Learning Symbolic Formulations in Design Optimization

Abstract

This paper presents a learning and inference mechanism for unsupervised learning of semantic concepts from purely syntactical examples of design optimization formulation data. Symbolic design formulation is a tough problem from computational and cognitive perspectives, requiring domain and mathematical expertise. By conceptualizing the learning problem as a statistical pattern extraction problem, the algorithm uses previous design experiences to learn design concepts. It then extracts this learnt knowledge for use with new problems. The algorithm is knowledge-lean, needing only the mathematical syntax of the problem as input, and generalizes quickly over a very small training data set. We demonstrate and evaluate the method on a class of hydraulic cylinder design problems.

A survey on automating configuration and parameterization in evolutionary design exploration

“…From the discovered relations, heuristics like "the thickness of a design has a strong influence on its weight" are derived. Sarkar et al (2008) analyzed multiple formulations of an optimization problem using the feature extraction method singular value decomposition. By means of singular value decomposition, latent syntactic relations among the used variables, constants, and functions were discovered.…”

“…Iteratively adjust constants of Objective functions (Parmee & Bonham, 1999;Parmee, 2002) 3 † Constraint functions (Ren & Papalambros, 2011) 3 † Extract information on design variables and associated attributes from design documentation (Ghani et al, 2006;Wong et al, 2008;Raju et al, 2009;Wu et al, 2009) 1 , 2 † † † Group attributed solutions to discover Design variables (Xu et al, 2006) 1 † New objective and constraint functions (Reich & Fenves, 1991;Veerappa & Letier, 2011) 2 † † Identify which problem elements belong together by Analyzing how problem elements interact with each other during optimization (Matthews et al, 2006;Bandaru & Deb, 2013) 1 , 2 , 3 † † † Examining what elements were used in combination over different problem formulations (Sarkar et al, 2008) 1 , 2 , 3 † † † Extracting semantic relations among elements from design documentation (Dong & Agogino, 1997;Yang et al, 2005;Li & Ramani, 2007;Wong et al, 2011;Liang et al, 2012) 1 , 2 , 3 † † † Computing objective functions by…”