Geometric Optimization Algorithms in Manufacturing

In this paper we review the recent progress in the design of efficient algorithms for several geometric optimization problems in manufacturing processes. We first describe the strong geometric characteristics of optimization problems in manufacturing. Three illustrative problems are then presented in details: the shortest contour touring problem in laminated object manufacturing, the minimum tool retractions problem in zigzag machining, and the minimum workpiece setups in 4-axis surface machining. We survey representative algorithms and techniques used to solve these three problems, with emphasis on both their practical significance and theoretical contributions.