Machine Learning in Optimal Design
Giuseppe Cerbone · 1991
Many important application problems can be formalized as constrained non-linear optimization tasks. However, numerical methods for solving such problems are brittle and do not scale well. This paper describes a novel framework for numerical optimization in engineering design that augments the traditional run-time optimization by a three step compilation. First, symbolic learning methods are used to partition task into sub-problems that can be solved more efficiently. This also produces specialized versions of the optimization tasks that are faster to evaluate than the original. Second, each sub-problem is further simplified by using inductive discovery techniques to reduce the number of independent variables. This introduces a further speedup in the optimization process of the individual functions. Third, novel ID3-like inductive learning algorithms are used to derive selection rules that associate problem instances to sets of candidate solutions. At run time, the problem solver uses these rules t o map the problem instance to a set of efficient numerical gradient-directed optimizations that can be performed in parallel. In the domain of 2-dimensional structural design, this procedure yields a 95% speedup over traditional optimization methods and decreases the dependence of the numerical methods on having a good starting point.