Layout design problems are frequently encountered in engineering design, where the envelope volume in space occupied by a series of cylinder-shaped objects needs to be minimized along with other objectives such as minimizing connective lines between the cylinders under various constraints.  Since in practical applications the objectives and constraints are usually complex, the formulation of computationally tractable optimization becomes difficult.  Moreover, unlike conventional multi-objective optimization problems, such layout design problems usually comes with a number of demanding constraints that are hard to satisfy, which results in the critical challenge of balancing solution feasibility with optimality.

At DSCL, we develop mathematical formulation for layout design problem with multiple hard constraints.  Specifically, enhanced multi-objective simulated annealing approaches are developed to solve the design problem.  To facilitate the optimization computationally, a versatile re-pick scheme that allows biased search while avoiding pre-mature convergence is designed.

We also explore pathfinding algorithms, as pathfinding problems, e.g., finding the shortest connection lines between parts, are commonly associated with layout optimization problems in the design of mechanical systems.