Sotiris L. Omirou

Differential evolution for sequencing and scheduling optimization

This paper presents a stochastic method based on the differential evolution (DE) algorithm to address a wide range of sequencing and scheduling optimization problems. DE is a simple yet effective adaptive scheme developed for global optimization over continuous spaces. In spite of its simplicity and effectiveness the application of DE on combinatorial optimization problems with discrete decision variables is still unusual. A novel solution encoding mechanism is introduced for handling discrete variables in the context of DE and its performance is evaluated over a plethora of public benchmarks problems for three well-known NP-hard scheduling problems. Extended comparisons with the well-known random-keys encoding scheme showed a substantially higher performance for the proposed. Furthermore, a simple slight modification in the acceptance rule of the original DE algorithm is introduced resulting to a more robust optimizer over discrete spaces than the original DE.

A locus tracing algorithm for cutter offsetting in CNC machining

Abstract This paper presents a new interpolation algorithm for tool motion generation along planar offset curves, an important manufacturing problem in CNC machining. The development of the algorithm is based on a locus tracing concept. The main advantage of the concept is the fact that is applicable not only when an analytic expression of the desired path is available but also in situations where, although the path is geometrically defined, its analytic description is either impossible to compute, or too cumbersome to work with. The presented locus tracing algorithm, uses the locus defining geometric property to generate a succession of points on the desired path (the offset), through repeated application of two analytically implemented construction operations. These operations are formulated on the basis of the direction and proximity criteria introduced by Danielson, which guarantee a locus position error of at most one step. The effectiveness and simplicity of the algorithm is demonstrated by two representative examples. The first example uses an ellipse as the generator curve while the second example treats with a more complex case such is the case of a free-form curve implemented in terms of a Bezier curve.

Space curve interpolation for CNC machines

Abstract Despite the tremendous development in CNC programming facilities, linear and circular cuts parallel to the coordinate planes continue to be the standard motions of modern CNC machines. However, the increasing industrial demand for parts with intricate shapes cannot be satisfied with only these standard motions. This paper proposes an efficient and accurate method for developing a class of precise interpolation algorithms which can drive the cutter of a CNC machine along three-dimensional (3D) trajectories. Engaging a pair of primitive shapes, the method uses their implicit or parametric definition to interpolate their intersection curve on the basis of Danielson’s step selection rules. The presence of Danielson’s criteria guarantees a position error of at most one step. A general-purpose computer for path generation and real-time control of the machine is employed. The user first chooses a suitable combination of shapes whose intersection gives the desired form of the 3D trajectory and then initiates the algorithm with the desired information of the two shapes.

3-Dimensional Circular Interpolation for CNC Machines

An efficient and accurate algorithm for generating circular arcs on arbitrary planes is presented and its implementation in the context of CNC is discussed. Besides having significant application potential as a CNC feature, it exemplifies a class of precise interpolation algorithms which can be developed on the basis of an integer programming formulation of Danielsons step selection criteria.

NC machining for revolved and swept surfaces with free-form profiles

Abstract An accurate, flexible and simple method is proposed for machining the surfaces obtained, either by revolving around an axis (surface of revolution), or by moving along a straight line (swept surface), a free-form profile which is implemented in terms of Bezier formulation. In the first case, the profile curve is coplanar with the symmetry axis, while in the second case it lies in a plane perpendicular to the direction of translation. The demand for manufacturing of such geometric shapes is frequently met in sculptured surfaces of molds, stamping dies, forging tools, rolling shapes, etc.

A Particle Swarm Optimization Algorithm for Scheduling Against Restrictive Common Due Dates

Focusing on the just-in-time (JIT) operations management, earliness as well as, tardiness of jobs’ production and delivery should be discouraged. In accordance to this philosophy, scheduling problems involving earliness and tardiness penalties are very critical for the operations manager. In this paper, a new population heuristic based on the particle swarm optimization (PSO) technique is presented to solve the single machine early/tardy scheduling problem against a restrictive common due date. This type of scheduling sets costs depending on whether a job finished before (earliness), or after (tardiness) the specified due date. The objective is to minimize a summation of earliness and tardiness penalty costs, thus pushing the completion time of each job as close as possible to the due date. The problem is known to be NP-hard, and therefore large size instances cannot be addressed by traditional mathematical programming techniques. The performance of the proposed PSO heuristic is measured over benchmarks problems with up to 1000 jobs taken from the open literature, and found quite high and promising in respect to the quality of the solutions obtained. Particularly, PSO was found able to improve the 82% of the existing best known solutions of the examined benchmarks test problems.

Assembly Line Balancing Using Differential Evolution Models

ABSTRACT There is a growing research interest on the application of evolutionary computation-based techniques in manufacturing optimization due to the fact that this field is associated with a plethora of complex combinatorial optimization problems. Differential evolution (DE), one of the latest developed evolutionary algorithms, has rarely been applied on manufacturing optimization problems (MOPs). A possible reason for the absence of DE from this research field is that DE was introduced as global optimizer over continuous spaces, while most of MOPs are of combinatorial nature with discrete decision variables. DE maintains and evolves floating-point vectors and therefore its application to MOPs that have solutions represented by permutations is not straightforward. This paper investigates the use of DE for the solution of the simple assembly line balancing problem (SALBP), a well-known NP-hard MOP. Two basic formulation types for SALBP are examined, namely type-1 and type-2: the former attempts to minimize the number of workstations required to manufacture a product in an assembly line for a given fixed cycle time; while the latter attempts to minimize the cycle time of the line for a given number of stations. Extensive experiments carried out over public benchmarks test instances estimate the performance of DE approach.

A CNC Parametric Programming Method for Manufacturing of Axisymmetric Mould Cavities

Abstract This paper presents a convenient and an easy to use manufacturing method for parts with axisymmetric geometry on CNC milling machines. The desired form of the cavities is achieved by selecting as generatrix curve any plane curve, implicitly or parametrically defined, which fulfills specific imposed by the user criteria (functional, aesthetic or other). Each machining pass is modelled as a path composed of generatrix curve segments and semicircular arcs. The surface quality is controlled by keeping the distance between successive scallops within a programmed value. Tool motion along the desired paths is generated by G-code algorithms that exploit the parametric programming technique, a powerful CNC programming tool. The effectiveness of the proposed method is verified by simulation tests for three representative curves.

A General G-Code Algorithm for Deep Hole Drilling

Abstract Hole drilling is the most common machining operation performed on computer numerical control (CNC) machine tools or machining workshops. Drilling appears to be a relatively simple process however; when it involves drilling deep holes, it becomes one of the most complicated metal cutting processes. Although modern machine tool controllers are equipped with special drilling canned cycles, these cycles have significant constraints mainly due to their limited framework of application. The present work proposes a general G-code algorithm intended to accommodate effective deep hole drilling. The algorithm is characterized by flexibility in the pecking strategy and adaptability to the needs of each individual drilling case. The development of the proposed algorithm is based on parametric programming which is a powerful CNC programming technique.

A CNC Manufacturing Method for Parts with Trochoidal Profile

Abstract This paper presents a manufacturing method for parts with trochoidal profile on CNC milling machines. The method is based on a new real-time interpolation algorithm capable to drive the cutter along the offset of trochoid curves with precision equal to the resolution of the machine. The structure of the presented algorithm may be adapted accordingly so as to be used either for parts with an epitrochoidal or a hypotrochoidal profile. Both types of curves, known as trochoid curves, have important industrial applications such as gears with trochoidal tooth-profile, cams, trochoidal-shaped housings for rotary internal combustion engines and rotary piston pumps etc. The effectiveness and accuracy of the proposed method is verified by simulation tests of the generated tool path for the machining of two representative mechanical parts, an inner rotor of a hypogerotor pump and an epitrochoidal-shaped housing.