SUMMARY

Most of the engineering design processes in use today in the field may be
considered as a series of successive decision making steps. The decision maker uses
information at hand, determines the direction of the procedure, and generates 
information for the next step and/or other decision makers. However, the information is
often incomplete, especially in the early stages of the design process of a complex
system. As the complexity of the system increases, uncertainties eventually become
unmanageable using traditional tools. In such a case, the tools and analysis values
need to be "softened" to account for the designer's intuition.
One of the methods that deals with issues of intuition and incompleteness is 
possibility theory. Through the use of possibility theory coupled with fuzzy inference, the
uncertainties estimated by the intuition of the designer are quantified for design 
problems. By involving quantified uncertainties in the tools, the solutions can represent
a possible set, instead of a crisp spot, for predefined levels of certainty.
From a different point of view, it is a well known fact that engineering design is a
multi-objective problem or a set of such problems. The decision maker aims to find
satisfactory solutions, sometimes compromising the objectives that conflict with each
other. Once the candidates of possible solutions are generated, a satisfactory solution
can be found by various decision-making techniques.

A number of multi-objective evolutionary algorithms (MOEAs) have been developed, 
and can be found in the literature, which are capable of generating alternative
solutions and evaluating multiple sets of solutions in one single execution of 
an algorithm. One of the MOEA techniques that has been proven to be very successful for
this class of problems is the strength Pareto evolutionary algorithm (SPEA) which
falls under the dominance-based category of methods. The Pareto dominance that
is used in SPEA, however, is not enough to account for the constraints, and there
has been no clear explanation for constraint handling in SPEA so far. In this thesis
work, it is proposed that through a slight modification of the notion of dominance, it
is possible to make SPEA manage constraints successfully.

In light of the notion of possibility, a concept of solution that ensures a certain
confidence level is proposed and implemented in a new evolutionary algorithm with
a newly defined fuzzified version of the multi-objective optimization problem 
statement. In the new problem statement, function values and constraints are softened by
possibility distributions that reflect the intuitive assessment of the expert. Multiple
alternative solutions to the problem are found by the modified SPEA.
Furthermore, the new method is applied to the sizing problem of a gyrodyne
configuration which employs a tip-jet-driven rotor on top of a fixed-wing aircraft.
The sizing environment includes a 6-DOF rotor trim model, a tip-jet model, a blade
duct model and engine models for various concepts of air compression. However, the
design problem of the gyrodyne is ill-defined, and there are only a few data available.
Therefore, a large portion of the analysis involves intuitive information. The intuitive
information is quantified, and sizing is performed through the possibilistic MOEA
investigating the influences of the various factors. The trade-off includes discrete
variables for engine type and an optional tip burner, as well as continuous variables
for rotor parameters and engine parameters.