Application of the Little’s Algorithm to Solve the Problem of Structural Optimization of Operations on Multi-purpose CNC Machines

Modern multi-purpose CNC machines provide the possibility of technological process development for machining parts based on the principle of concentrating machining steps into a single operation. During the development of such operation, the task of selecting the machining step sequence within the route of part surface machining arises, minimizing the auxiliary time of idle movements of the machine tool. When the number of machining steps is small, their sequence is determined by the technologist based either on personal experience or intuitively. When the number of machining steps is large, a formal method to solve the defined problem similar to the well-known traveling salesman problem in operations research is required. This work is devoted to the modification of the traveling salesman problem in order to optimize the sequence of machining steps within the processing route of a large number of holes of different diameters and accuracy levels in body and flat parts on multi-purpose CNC machines. To solve this problem, an improved method of searching all possible options, known as the Little’s algorithm, has been chosen. The proposed model of formalizing machining steps has allowed for a structured, mathematical, and logically organized presentation of the complete description of the operation in the problem initial data, thereby improving the accuracy of optimization based on the criterion of minimizing the duration of idle movements. The definition and solution of the problem are based on the trend of improving machining paths in CAM systems, which aims to reduce operation time, increase productivity, and shorten the payback period for expensive multi-purpose CNC machines.