Therefore, the rik of a force tructure produced by optimizing SaFE not being able to atify all of the demand in a given iteration may be greater than E rik. Figure 3: Plot of Objective Value for Configuration in the Non-Dominated Front A mentioned previouly, the ame force tructure can be computed from different configuration. For example, configuration A and B hown in Figure 3 both reult in the ame force tructure, but configuration A ha lower E rik (0.27 v. 0.36) and higher E time (7.06 v. 7.05). Thee difference are due to difference in the aet aigned to each cenario and the bae from which the aet are aigned. Within the 81 non-dominated configuration, there are 24 ditinct force tructure. The range of number of each aet type over thee tructure are hown in Table 1. When compared to the force tructure run through Tyche (three ditinct force tructure were ued to eed the initial value for two eparate optimization to produce ix final tructure), the upper bound on thee range are imilar to or lightly le than the SME force tructure for mot aet. Thi reult indicate that the SME force tructure could theoretically atify the average iteration requirement with repect to the duration of aet uage with ome unued aet capacity. The force tructure from the optimization conducted uing Tyche are much larger in number for mot aet type than the upper bound on the range of nondominated tructure, indicating that they could theoretically atify the average iteration requirement with a large amount of unued aet capacity (which may be neceary to meet cheduling contraint). Comparion of Suggeted Force Structure The force tructure compoition produced uing the SaFE model were run back through the Tyche Table 1: Range of Number of Aet in Recommended Force Structure Type 1 Type 2 Type 3 Type 4 Type 5 Type 6 Type 7 Type 8 Bae A B A B A B A B A B A B A B A B SaFE SME Tyche

7 imulation in order to compare reult with common metric. Each force tructure wa run for iteration. Of the three SaFE objective, only E ize, a good indicator of force tructure ize, i independent of the model. E time and E rik are aociated with pecific aet to cenario aignment configuration, of which there may be multiple for the ame force tructure compoition, and cannot readily be generated for the SME or Tyche recommended force tructure. A a reult, comparion will primarily be made on correlation between E ize, political rik, and E rik. The et of force tructure choen for thi comparion comprie all of the force tructure from the final generation of the NSGA-II, not jut the 24 in the nondominated front. Thi et comprie 274 ditinct tructure, and wa choen to provide a better tatitical analyi. In the amount of time it took to run an evolutionary optimization procedure to find 24 nondominated force tructure (le than 24 hour), the Tyche imulation wa only able to evaluate approximately 77 force tructure (2.5 hour per force tructure, running 8 imulation in parallel). Performance evaluation uing SaFE are not a precie when compared to Tyche becaue the SaFE evaluation are baed on average requirement. In addition, the rik meaure ued are not directly comparable, ince the political rik objective i a weighted um of tochatic cenario performance, where each cenario i weighed according to the political impact of not being able to provide it required capability. The E rik objective, on the other hand, doe not ditinguih between the importance of different cenario. Another iue with comparing E rik and the political rik for a force tructure i that there may be multiple value of E rik for a given tructure due to the poibility of multiple configuration for the aet to tak aignment. In order to determine which value of E rik to ue for each force tructure, the correlation coefficient i computed between the tructure political rik and each of the minimum, mean, and maximum value of E rik. The reulting correlation coefficient value are 0.62, 0.63, and 0.63, repectively; thu indicating that there i very little difference among thee value. All that can be aid here i that the higher value of E rik for a force tructure may be lightly more reflective of the political rik computed uing Tyche than the lower value. The mean value of E rik will be ued for the remainder of thi ection with the aumption that uing either of the other value will not ignificantly change the analyi. The poitive correlation obtained here how that there i ome potential in uing SaFE to etimate the rik of a force tructure, although Figure 4 how that there are force tructure with lower total political rik but larger E rik than other tructure; therefore, more work would be required to formulate a rik meaure uable with SaFE that i more reflective of the political rik meaure. Figure 4: E rik v. Total Political Rik for the SaFEproduced Force Structure By plotting E ize veru total political rik for the 274 SaFE, 2 SME, and 6 Tyche-recommended force tructure, Figure 5 i obtained. There are three ditinct cluter in the graph: the low political rik tructure recommended by the Tyche optimization, the maller SME-recommended tructure with higher rik, and the even maller SaFE generated tructure with yet higher rik. From thi plot, it can be een that SaFErecommended tructure have the highet political rik and lowet ize, while Tyche-recommended tructure have the lowet political rik and the larget ize. Figure 5: Size v. Total Political Rik Objective for All Recommended Force Structure In SaFE, the aumption i that the occurrence of all tak can be arranged in the mot advantageou way for the entire force tructure over time. It i clear that computing a force tructure uing a model baed on everal problem implification uch a SaFE reult in tructure of lower ize and, a a conequence, higher political rik. Figure 5 how that SaFE and Tyche could be ued a lower and upper bound, repectively, on the number of aet needed within a force tructure, and thu provide deciion maker with realitic force tructure ize bound. CONCLUSIONS The SaFE model wa uccefully ued in a multiobjective optimization framework to find optimal force tructure with objective to minimize fleet ize,

8 cenario duration, and rik of failure. A et of SaFEderived force tructure wa then evaluated uing the Tyche imulator in order to ae their political rik. The reult howed that SaFE-recommended force tructure have the highet political rik and lowet ize, while the Tyche-recommended force tructure have the lowet political rik and the larget ize. Thu, reult from SaFE and Tyche could be ued repectively a lower and upper bound on the number of aet required within a force tructure, and provide deciion maker with more realitic bound on the political rik objective. SaFE appear to provide a lower bound on the force tructure ize ince it i a model baed on everal contraint relaxation. In addition, there i ome correlation between total political rik and E rik although E rik wa not deigned to etimate political rik. The amount of time required to find the SaFE nondominated configuration wa le than 24 hour, wherea running a Tyche imulation required 2.5 hour per force tructure; therefore, SaFE hould be invetigated further a a quick preproceing tool that can ort through vat number of tructure which can then be analyzed in more detail in Tyche. Furthermore, SaFE can alo be modified to compute force tructure that are capable of atifying different level of iteration requirement. For example, intead of uing mean aet duration, the aet duration could be choen uch that they are greater than thoe of a uer-pecified percentage of iteration. ACKNOWLEDGEMENTS Dr. Wojtazek contribution to the work reported on in thi publication wa performed while he wa employed at DRDC CORA. The author would like to thank Leanne Stuive, a co-operative education tudent from the Univerity of Waterloo, who aited in the initial application of SaFE to the dataet dicued herein. REFERENCES Bui, L.T.; M. Barlow; and H. Abba "A Multi- Objective Rik-Baed Framework for Miion Capability Planning." New Mathematic and Natural Computation (NMNC), No.5 (2), Deb, K "Multi-Objective Optimization." In Search Methodologie, Burke, E.K. and G. Kendall (Ed.). USA, Springer, Deb, K.; A. Pratab; S. Agarwal; and T. Meyarivan "A Fat and Elitit Multiobjective Genetic Algorithm: NSGA- II." IEEE Tranaction on Evolutionary Computation, No.6 (2), Eiler, C. and D. Allen "A Strategic Simulation Tool for Capability-Baed Joint Force Structure Analyi." In Proceeding of the International Conference on Operation Reearch and Enterprie Sytem (Vilamoura, Portugal, Feb. 4-6) INSTICC, Fleicher, M "The Meaure of Pareto Optima: Application to Multi-Objective Metaheuritic." In Evolutionary Multi-Criterion Optimization, Foneca, C.; P. Fleming; E. Zitzler; L. Thiele; and K. Deb (Ed.). Springer Berlin / Heidelberg, Hooke, R. and T.A. Jeeve ""Direct Search" Solution of Numerical and Statitical Problem." J. Aoc. for Computing Machinery, No.8 (2), Payton, M.E.; M.H. Greentone; and N. Schenker "Overlapping Confidence Interval or Standard Error Interval: What Do They Mean in Term of Statitical Significance?" Journal of Inect Science, No.3 (34), 1-6. Robert, C.P. and G. Caella Monte Carlo Statitical Method. Springer-Verlag, New York, NY. Willick, K.; S. Weolkowki; and M. Mazurek "Multiobjective Evolutionary Algorithm with Rik Minimization Applied to a Fleet Mix Problem." In Proceeding of the IEEE Congre on Evolutionary Computation (Barcelona, Spain, Jul ). Wojtazek, D. and S. Weolkowki "Military Fleet Mix Computation and Analyi." IEEE Computational Intelligence Magazine, (Aug), Wojtazek, D. and S. Weolkowki "Evaluating the Flexibility of Military Air Mobility Fleet." Sytem, Man, and Cybernetic: Sytem, IEEE Tranaction on, No.44 (4), Wu, T.T.; W.B. Powell; and A. Whiman "The Optimizing-Simulator: An Illutration Uing the Military Airlift Problem." ACM Tranaction on Modeling and Computer Simulation, No.19 (3), AUTHOR BIOGRAPHIES MS. CHERYL EISLER obtained her M.A.Sc. from Carleton Univerity in aeropace engineering. She work for DRDC CORA, where he lead reearch in the field of imulation for force tructure analyi. DR. SLAWOMIR WESOLKOWSKI i a cientit with DRDC CORA. He i alo an Adjunct Profeor with the Univerity of Waterloo, where he obtained hi Ph.D. in ytem deign engineering. He i intereted in operation reearch problem and rik analyi. DR. DANIEL WOJTASZEK received a Ph.D. degree in electrical engineering and joined DRDC CORA for two year a Pot-Doctoral fellow, before taking a full time poition a an Operation Reearch Analyt with Atomic Energy of Canada Ltd. COPYRIGHT NOTICE The author of thi paper (hereinafter the Work ) carried out reearch on behalf of Her Majety the Queen in right of Canada. Depite any tatement to the contrary in the conference proceeding, the copyright for the Work belong to the Crown. ECMS 2014 wa granted a non-excluive licene to tranlate and reproduce thi Work. Further reproduction without written conent i not permitted.