Abstract— In this paper, we present an efficient solution to determine the best sequence of G commands of a set of holes for a printed circuit board in order to find the hole-cutting sequence that shortens the cutting tool travel path. A Parallel proposal of Ant Colony Optimization was used to find an optimal travel path, then the new G-codes sequence is used instead the original sequence as part of the process program. This application can be formulated as a special case of the Traveling Salesman Problem (TSP). Index Terms— Ant Colony Optimization, ACO, Computer Numerical Control, CNC, Traveling Salesman Problem, TSP, drilling. I. INTRODUCTION omputer Numerical Control (CNC) refers to the automation of machine tools, which is of primordial importance in any automated industrial process for manufacturing products. Today manual machine tools have been largely replaced by CNC machines where all movements of the machine tools are programmed and controlled electronically rather than by hand [15], reducing time and avoiding human errors. The productivity of CNC machine tools is significantly improved by using Computer Aided Design (CAD) and Computer Aided Manufacturing (CAM) systems for automated Numerical Control (NC) program generation. Currently, many CAD/CAM packages that provide automatic NC programming have been developed for various cutting processes, being one of those process the hole – cutting operation or drilling. There are several studies that focus on the study of reducing the cutting time by optimizing some parameters such as part geometry, material and tool type. This paper analyzes the cutting time, which is the time that the cutting tool moves with cutting speed in air or in material. A survey of the literature shows that much research has been done on minimizing the cutting time [1, 2]; however, there is a lack of literature that studies the travel time between operations. In order to minimize the travel time, the cutting tool travel path between operations should be minimized. Manuscript received July 10, 2011; and accepted August 15, 2011. Nataly Medina Rodríguez is a PhD student in Intelligent Systems in Instituto Politécnico Nacional - CITEDI. Av. del Parque 1310, Otay, Tijuana, B.C., México. (e-mail: nmedina@citedi.mx). Oscar H. Montiel Ross is with Instituto Politécnico Nacional - CITEDI. (Corresponding author phone: 52(664)-623-1344; e-mail: o.montiel@ieee.org.) Roberto Sepúlveda is with Instituto Politécnico Nacional - CITEDI. e-mail: r.sepulveda@ieee.org. Oscar Castillo is with Tijuana Institute of Technology in the Department of Computer Science in the Graduate Division. Calzada Tecnológico S/N, Tijuana, B. C., México. (e-mail ocastillo@hafsamx.org). This travel path can be formulated as a special case of the traveling salesman problem (TSP) [3]. II. ANT COLONY OPTIMIZATION FOR THE TRAVELING SALESMAN PROBLEM The TSP problem [13][14] is the problem of a salesman who, starting from his hometown, wants to find a shortest tour that takes him through a given set of costumer cities and then back home, visiting each customer city exactly once. The TSP can be represented by a complete weighted graph [4] with being the set of nodes representing the cities, and being the set of arcs. Each arc has assigned a value (length) , which is the distance between cities i and j. Ant Colony Optimization was introduced by Marco Dorigo [4]. Using very simple communication mechanisms, an ant group is able to find the shortest path between any two points by choosing the paths according to pheromone levels. After several years that ACO was introduced, many papers have described applications that use this algorithm. For example in robotic, in [16] the Simple ACO was applied to obtain the optimal path for a mobile robot, here was considered static and dynamic obstacle avoidance, a memory capacity for the ants was proposed, and a fuzzy cost function was used. In [17] and [18] the ACO was applied to tune fuzzy parameters of a fuzzy logic controller for a wheeled mobile robot, in [19] a comparison of ACO and Genetic Algorithms applied to fuzzy system optimization was presented. ACO metaheuristics can be applied to the TSP, where the pheromone trails are associated with arcs and therefore refers to the desirability of visiting city j directly after city i. The heuristic information is chosen as ; that is, the heuristic desirability of going from city i to city j is inversely proportional to the distance between the two cities. For implementation purposes, pheromone trails are collected into a pheromone matrix whose elements are the . Tours are constructed by applying the following simple constructive procedure to each ant: 1. Each ant chooses, according to some criterion, a start city at which the ant is positioned. 2. Each ant uses a pheromone and heuristic values to probabilistically construct a tour by iteratively adding cities that the ant has not visited yet, until all cities have been visited. 3. Each ant goes back to the initial city. 4. After all ants have completed their tour, they may deposit pheromone on the tours they have followed. Tool Path Optimization for Computer Numerical Control Machines based on Parallel ACO Nataly Medina-Rodríguez, Oscar Montiel-Ross, Roberto Sepúlveda, and Oscar Castillo C Engineering Letters, 20:1, EL_20_1_13 (Advance online publication: 27 February 2012) ______________________________________________________________________________________