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In this research, we investigate the subject of path-finding. A pruned version of visibility graph based on Candidate Vertices is formulated, followed by a new visibility check technique. Such combination enables us to quickly identify the useful vertices and thus find the optimal path more efficiently. The algorithm proposed is demonstrated on various path-finding cases. The performance of the new technique on visibility graphs is compared to the traditional A* on Grids, Theta* and A* on Visibility Graphs in terms of path length, number of nodes evaluated, as well as computational time. The key algorithmic contribution is that the new approach combines the merits of grid-based method and visibility graph-based method and thus yields better overall performance.

This research concerns a type of configuration optimization problems frequently encountered in engineering design and manufacturing, where the envelope volume in space occupied by a number of components needs to be minimized along with other objectives such as minimizing connective lines between the components 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 configuration 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. In this research, we first present the mathematical formulation for a representative problem of configuration optimization with multiple hard constraints, and then develop two versions of an enhanced multi-objective simulated annealing approach, referred to as MOSA/R, to solve this problem. To facilitate the optimization computationally, in MOSA/R, a versatile re-seed scheme that allows biased search while avoiding pre-mature convergence is designed. Our case study indicates that the new algorithm yields significantly improved performance towards both constrained benchmark tests and constrained configuration optimization problem. The configuration optimization framework developed can benefit both existing design/manufacturing practices and future additive manufacturing.