Reginald Dewil

An improvement heuristic framework for the laser cutting tool path problem

This paper deals with generating cutting paths for laser cutting machines by representing a tool path in a novel way. Using the new representation, the tool path problem can be viewed as finding a partitioning of contours which minimises the sum of the costs of a rooted directed minimum spanning tree to connect the partitions and the costs of a generalised travelling salesman problem (GTSP) solutions within each partition. Using Edmond–Liu’s algorithm to solve the arborescence problem, an improved Lin–Kernighan heuristic to solve the GTSP and a heuristic-repartitioning approach, tool paths can be generated that are 4.2% faster than those generated by an existing tool path construction heuristic.

Construction heuristics for generating tool paths for laser cutters

This paper deals with generating paths for cutting irregular parts nested on thin or thick metal sheets. The objective is to minimise the total time required to cut all parts from the metal sheet explicitly taking the cost of piercing and pre-cutting into account. The problem is modelled as a generalised travelling salesperson problem with special precedence constraints. A set of construction heuristics is presented that incorporates the constraints originating from inner–outer contours, common cuts, piercing points and pre-cuts. Computational tests on a set of real-life cutting problems show that our solution approach is able to generate tool paths that for thick plates spend on average 33.4% less time than those generated by a commercial package for air movements, pre-cuts and sharp angle macros with cutting and piercing times being equal.

Cutting Path Optimization Using Tabu Search

This paper deals with generating paths for cutting irregular parts nested on a metal sheet. The objective is to minimize the total non-cutting time for the cutter head starting at a known location, cutting all the required elements and returning to the known location. In contrast to most literature on this topic, a part does not have to be cut at once. If this reduces the total non-cutting time, it is possible to cut a number of elements on a given part, then cut other parts and then return later to finish cutting the given part. The problem is modeled as a generalized traveling salesperson problem with special precedence constraints. An initial feasible solution is generated and improved by local moves embedded in a tabu search framework. The proposed algorithm shows promising results in comparison with a commercial software package on a limited set of test cases.

Sheet Metal Laser Cutting Tool Path Generation: Dealing with Overlooked Problem Aspects

This paper deals with non-trivial problem aspects of laser cutting tool path generation that, to the best of our knowledge, received relatively little attention in the scientific literature. It is shown that some aspects such as plate edge nesting, skeleton and remnant cutting, and clamp positioning can be modeled and solved with little additional effort using existing tool path algorithms. However, concepts such as collision avoidance, pre-cut optimization, and bridge utilization prove to be more challenging and will require more profound algorithmic adjustments if these have to be taken into account fully. An even harder problem aspect is generating tool paths that are thermally feasible. Since laser cutting introduces net heat into the metal sheet, the metal sheet tends to heat up as the cutting progresses. Quality deterioration can occur if the laser spends too much time cutting in the same region. It is shown how to model the easy problem extensions in order to handle them using existing problem approaches and solution approaches are suggested to tackle the harder concepts. In addition, a proof of concept is presented that shows that thermal feasible tool paths can be generated through a multi-start heuristic utilizing a thermal penalty function. A finite difference method iteratively (or concurrently dependent on the used heuristic) evaluates the thermal feasibility and updates the penalty function.

A minimum cost network flow model for the maximum covering and patrol routing problem

This paper shows how the maximum covering and patrol routing problem (MCPRP) can be modeled as a minimum cost network flow problem (MCNFP). Based on the MCNFP model, all available benchmark instances of the MCPRP can be solved to optimality in less than 0.4s per instance. It is furthermore shown that several practical additions to the MCPRP, such as different start and end locations of patrol cars and overlapping shift durations can be modeled by a multi-commodity minimum cost network flow model and solved to optimality in acceptable computational times given the sizes of practical instances.

Face Split Interpretations in Sheet Metal Design

Most of the modern CAD systems have capabilities to work with sheet metal parts. However, the functionality of these modules is limited to modelling, unfolding and delivering project documentation. In some cases the proposed design cannot be manufactured without splitting one or more faces of the part. In the current work, the graph representation of sheet metal parts and corresponding flat patterns are discussed. A splitting procedure is introduced which keeps all existing connections between faces intact. In addition, three interpretations for splitting are presented and recommendations for possible usage are given. The splitting procedure is found to be a convenient option to create feasible flat patterns. In addition, the different splitting interpretations present more flexibility to the designer.