In multidisciplinary optimization the designer needs to fi d a solution to an optimization problem that includes a number of usually contradicting criteria. Such a problem is mathematically related to the fiel of nonlinear vector optimization with constraints. It is well-known that the solution to this problem is far from unique and given by a Pareto surface. In the real-life design the decision-maker is able to analyze only several Pareto optimal (trade-off) solutions. Therefore, a well-distributed representation of the entire Pareto frontier is especially important. At present, there are only a few methods that are capable of even generating a Pareto frontier in a general formulation. In the present work they are compared to each other, with the main focus being on a general strategy combining the advantages of the known algorithms. The approach is based on shrinking a search domain to generate a Pareto optimal solution in a selected area on the Pareto frontier. The search domain can be easily conducted in the general multidimensional formulation. The efficien y of the method is demonstrated on different test cases. For the problem in question, it is also important to carry out a local analysis. This provides an opportunity for a sensitivity analysis and local optimization. In general, the local approximation of a Pareto frontier is able to complement a quasi-even generated Pareto set.
|Title of host publication||Handbook of Optimization Theory|
|Subtitle of host publication||Decision Analysis and Application|
|Publisher||Nova Science Publishers, Inc.|
|Number of pages||25|
|Publication status||Published - Jan 2011|