Configuration Design of Mechanical Assemblies using an Estimation of Distribution Algorithm and Constraint Programming

TL;DR

The paper addresses configuration design of mechanical assemblies as a discrete, constrained, black-box optimization problem with expensive fitness evaluations. It combines Bivariate Marginal Distribution Algorithm with Gibbs sampling (BMDA-GS) to learn and exploit pairwise dependencies, and imposes feasibility via constraint programming (CP) repairs, including an adaptive chi-square test for dependency discovery. Key contributions include extending BMDA with chi-square-based dependency detection and Gibbs sampling, and developing a CP model with repair operations to guarantee feasible configurations, demonstrated on a suspension-system problem. Results show BMDA-GS-CP converges faster and to better solutions than a GA, with MOA failing on this task, and CP repairs improving solution quality by removing unnecessary components and enforcing constraints. The approach reduces costly evaluations, provides interpretable probabilistic guidance for designers, and lays the groundwork for bi-level optimization and broader applications in mechanical design.

Abstract

A configuration design problem in mechanical engineering involves finding an optimal assembly of components and joints that realizes some desired performance criteria. Such a problem is a discrete, constrained, and black-box optimization problem. A novel method is developed to solve the problem by applying Bivariate Marginal Distribution Algorithm (BMDA) and constraint programming (CP). BMDA is a type of Estimation of Distribution Algorithm (EDA) that exploits the dependency knowledge learned between design variables without requiring too many fitness evaluations, which tend to be expensive for the current application. BMDA is extended with adaptive chi-square testing to identify dependencies and Gibbs sampling to generate new solutions. Also, repair operations based on CP are used to deal with infeasible solutions found during search. The method is applied to a vehicle suspension design problem and is found to be more effective in converging to good solutions than a genetic algorithm and other EDAs. These contributions are significant steps towards solving the difficult problem of configuration design in mechanical engineering with evolutionary computation.

Figures (6)

• Figure 1: Configuration design problem for a mechanical assembly.
• Figure 2: Repairing an infeasible configuration by removing a component (Top) and adding a component (Bottom).
• Figure 3: Illustration of the suspension design problem. Non-filled dots are variable joints. $r^{(\text{q[i]})}$ represent the points considered in the fitness function. $r^{(\text{c[i]})}$ represent the center-of-mass for each environment object. Boundary conditions are defined on $r^{(\text{b[i]})}$ and load conditions are defined on $r^{(\text{d[i]})}$.
• Figure 4: Comparison of algorithms.
• Figure 5: Visualization of dependencies between component variables. The numbers inside the parentheses are cumulative chi-square test values.