Impacts of Fuzzy Logic Modeling for Constraints Optimization

Today's US naval vessels are required to perform an ever more complicated array of missions, thus increasing the number of constraints imposed on the ship design. As designers we struggle to find a means to effectively express the relationships of these competing, interdependent, and often subjective constraints. The majority of current optimization schemes require designers to define crisp‐valued constraints even when in the presence of subjective “soft” constraints, thereby ignoring the uncertainty that is inherent during the definition of early‐stage design constraints. One method capable of handling these subjective constraints is Fuzzy Logic (FL). FL is a rule‐based method for soft computing that can be used to model the uncertainty of crisp‐valued objective data, as well as for the modeling of subjective linguistic variables. A Fuzzy Logic System (FLS) is unique in its ability to concurrently consider multiple input design constraints of different types, such as objective and subjective, and of different units, such as length and area. A key component of FL modeling is the fuzzification of crisp input design constraints. Fuzzification itself is the act of mapping a crisp input constraint to a membership function (MF), also called a fuzzy utility curve. The MFs are used by the FLS to model uncertainty of the input data. Taken the current state of optimization techniques, it is believed that further improvement in optimization may be possible by introducing the modeling capabilities of FL. In this paper the authors investigate the impacts of using FL to quantify and model the subjectivity of design constraints associated with a general ship arrangements optimization process. A brief overview of FLSs is given, followed by a discussion of the methodology used to design a FL constraint MF. The University of Michigan Intelligent Ship Arrangements (ISA) system, a program designed to assist in the development of optimized ship arrangements, is used for the platform of this study. In one example the ISA program is run using crisp constraint inputs, the program output is then compared to the output of the same run when using fuzzy inputs. This process serves to highlight the significance of utilizing FL for the modeling of design constraints during optimization. Another ISA run, showing an example of the arrangements process, is used to help the reader understand the critical process of choosing the correct fuzzifier for modeling of an input constraint.