Abstract

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.