APPROXIMATION ASSISTED MULTIOBJECTIVE AND COLLABORATIVE ROBUST OPTIMIZATION UNDER INTERVAL UNCERTAINTY

Optimization of engineering systems under uncertainty often involves problems that have multiple objectives, constraints and subsystems. The main goal in these problems is to obtain solutions that are optimum and relatively insensitive to uncertainty. Such solutions are called robust optimum solutions. Two classes of such problems are considered in this dissertation. The first class involves Multi-Objective Robust Optimization (MORO) problems under interval uncertainty. In this class, an entire system optimization problem, which has multiple nonlinear objectives and constraints, is solved by a multiobjective optimizer at one level while robustness of trial alternatives generated by the optimizer is evaluated at the other level. This bi-level (or nested) MORO approach can become computationally prohibitive as the size of the problem grows. To address this difficulty, a new and improved MORO approach under interval uncertainty is developed. Unlike the previously reported bi-level MORO methods, the improved MORO performs robustness evaluation only for optimum solutions and uses this information to iteratively shrink the feasible domain and find the location of robust optimum solutions. Compared to the previous bi-level approach, the improved MORO significantly reduces the number of function calls needed to arrive at the solutions. To further improve the computational cost, the improved MORO is combined with an online approximation approach. This new approach is called Approximation-Assisted MORO or AA-MORO. The second class involves Multiobjective collaborative Robust Optimization (McRO) problems. In this class, an entire system optimization problem is decomposed hierarchically along user-defined domain specific boundaries into system optimization problem and several subsystem optimization subproblems. The dissertation presents a new Approximation-Assisted McRO (AA-McRO) approach under interval uncertainty. AA-McRO uses a single-objective optimization problem to coordinate all system and subsystem optimization problems in a Collaborative Optimization (CO) framework. The approach converts the consistency constraints of CO into penalty terms which are integrated into the subsystem objective functions. In this way, AA-McRO is able to explore the design space and obtain optimum design solutions more efficiently compared to a previously reported McRO. Both AA-MORO and AA-McRO approaches are demonstrated with a variety of numerical and engineering optimization examples. It is found that the solutions from both approaches compare well with the previously reported approaches but require a significantly less computational cost. Finally, the AA-MORO has been used in the development of a decision support system for a refinery case study in order to facilitate the integration of engineering and business decisions using an agent-based approach

The Component Packaging Problem: A Vehicle for the Development of Multidisciplinary Design and Analysis Methodologies

This report summarizes academic research which has resulted in an increased appreciation for multidisciplinary efforts among our students, colleagues and administrators. It has also generated a number of research ideas that emerged from the interaction between disciplines. Overall, 17 undergraduate students and 16 graduate students benefited directly from the NASA grant: an additional 11 graduate students were impacted and participated without financial support from NASA. The work resulted in 16 theses (with 7 to be completed in the near future), 67 papers or reports mostly published in 8 journals and/or presented at various conferences (a total of 83 papers, presentations and reports published based on NASA inspired or supported work). In addition, the faculty and students presented related work at many meetings, and continuing work has been proposed to NSF, the Army, Industry and other state and federal institutions to continue efforts in the direction of multidisciplinary and recently multi-objective design and analysis. The specific problem addressed is component packing which was solved as a multi-objective problem using iterative genetic algorithms and decomposition. Further testing and refinement of the methodology developed is presently under investigation. Teaming issues research and classes resulted in the publication of a web site, (http://design.eng.clemson.edu/psych4991) which provides pointers and techniques to interested parties. Specific advantages of using iterative genetic algorithms, hurdles faced and resolved, and institutional difficulties associated with multi-discipline teaming are described in some detail

New Approaches to Multidisciplinary Design and Optimization

Research under the subject grant is being carried out in a jointly coordinated effort within three laboratories in the School of Aerospace Engineering and the George Woodruff School of Mechanical Engineering. The objectives and results for Year 2 of the research program are summarized. The "Objectives" and "Expected Significance" are taken directly from the Year 2 Proposal presented in October 1994, and "Results" summarize the what has been accomplished this year. A discussion of these results is provided in the following sections. A listing of papers, presentations and reports that acknowledge grant support, either in part or in whole, and that were prepared during this period is provided in an attachment

An Algorithm for Integrated Subsystem Embodiment and System Synthesis

Consider the statement,'A system has two coupled subsystems, one of which dominates the design process. Each subsystem consists of discrete and continuous variables, and is solved using sequential analysis and solution.' To address this type of statement in the design of complex systems, three steps are required, namely, the embodiment of the statement in terms of entities on a computer, the mathematical formulation of subsystem models, and the resulting solution and system synthesis. In complex system decomposition, the subsystems are not isolated, self-supporting entities. Information such as constraints, goals, and design variables may be shared between entities. But many times in engineering problems, full communication and cooperation does not exist, information is incomplete, or one subsystem may dominate the design. Additionally, these engineering problems give rise to mathematical models involving nonlinear functions of both discrete and continuous design variables. In this dissertation an algorithm is developed to handle these types of scenarios for the domain-independent integration of subsystem embodiment, coordination, and system synthesis using constructs from Decision-Based Design, Game Theory, and Multidisciplinary Design Optimization. Implementation of the concept in this dissertation involves testing of the hypotheses using example problems and a motivating case study involving the design of a subsonic passenger aircraft

ONLINE APPROXIMATION ASSISTED MULTIOBJECTIVE OPTIMIZATION WITH HEAT EXCHANGER DESIGN APPLICATIONS

Computer simulations can be intensive as is the case in Computational Fluid Dynamics (CFD) and Finite Element Analysis (FEA). The computational cost can become prohibitive when using these simulations with multiobjective design optimization. One way to address this issue is to replace a computationally intensive simulation by an approximation which allows for a quick evaluation of a large number of design alternatives as needed by an optimizer. This dissertation proposes an approach for multiobjective design optimization when combined with computationally expensive simulations for heat exchanger design problems. The research is performed along four research directions. These are: (1) a new Online Approximation Assisted Multiobjective Optimization (OAAMO) approach with a focus on the expected optimum region, (2) a new approximation assisted multiobjective optimization with global and local metamodeling that always produces feasible solutions, (3) a framework that integrates OAAMO with multiscale simulations (OAAMOMS) for design of heat exchangers at the segment and heat exchanger levels, and (4) applications of OAAMO combined with CFD for shape design of a header for a new generation of heat exchangers using Non-Uniform Rational B-Splines (NURBS). The approaches developed in this thesis are also applied to optimize a coldplate used in electronic cooling devices and different types of plate heat exchangers. In addition many numerical test problems are solved by the proposed methods. The results of these studies show that the proposed online approximation assisted multiobjective optimization is an efficient approach that can be used to predict optimum solutions for a wide class of problems including heat exchanger design problems while reducing significantly the computational cost when compared with existing methods

Multidisciplinary Design Optimization for Space Applications

Multidisciplinary Design Optimization (MDO) has been increasingly studied in aerospace engineering with the main purpose of reducing monetary and schedule costs. The traditional design approach of optimizing each discipline separately and manually iterating to achieve good solutions is substituted by exploiting the interactions between the disciplines and concurrently optimizing every subsystem. The target of the research was the development of a flexible software suite capable of concurrently optimizing the design of a rocket propellant launch vehicle for multiple objectives. The possibility of combining the advantages of global and local searches have been exploited in both the MDO architecture and in the selected and self developed optimization methodologies. Those have been compared according to computational efficiency and performance criteria. Results have been critically analyzed to identify the most suitable optimization approach for the targeted MDO problem