Abstract

During the product design process, the optimization of the parameters (dimensions, shapes, materials) has been, until recently, the exclusive domain of the part design stage. This optimization is now spreading into two directions: first, to the conceptual design stage during which approximated mathematical models are solved to find the global parameters driving the design; second to the sub-assembly and assembly design stage during which the components are united to form the final product. It is only at this stage that system level characteristics, strongly linked to the desire of the customers, can be checked. These characteristics, considered as objectives by the engineer, and reflecting different knowledge fields, link parameters at various levels of the system and thus break the well established hierarchical organization of the full system. At present, no satisfactory solution is implemented to optimize these additional relations that transform the assembly design from a constraint satisfaction problem into a non-linear constrained multi objective optimization problem. Hence, this work presents a method for optimizing system level assembly characteristics of complex mechanical assemblies by placement of freeform components. This method finds multiple solutions to the Configuration Design Problem and proposes a simple cooperation scheme with the engineer. The review of the industrial applications showed that no assumptions could be made on the type of components and systems. However, system optimization usually occurred after components shapes and their functional links were settled. From the mathematical representation point of view, the variables can then be restricted to displacements and can be considered as continuous in all cases. Once this is assumed, three areas are necessary to address the goal:define the complexity of an Engineering Configuration Design Problem (ECDP), define the method, measure its performance. In order to address the first goal, a mathematical formulation is adopted, that, unlike many formulations found in the literature review, could address any type of components (involving non convex, hollow, sharp edges components). This formulation relies on the use of continuous variables for defining the authorized movements of the components with respect to each others and on penalty functions for penalizing unfeasible configurations. Then, based on the notion of function landscape, four criteria are chosen to answer the first need i.e. evaluating the complexity of the ECDPs. Trend, Roughness, Dilution of the feasible area and Dilution of the solution were defined for any type of C1 functions and linked to simple characteristics of the ECDPs (size and number of the components, size of the system). The second goal, the definition of the method, is addressed as finding multiple global extrema of a non-linear optimization problem. A Genetic Algorithm working on population of sets instead of population of individual points is proposed to search the variables space and to provide multiple solutions for three reasons. First, the GA works on several designs at the same time; second, it is able to deal with highly non-linear functions; and third it capitalizes on the knowledge acquired at previous trials. The analysis of the complexity classification of some well-known packing problems provided clues for proposing three enhancements to this initial method. First, the penalty should always be combined with the objective function for unfeasible configurations evaluation, then, the use of a Local Search, and Relative Placement contribute to decrease the CDP's complexity. Eventually, to increase the chances of escaping local minima, an adaptive range strategy was suggested. Before verifying the validity of these choices, some criteria had to be designed to measure the quality of the Pareto set obtained using the CDOM. Three criteria are chosen to measure the quality of the set itself (distance from the extreme planes, distribution of the points, flatness) and two for measuring the performance of the CDOM (speed and repeatability). A series of cubes CDPs and two engineering cases were submitted to the method for validating the enhancements and the complexity classification. The conclusion of this part of the study pointed out that the Local Search and Range Adaptation enhancements were the most effective. Relative placement did not bring a clear advantage over the base strategy when dealing with CDPs in which the relative motion is not linked to a functional need. Among the two types of criteria proposed for first rating the CDPs complexity and second for rating the CDOM, only the former were clearly satisfactory and can be reused in further studies. To assess the quality of a Pareto set, several criteria should be rethought. The CDOM successfully produces multiple solutions to the test cases submitted. Its drop in performance is linear while the CDPs complexity increases exponentially. It also proved to be able to handle any type of components. The lack of assumptions made on the type of objective functions makes it robust for handling continuous and discrete objectives. Working with displacements on one hand and, on the other hand, having the possibility to choose which components can move and which remain static, helps the engineer to keep a close contact with the optimization process. The limitations of the method concern the low number of moving components that can be taken into account at the same time (less than 10 system components using relative placement).