Gray_Paper

Distribution Statement A: Approved for Public Release; Distribution Unlimited 

Dr. Alexander Gray 1 , Brian Cuneo 2 , Dr. Nickolas Vlahopoulos 2 , Dr. David Singer 2 

1 NAVSEA Carderock, 2 University of Michigan 

The Rapid Ship Design Environment – 

Multi-Disciplinary Optimization of a U.S. Navy Frigate 

ABSTRACT 

Early-stage design decisions directly impact the 

ultimate quality and cost of a design. The goal 

of the U.S. Navy’s Rapid Ship Design 

Environment (RSDE) is to enhance early-stage 

ship design by utilizing higher fidelity design 

and analysis tools, earlier in the ship design 

process to intelligently search for an optimal 

ship design. In the RSDE, Multi-disciplinary 

optimization (MDO) will be utilized to link 

existing ship synthesis and analysis tools to 

create a design system capable of providing 

intelligent decision support. Knowledge is 

necessary to make intelligent decisions. RSDE 

applies MDO routines in such a way as to 

facilitate design space exploration (DSE) and 

utilization of design of experiments (DOE). By 

using a mixture of gradient and non-gradient 

based, discrete and continuous MDO 

methodologies, the RSDE will be capable of 

representing the inherent uncertainty of earlystage 

ship design requirements and design 

values. The use of DSE and uncertainty 

representation together will allow for a shift 

from the classical, point-based, design-spiral 

approach, towards a modern set-based design 

(SBD) approach for early-stage ship design. 

The focus of this paper will be the MDO 

capabilities within the RSDE. 

To date, a ship analysis Use Case has been 

developed to test the current RSDE MDO 

capabilities. The goal of the initial Use Case 

was to test the ability of RSDE to handle 

continuous design variables while developing a 

robust, optimal hullform. The MDO algorithms 

1 

utilized two discipline optimizations, 

minimizing lifetime power requirements and 

maximizing the percent time operational. 

Preliminary results have shown the MDO 

algorithms to be capable of reaching an optimal 

solution within the boundary of the stated Use 

Case. The RSDE will act as a foundation for the 

continued growth and development of a SBD 

capability for the U.S. Navy and will aid the 

workforce in producing more robust ship 

designs, reducing the need for costly late-stage 

design changes. 

INTRODUCTION 

As budgets continue to decrease and 

shipbuilding costs increase, it has become 

increasingly important to design ships that 

perform well for multiple mission scenarios. 

Designing these multi-mission, flexible, and 

highly robust ships requires a paradigm shift in 

the methodologies utilized for the ship design 

process itself. To successfully implement a 

change in design theology, the paradigm shift 

must begin as early-on as the concept design 

phase. Designers can no longer afford to follow 

the traditional design spiral approach, Fig. 1, of 

fixing a few key design parameters early-on and 

then immediately searching for a single feasible 

solution, entirely dependent on the initially 

selected key design values, to meet the design 

objectives. 

Historically, the point-based design method has 

resulted in a struggle to maintain a feasible 

design during detailed design, which in turn has


led to compromised design objectives, costly 

late-stage design fixes, and sub-optimal ship 

designs balancing on the edge of feasibility. 

Fig. 2 shows a general description of how costs 

steadily increase throughout the life-cycle of a 

naval design project. 

Fig. 1 Classic Design Spiral for Point-Based 

Design [Evans 1959] 

Fig. 2 Design and Construction Life-Cycle 

Costs [Keane and Tibbitts 1996] 

Recently, the U.S. Navy has expressed interest 

in utilizing set-based design (SBD) to facilitate 

the necessary paradigm design shift [Kassel, 

Cooper, and Mackenna 2010; Eccles 2010; 

Doerry and Steding 2009; Sullivan, 2008; 

Singer, Doerry, and Buckley, 2010]. Set-based 

design is a design theory that encourages 

exhaustive investigation of a set of solutions and 

sets of design values during early-stage design. 

Bernstein [1998], provides an excellent 

2 

description of the intricate details of the SBD 

process and applications of SBD in industry. 

One key aspect of SBD theory is the intentional 

delay of early-stage design decisions until 

design trade-offs are fully understood, allowing 

for a gradual narrowing of the design space 

through the elimination of infeasible and less 

desirable design solutions [Gray 2011]. 

Although paradoxical, research has shown that 

the SBD method of delaying decisions reduces 

costs by investing more resources up-front to 

perform DSE [Ward et al. 1995] . The benefits 

of the up-front time investment are an increase 

in knowledge and a decrease in uncertainty, 

enabling designers to make well-informed earlystage 

design decisions. Fig. 3, illustrates the 

changes in design knowledge and uncertainty 

over time and the points at which key earlystage 

decisions are made for the point-based and 

set-based design methods. 

Fig. 3 Key Decision Points for Point-Based 

and Set-Based Design Methods 

The influence of SBD theory on the design 

process is shown in Fig. 4. The figure illustrates 

how through the set-based practice of the 

delaying of design decisions, there is a parallel 

delay of committed costs, as well as a shift in the 

strength of managerial influence over the life of 

the project. 

The drawback of the SBD process is that many 

designers and engineers are so accustomed to 

utilizing the point-based design approach that 

the switch to a design method that relies upon


the communication of information using sets of 

design values and solutions can be extremely 

difficult. Liker et. al., discuss the need for the 

development of design tools to, “facilitate a 

proper exchange of information”, including setbased 

information [1996]. This is where a 

design tool such as the rapid ship design 

environment (RSDE) comes into play. 

Fig. 4 Influence of Set-Based Design on the 

Design Development Process 

With the current push in the Navy to utilize SBD 

practices, and with the overall goal of RSDE in 

mind, a move to an integrated design framework 

is necessary. Fig. 5 shows the overall structure 

of the RSDE, within this framework various 

technologies are being developed in parallel. 

One part of the RSDE architecture currently 

undergoing testing is the Multi-Disciplinary 

Optimization (MDO) capability using the data 

structure provided by the Leading Edge 

Architecture for Prototyping Systems (LEAPS). 

Within the RSDE environment the ability to use 

MDO can help designers and functional design 

groups develop a better understanding of the 

design space. By identifying optimum values 

within a design space, the designers can narrow 

their search for preferred solutions, while also 

3 

gaining information about the space, all without 

requiring premature design decisions. 

Fig. 5 RSDE Hierarchy 

The MDO capabilities being developed for the 

RSDE will allow for rapid searching of design 

spaces while considering multiple design goals 

at the same time. Along with analyses tools 

compatible with LEAPS, the MDO abilities 

provides automated design space exploration 

using models that can contain both continuous 

and discrete design variables. 

Rapid Ship Design Environment 

SBD practice places an emphasis on making the 

right decisions the first time, as early decisions 

impact all subsequent design decisions, as well 

as the ultimate cost, delivery, produce-ability, 

and robustness of a design. To facilitate the 

SBD process, tools are needed to aid designers 

in generating information on design space tradeoffs 

during early-stage design and promoting 

communication of the information in a set-based 

manner [Liker, et. al., 1996]. 

The Rapid Ship Design Environment (RSDE) is 

being developed by NAVSEA-Carderock under 

the CREATE-Ships Rapid Design Integration 

(RDI) program. RSDE is designed to harness 

physics based design tools to provide designers 

with a methodology to intelligently explore the 

design space and analyze design trade-offs. 

Specifically RSDE will utilize, the Advanced 

Ship and Submarine Evaluation Tool (ASSET)


for design [ASSET 2012] and LEAPS for the 

aggregation of design data [LEAPS, 2012]. 

In addition to the DOE capabilities of the RSDE, 

a decision support toolkit (DST) is being 

developed to provide information about the 

design space. The DST is designed to provide 

users with an array of multi-disciplinary 

optimization (MDO) methods, including 

gradient and non-gradient based methods for use 

with both discrete and continuous design 

variables. Some of the non-gradient based 

methods include the use of genetic algorithms 

and fuzzy logic methods. As a whole, the RSDE 

and the MDO methods provided by the DST 

should help to move the Navy towards meeting 

the goals outlined in the memorandum by 

Admiral Sullivan [2008], Commander of the 

Naval Sea Systems Command. The memo 

expressed a desire for ever more sophisticated 

design and analysis tools capable of facilitating 

advanced design methods. 

To support MDO in early-stage ship design, a 

decision support toolkit (DST) has been jointly 

developed by NAVSEA Carderock, Michigan 

Engineering Service, and the University of 

Michigan. The DST provides several methods 

of performing design optimization with the 

intent of providing information that can be used 

to make intelligent, informed design decisions. 

Currently the MDO portion of the DST contains 

optimization methods capable of performing 

discipline level and system level (MDO) 

optimizations using both discrete and continuous 

design variables. 

Four optimization methods have been developed 

within the DST to this point, one utilizing a 

gradient based algorithm called NEWSUMT 

[Miura and Schmit 1979], two using genetic 

algorithms referred to as the RGA [Deb, Dhiraj, 

and Ashish 2001] and NSGA2 [Deb et al. 2000] 

optimizers, and one fuzzy logic system [Mendel 

2001]. The remainder of this paper discusses the 

4 

work that has been completed on the MDO 

portion of the DST and an initial Use Case that 

was specifically developed to validate the 

performance of the discipline and system level 

MDO algorithms for continuous design 

variables. 

Multi-Disciplinary Optimization 

The desire for more cost effective ship designs 

has led to a push for multi-functional, multimission, 

robust ship design solutions. As a 

result, ship designs are now heavily influenced 

by multiple stakeholders each representing 

unique design disciplines, where each discipline 

has its own unique design goal(s). In these types 

of multi-disciplinary design environments, the 

unique goals of each discipline evoke a constant 

struggle for controlling influence of design 

parameters. MDO involves the attempt to use 

mathematical methods to develop an optimized 

solution for all participating design disciplines, 

while simultaneously taking into consideration 

the often competing and conflicting design goals 

of each discipline. MDO has been successfully 

used in many industries that involve the design 

of complex engineering systems including 

power generation [Wang and Singh 2006], 

aerospace [Kuan et al. 2010; Vlahopoulos, 

Zhang, and Sbragio 2011], automotive [H. M. 

Kim et al. 2002], and naval architecture 

[Hannapel and Vlahopoulos 2010; H. Y. Kim 

and Vlahopoulos 2012]. 

The unique design goals of each design 

discipline result in equally unique discipline 

level optimization solutions. A discipline level 

optimization is defined as an optimization that 

considers the design goals of a single design 

discipline only, regardless of other disciplines. 

As an example, the optimization of a ship’s 

weight would likely result in different optimal 

solutions for the Stability, Resistance, and 

Survivability design disciplines. Applying an 

MDO to optimize the ship weight from a system


level perspective, simultaneously considering 

the design goals of the all three unique 

disciplines, would likely result in yet another 

distinct optimal ship weight. Fig. 6 shows 

theoretical results of the discipline level, and 

system level (MDO) optimizations for a ship’s 

weight. 

Fig. 6 Example Results for Optimization of 

Ship Weight at the Discipline Levels and 

MDO System Level 

When the system level MDO solution is 

compared to the solution of a discipline level 

optimization, the MDO solution may appear to 

be sub-optimal compared to that one discipline. 

Consider the comparison of the Resistance 

discipline optimization versus the MDO result; 

Fig. 6. The higher weight of the system level 

MDO solution is due to the necessary 

compromises and design trade-offs the MDO 

makes to satisfy the added design disciplines of 

Stability and Survivability. The MDO develops 

a solution that is optimal when accounting for all 

discipline level design goals. As a result, the 

MDO solution may not be optimal for any one 

discipline, but it is optimal from a systems 

engineering viewpoint. 

A multi-level optimization approach is used in 

the DST to support MDO; Fig. 7. The bottom 

level of the MDO consists of individual 

discipline level optimizations. The discipline 

level optimizers pass information to the top, 

system level, optimization algorithm which 

combines the information to determine a single 

MDO result. The system level MDO result is 

5 

then passed back to the discipline level 

optimizers to influence the optimization search 

process. The swapping of information between 

the discipline levels and system level continues 

in an iterative fashion until the system level 

convergence criteria are met. Fig. 7 shows a 

diagram of the general operating procedure for 

the multi-level MDO approach. 

Fig. 7 Multi-Level, MDO Algorithm Search 

Process Diagram 

To date, two system level algorithms for use in a 

multi-level MDO problem have been 

implemented in the DST. Both algorithms were 

developed by Dr. Nick Vlahopoulos at 

University of Michigan and can be found in 

references [Hannapel and Vlahopoulos 2010] 

and [H. Y. Kim and Vlahopoulos 2012]. The 

system level algorithm used in the Use Case is 

described in [H. Y. Kim and Vlahopoulos 2012] 

and summarized below. This MDO system level 

algorithm scales each discipline by a Plausible 

Reduction Range (prr) to weight each discipline 

evenly. The prr for each discipline is calculated 

by finding the maximum difference between the 

discipline’s objective function optimum ( ) 

,where are the design variable values for 

the optimum of discipline and the discipline 

objective value at the optimal design variable 

values of all other disciplines ( ). Show in 

equation 1. 

( ( ) ) 

(1) 

During each iteration of the MDO, the current 

values of the design variables are used as 

starting points for each of the discipline level


optimizations. The optimal values from each 

discipline are then located, communicated back 

to the system level optimizer, and used in the 

system level objective function shown in 

equation 2. 

( ) 

(∑ ( ) ) 

(2) 

The system level objective function 

represents the distance from the discipline 

optimum ( ) to the discipline value, 

( ), at the current design variable value(s) x, 

scaled by the . The system level optimization 

formulation is shown in equation 3. 

( ) 

(3) 

In equation 3, represents the system 

level inequality constraints, which include any 

system level constraints, as well as all discipline 

level constraints. represents the system 

level equality constraints, which again contain 

all system and discipline level constraints. 

and are the lower and upper 

bounds of the variables, which take into account 

all system and discipline level bounds. The 

system level constraints and bounds consider all 

disciplines to ensure that the final optimum point 

is feasible for all disciplines involved. 

MDO Use Case Definition 

The goal of the first Use Case for the MDO 

portion of the DST was to demonstrate the MDO 

algorithms using all continuous variables. Use 

Case 1 (UC-1) conducts an optimization on the 

hydrodynamic performance of a surface 

combatant based on the hullform of the Oliver 

Hazard Perry (FFG 7). The hullform was 

optimized with respect to two design disciplines, 

minimizing the lifetime power requirements of 

6 

the ship, and maximizing the average percent 

time operational. Each discipline was subject to 

various constraints to ensure hydrostatic stability 

and feasible designs. The MDO formulation 

used 11 continuous design variables, which were 

inputs to the LEAPS Hullform Transformation 

Utility (HFT). The design variables listed in 

Tabel 1. Are all shape factors (SF) used by the 

HFT. 

Table 1: Design Variable List 

Design Variable 

Length 

Depth 

Beam 

Longitudinal Fullness Forward 

Longitudinal Fullness Aft 

Vertical Fullness Above WL 

Vertical Fullness Below WL 

Transverse Fullness 

Hullform Angle Bow 

Hullform Angle Stern 

Hullform Angle port/starboard 

The SF design variables manipulate the hull in 

multiple ways and all have values that range 

from -1 to 1. The parent hull is found when all 

SFs are set equal to zero. The dimensional SF 

(Length, Depth, and Beam) correspond to the 

respective values on the bounding box around 

the ship hull. The longitudinal fullness factors 

control what percentage of the ship hull fills the 

bounding box forward and aft of midships. The 

vertical fullness factors control what percentage 

of the ship hull fills the bounding box above and 

below the waterline, and the transverse fullness 

factor controls the port and starboard fullness 

with respect to the bounding box. The bow and 

stern angle controls the angle of the front and 

end of the bounding box respectively. Finally, 

the port/starboard angle controls the angles of 

the sides of the bounding box (see Hull Transfer 

Utility [2012] for more information). Fig. 8, 

shows pictures of the baseline hullform and 

transformed hullform utilizing SFs. In the


optimization process the HFT is called to 

automatically shape the hullform for further 

7 

design analyses. 

Fig. 8 Demonstration of the Use of Shape Factors in the Hullform Transfer Utility 

The first of the two design disciplines attempts 

to minimize the lifetime power requirements of 

the ship. The lifetime power requirements are 

based on the KW-hours required to overcome 

the ships resistance at the speed profile given in 

Table 2. The ship was given an assumed ship 

time at sea of 4000 hours per year, and a ship 

service life of 30 years. 

Table 2: Speed Profile 

Ship Speed (knots) Time at Speed (%) 

10 50 

15 30 

20 15 

25 3 

30 2 

The analysis of the ship resistance at each speed 

was calculated using the LEAPS Total Ship 

Drag (TSD) program, which predicts the total 

ship resistance based on the methods described 

in, “Rapid Resistance Evaluation of High-Speed 

Ships” [Metcalf et al]. For each hull form 

analyzed by the optimizer, the resistance 

characteristics are found for each of the speeds 

listed in Table 2, with the results used in 

Equation 4. In Equation 4, N is the total number 

of speeds, TDi is the total drag at speed i in N, 

and Vi is the velocity at speed i in m/s. The 

number is converted to KW-hrs giving the 

objective function for the lifetime power 

minimizer, SLP. 

(∑ 

) 

(4) 

The second discipline attempts to maximize the 

percent time operational (PTO) of the ship. The 

PTO is a function of the ship mission. For UC- 

1, the ship was assumed to be operational if it 

could launch and recover a helicopter. Table 3 

shows the upper limits on four motions which 

must be satisfied to complete helicopter 

operations.


Table 3: Upper Limits on Motions for 

Helicopter Operations 

Motion Operational 

Limit 

Roll 8 [degrees] 

Pitch 3 [degrees] 

Vertical Acceleration 0.4 [g] 

Horizontal Acceleration 0.4 [g] 

To find the average PTO, the hullform was 

tested in a variety of sea states based on 

historical data to give a yearly wave profile in 

multiple locations. The analysis was conducted 

using the LEAPS Ship Motions Program (SMP). 

SMP calculates the ships motions using methods 

described in [Conrad 2005]. Using all of the 

yearly wave profiles available the resultant ship 

motions were inspected with respect to 

maximum pitch and roll values, and the vertical 

and horizontal acceleration at the helicopter 

deck. The helicopter deck was assumed to be 

located at 90% of the ship’s length overall. The 

average PTO was calculated to give the 

objective function value. 

For UC-1 both disciplines were subject to the 

same constraints. The constraints were designed 

to ensure that the ship was hydrostatically stable. 

The longitudinal center of buoyancy (LCB) was 

constrained to be within 0.5% of the length 

water line (LWL) to the longitudinal center of 

gravity (LCG). The ship GMT had to be greater 

than 10% of the beam (B). The final constraint 

for hydrostatics ensured that the weight of the 

ship was equal to the displacement . 

Additional constraints were used to simplify 

calculations. The vertical center of gravity 

(VCG) was constrained to be equal to 57% of 

the ship depth. The LCG was required to be 51% 

of the ship LWL. The weight of the ship was 

calculated based on the hull volume by using a 

ship density factor of 0.4 MT/m 3 . The final set 

of constraints ensured that the displacement of 

8 

the ship was between 4000 and 7000 metric 

tonnes. All constraints are shown in equations 

5-13. 

Due to limitations in the analysis software, for 

UC-1, genetic algorithm solvers were used for 

the optimization process. Different combinations 

of design variables caused irregular shapes 

which would fail to run in the analysis tools. 

This would lead to discontinuities in the design 

space, which would cause gradient based 

optimization solvers to give sub-optimal results. 

For all results presented below, the NSGA-II 

solver was used for both system and discipline 

level optimization solvers. 

Results 

(5) 

(6) 

(7) 

(8) 

(9) 

(10) 

(11) 

(12) 

(13) 

Although an exhaustive search of the design 

space has not been completed, the MDO portion 

of the DST displayed promising results. Using 

the NSGA-II solver, the DST was successfully 

run to pre-determined stopping criteria to select 

the “optimal” solution. When the MDO finished 

running, the results indicated an improvement in 

the objective function, showing that the process 

was moving in the correct direction towards an 

optimal solution.


To analyze the optimization processes, first the 

parent hullform was optimized with respect to 

each of the individual disciplines. The parent 

hullform is shown in Fig. 9. The principal 

dimensions and values for lifetime power and 

PTO of the parent hullform are shown Table 4. 

Fig. 9 Parent Hullform (FFG 7) 

Table 4: Parent Hull Principle Dimensions 

and Objective Function Values 

LOA 127.63 [m] 

B 13.85 [m] 

T 5.07 [m] 

D 9.15 [m] 

L/B 9.22 

B/T 2.73 

B/D 1.51 

Lifetime Power 1,353,502 [kW-hr] 

PTO 32.2 [%] 

The results of the individual optimizations are 

shown below in Fig. 10 and Table 5 for the 

lifetime power minimization, and Fig. 11 and 

Table 6 for the average PTO maximization. 

Due to the shape factors used, some of the final 

hull forms seem unconventional. The use of the 

HFT is one aspect that makes this optimization 

problem unique, as most early stage design 

optimization processes are limited to only using 

parametric equations for analyses, or can only 

stretch/shrink a hull using parametric 

transformations. Even with the unique hull 

shapes, the trends that are shown follow a naval 

architect’s intuition to the individual optimums. 

In the case of the hullform that was optimized 

for lifetime power, the hull grew longer, 

approached the minimum displacement, and the 

9 

beam decreased. The average PTO 

maximization resulted in a hull with a greater 

displacement, and a very full ship under the 

waterline. 

Fig. 10 Lifetime Power Minimization 

Optimized Hullform 

Table 5: Lifetime Power Minimization 

Optimized Dimensions and Objective 

Function Values 

LOA 144.5 [m] 

B 13.4 [m] 

T 4.8 [m] 

D 8.9 [m] 

L/B 10.78 

B/T 2.79 

B/D 1.51 


PTO 28.9 [%] 

Fig. 11 PTO Maximization Optimized Hullform 

Table 6: PTO Maximization Optimized 

Principal Dimensions and Objective Function 

Values 

L 123.9 [m] 

B 23.5 [m] 

T 7.9 [m] 

D 11.9 [m] 

L/B 5.27 

B/T 2.98 

B/D 1.98 


PTO 45.8 [%]


The ship was then optimized considering both 

disciplines’ objectives simultaneously using the 

in the complete MDO process. The results are 

shown in Fig. 12 and Table 7. 

Fig. 12 MDO Optimized Hullform 

Table 7: MDO Optimized Principal 

Dimensions and Objective Function Values 

L 172.5 [m] 

B 16.0 [m] 

T 3.95 [m] 

D 8.6 [m] 

L/B 10.78 

B/T 4.05 

B/D 1.86 


PTO 41.2 [%] 

The results observed for the MDO showed 

improvement in the objective function for that 

process. When comparing the MDO results to 

the original hullform, the equal weighting of the 

disciplines is visible. The lifetime power 

requirements of the ship increased, while the 

PTO increased by a larger percentage than the 

percent increase of the lifetime power. When 

compared to the original parent hullform, the 

MDO optimized hullform experienced a 28.0% 

increase in lifetime power while the PTO was 

increased by 28.5%. Note that for lifetime 

power, a percent increase indicates a less 

favorable condition, whereas a percent decrease 

indicates a more favorable design, one using less 

power than the comparable hullform. 

The tradeoffs made by the MDO solution are 

also shown in comparing the solution to the 

lifetime power and PTO optimized solutions. 

The lifetime power for the MDO solution 

increased by 28.0% from parent hull, while the 

lifetime power optimized solution was able to 

10 

achieve a 10.2% decrease from the parent hull. 

However, the lifetime power optimized solution 

experienced a 10.5% decrease in PTO. The PTO 

of the MDO hull increased by 28.5% from the 

parent hull, while the PTO optimized hull form 

was able to increase by 42.2% from the parent 

hull. Table 8 shows the change in lifetime power 

and PTO for the MDO solution when compared 

to the parent and optimized hullform types using 

a percent error formula. 

Table 8: Percent Error of MDO, Lifetime Power 

Optimized, and PTO Optimized Solutions versus 

Parent Hullform 

Parameter Parent/ 

Lifetime 

MDO 

Parent/ 

LTP 

Parent/ 

PTO 

Power (+)28.0% (-)10.2% (+)143% 

PTO (+)28.5% (-)10.5% (+)42.2% 

Conclusions 

The current status of the MDO capabilities 

within the DST show promising results even 

given the current limitations. The optimization 

algorithms have given correct results to test 

problems with known analytical solutions. In 

UC-1, the algorithms did move toward improved 

solutions, and in all optimizations, the objective 

function improved. Additionally, UC-1 

demonstrated how competing and conflicting 

design goals force a MDO solution to make 

design compromises that result in performance 

characteristics that are sub-optimal when 

compared to individual performance based 

optimizations. However, the results of the MDO 

solution are optimal when looking at the 

performance of the ship from a combined multidisciplinary 

systems view. 

Currently, improvements are being completed to 

allow for faster more complete optimization 

runs. A second use case is also being developed 

to test more capabilities of the DST. Use Case 2


will test the DST’s ability to handle discrete 

design variables and will add an additional 

mission specific discipline, a high speed transit 

scenario. 

As the DST continues to grow capabilities, the 

overall goal is to integrate the DST into the 

RSDE. Within RSDE, the MDO capabilities can 

help lead engineers to regions of the design 

space with higher preferences. This can help for 

communicating preferences between design 

groups and facilitate the narrowing of the design 

space for SBD. 

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Author Biographies 

Alexander Gray graduated with his Ph.D. in 

Naval Architecture and Marine Engineering 

(NA&ME), from the University of Michigan in 

2011. He now works as an engineer at 

NAVSEA, Carderock. He holds master’s 

degrees in Industrial operations engineering and 

NA&ME, as well as bachelor’s degrees in 

Mechanical and Aerospace engineering. His 

research interests include fuzzy logic, 

optimization, and set-based design theory. 

Brian Cuneo is a Ph.D. Candidate at the 

University of Michigan in the department of 

Naval Architecture and Marine Engineering. He 

has earned a BSE and MEng in the same major 

from the University of Michigan. Brian is 

currently a Research Assistant working with 

NAVSEA Carderock Division on a Naval 

Design Optimization Project. His current 

research is on developing a heuristic method of 

Multi-Disciplinary Design Optimization using 

methodologies from Hierarchical Fuzzy Logic 

Controllers. 

Nick Vlahopoulos is a Professor in the 

Department of Naval Architecture and Marine


Engineering at the University of Michigan. He 

joined the University of Michigan in 1996 after 

working in the Industry for seven years. He has 

graduated 15 Ph.D. students, published 70 

journal papers and over 80 conference papers. 

The areas of his research are: numerical methods 

in structural-acoustics, and design of complex 

systems. 

David J. Singer is an Assistant Professor in the 

Department of Naval Architecture and Marine 

Engineering (NAME) at the University of 

Michigan. Dr. Singer obtained a B.S.E. degree 

in NAME, M.Eng. degree in Concurrent Marine 

Design, M.S.E. degree in Industrial and 

Operations Engineering and a PhD in NAME, 

all from the University of Michigan. 

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