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Methods to Find Best Designs Among Infeasible Design Data Sets for Highly Constrained Design Optimization Problems
Abstract:
In recent years, the use of engineering design optimization techniques has grown multifold and formal optimization has become very popular among design engineers. However, the real world problems are turning out to be involved and more challenging. It is not uncommon to encounter problems with a large number of design variables, objectives and constraints. The engineers’ expectation, that an optimization algorithm should be able to handle multi-objective, multi-constrained data is leading them to apply optimization techniques to truly large-scale problems with extremely large number of constraints and objectives. Even as newer and better optimization algorithms are being developed to tackle such problems, more often than not, the optimization algorithms are unable to find a single feasible design that satisfies all constraints. It is common to see designers spending large amounts of computational resources in evaluating infeasible designs mainly because either the algorithms take time to get to the feasible regions of the design space, or no feasible designs are obtained after all the allowed optimization iterations.
Even with surrogate based or meta-model based optimization, which enables designers to evaluate thousands of solutions with negligible computational efforts, finding a feasible design remains a challenge due to large number of optimization parameters and the highly constrained nature of the design problem. In such a case where no feasible design is available, it becomes very important to analyze the available data and find the best designs among a large number of infeasible designs.
The aim of this study is to research applicability of methods such as Multi-Criteria Decision Making (MCDM) and constraint relaxation to identify best designs among infeasible designs. Such methods aid the time-constrained engineer to make sense of the already available, albeit infeasible design data to better understand the design space. It is possible to identify regions of design space by slightly relaxing a few constraints. In this paper, two methods - Constraint Relaxation Technique and Multi-criteria Decision Making - are first applied to mathematical test problems and then to a real world automotive problem, involving different load cases with the objectives of weight reduction and performance improvement.
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