Abstract. This chapter presents a number of illustrative case studies of a wide range of applications of multiobjective optimization methods, in areas ranging from engineering design to medical treatments. The methods used include both conventional mathematical programming and evolutionary optimization, and in one case an integration of the two approaches. Although not a comprehensive review, the case studies provide evidence of the extent of the potential for using classical and modern multiobjective optimization in practice, and opens many opportunities for further research. IntroductionThe intention with this chapter is to provide illustrations of real applications of multiobjective optimization, covering both conventional mathematical programming approaches and evolutionary multiobjective optimization. These illustrations do cover a broad range of application, but do not attempt to provide a comprehensive review of applications.
This paper outlines an approach for the determination of economically viable robust design solutions using the High Speed Civil Transport (HSCT) as a case study. Furthermore, the paper states the advantages of a probability based aircraft design over the traditional point design approach. It also proposes a new methodology called Robust Design Simulation (RDS) which treats customer satisfaction as the ultimate design objective.RDS is based on a probabilistic approach to aerospace systems design, which views the chosen objective as a distribution function introduced by so called noise or uncertainty variables. Since the designer has no control over these variables, a variability distribution is defined for each one of them. The cumulative effect of all these distributions causes the overall variability of the objective function. For cases where the selected objective function depends heavily on these noise variables, it may be desirable to obtain a design solution that minimizes this dependence. The paper outlines a step by step approach on how to achieve such a solution for the HSCT case study and introduces an evaluation criterion which guarantees the highest customer satisfaction. This customer satisfaction is expressed by the probability of achieving objective function values less than a desired target value.
Within the context of multi-disciplinary aircraft analysis and design, a new approach has been formulated and described which allows for the rapid technical feasibility and economic viability assessment of multiattribute, multi-constrained designs. The approach, referred to here as Virtual Stochastic Life Cycle Design, facilitates the multi-disciplinary consideration of a system, accounting for life-cycle issues in a stochastic fashion. The life-cycle consideration is deemed essential in order to evaluate the emerging, all encompassing system objective of affordability. The stochastic treatment is employed to account for the knowledge variation/uncertainty that occurs in time through the various phases of design. Variability found in the treatment of assumptions, ambiguous requirements, code fidelity (imprecision), economic uncertainty, and technological risk are all examples of categories of uncertainty that the proposed probabilistic approach can assess. For cases where the problem is over-constrained and a feasible solution is not possible, the proposed method facilitates the identification and provides guidance in the determination of potential barriers which will have to be overcome via the infusion of new technologies. The specific task of examining system feasibility and viability is encapsulated and outlined in a series of easy to follow steps. Finally, the method concludes with a brief description and discussion of proposed decision making techniques to achieve optimal designs with reduced variability. This decision making is achieved through a combined utility theory and Robust Design Simulation approach.
Design for robustness and its subset design for economic robustness and viability are two areas in current design methodology and optimization research attracting a lot of attention, as the increasing number of publications and industry position papers in this field indicate. In fact, these publications attempt to address the paradigm shift taking place in industry, where design for performance is being replaced by design for affordability. That is designing and optimizing a system for a high yield while reducing the variation from that optimum yield. The study presented here can be viewed as a proof of concept for a proposed approach to design for robustness, called Robust Design Simulation (RDS).The paper outlines an alternative approach to Taguchi's, assigning probability distributions to uncontrollable factors (noise variables) which result in a distribution for the design objective instead of a point solution.The study also illustrates that indeed one is able to manipulate the mean and variance of the design objective concurrently, hence, optimizing a new Overall Evaluation Criterion (OEC) that is comprised of both the mean and variance of the design objective. The High Speed Civil Transport (HSCT) was utilized as an illustrative case to demonstrate the implementation of RDS. The objective of this case study is to show and quantify the effects of mission and aircraft sizing parameters on the mean and variance of direct and total operating cost as well as the required average yield per revenue passenger mile ($/RPM). Finally, the optimal mission requirement settings which yield an OEC that concurrently minimizes the mean $/RPM as well as its variance are identified for the HSCT configuration studied.
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