This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also...

This work presents a genetic symbiotic algorithm to solve the one-dimensional cutting stock problem with multiple objectives. We considered two important objectives for an industry (1) cost of trim loss and (2) cost of setup. We use a symbiotic relationship, between the population of solutions and the population of cutting patterns, together with a niche strategy to obtain an approximation of t...

Cutting force has a significant influence on the dimensional accuracy due to cutting toolholder deflection. The problem of tool holder deflection is faced frequently in a variety of engineering surface products, and to achieve this goal passive technique can be used. The need for passive technique arises from the complexities that brought to the structures by active control techniques and energ...

Simulating cutting processes of human tissue is an important feature in virtual reality systems for medical training and rehearsal. In this paper we present a method to simulate the cutting operation in voxel-based virtual reality objects intended to simulate volume cutting in transurethral resection of the prostate. The method allows the user to directly interact with the three dimensional mod...

The MIRUP (Modified Integer Round-Up Property) leads to an upper bound for the gap between the optimal value of the integer problem and that of the corresponding continuous relaxation rounded up. This property is known to hold for many instances of the one-dimensional cutting stock problem but there are not known so far any results with respect to the two-dimensional case. In this paper we inve...

The MIRUP (Modiied Integer RoundUp Property) leads to an upper bound for the gap between the optimal value of the integer problem and that of the corresponding continuous relaxation rounded up. This property is known to hold for many instances of the one-dimensional cutting stock problem but there are not known so far any results with respect to the two-dimensional case. In this paper we invest...