Incremental and Direct Design Optimization Using Mathematical Programming and Symbolic Regression

Abstract Long-term product line planning often requires identifying a sequence of designs with small changes and progressively improved performance. This is to enable a gradual transition of users from an existing product to an optimized design. We refer to this process as incremental design in this study. The intermediate designs identified in the process are crucial to avoid abrupt changes that may negatively affect user experience and market acceptance. Evolutionary algorithms have been used in recent literature to identify such designs, but this is achieved at a high cost in terms of the number of design evaluations. In this article, we show that this problem can instead be posed as a mixed-integer nonlinear programming (MINLP) problem and solved more efficiently. The effectiveness of the approach is demonstrated using a geometric path planning problem and a constrained welded-beam design optimization problem, both defined using explicit algebraic expressions. Furthermore, in engineering design, since such explicit expressions may not always be available, we extend the approach by coupling MINLP with symbolic regression (SR) that extracts interpretable expressions from sampled data. An SR-embedded NLP approach is also developed, which can be used for direct optimization as a form of surrogate-assisted optimization (SAO) approach, achieving near-global optimality significantly faster than conventional SAO algorithms.