Search Results

Design optimization techniques are widely used to drive designs toward a global or a near global optimal solution. However, the achieved optimal solution often appears to be the only choice that an engineer/designer can select as the final design. This is caused by either problem topology or by the nature of optimization algorithms to converge quickly in local/global optimal or both. Problem topology can be unimodal or multimodal with many local and/or global optimal solutions. For multimodal problems, most global algorithms tend to exploit the global optimal solution quickly but at the same time leaving the engineer with only one choice of design. The paper explores the application of genetic algorithms (GA), simulated annealing (SA), and mixed integer problem sequential quadratic programming (MIPSQP) to find multiple local and global solutions using single objective optimization formulation.

With the increase in computational capability, there is an increase in classes of engineering optimization problems that are considered solvable. Not all problems benefit from similar types of approaches when searching for an optimal solution. Some have objective functions that can be described as largely unimodal while others have complex behavior with multiple local optima. Further, there are problems that have behavior that is not clearly apparent due to the involvement of CAD/CAE tools and high number of inputs/factors. There has been a push to combine dissimilar optimization approaches in order to tackle such hard-to-solve problems for a variety of reasons. One such combination is the “Hybrid” optimization algorithm developed by ESTECO for their commercial optimization software “modeFRONTIER”. This paper gives the reader some examples and results from problems where the Hybrid algorithm has proved to be a worthy choice.

Robustness/Reliability Assessment and Optimization (RRAO) is often computationally expensive because obtaining accurate Uncertainty Quantification (UQ) may require a large number of design samples. This is especially true where computationally expensive high fidelity CAE simulations are involved. Approximation methods such as the Polynomial Chaos Expansion (PCE) and other Response Surface Methods (RSM) have been used to reduce the number of time-consuming design samples needed. However, for certain types of problems require the RRAO, one of the first question to consider is which method can provide an accurate and affordable UQ for a given problem. To answer the question, this paper tests the PCE, RSM and pure sampling based approaches on each of the three selected test problems: the Ursem Waves mathematical function, an automotive muffler optimization problem, and a vehicle restraint system optimization problem.

Need for accounting Robustness and Reliability in engineering design is well understood and being researched. However, the actual practice of applying robustness and reliability methods to high fidelity CAE based simulations, especially during optimization is just starting to gain traction in last few years. Availability of computing power is helping the use of such methods, but, at the same time the demand for modeling stochastic behavior with high fidelity CAE simulations and considering large number of stochastic variables still makes it prohibitive. Typically, Robust Design Optimization (RDO) formulations calculate mean and standard deviation of responses based on sampling. On the other hand Reliability Based Design Optimization (RBDO) formulations have been using methods like First Order Reliability Method (FORM) or Second Order Reliability Method (SORM) which require nested optimization to evaluate joint probability distribution and reliability factor.