Homogenous Strips Research Articles

Balanced approach for the two-dimensional rectangular guillotine cutting stock problem with setup cost

The main optimization objective of two-dimensional rectangular guillotine cutting stock problem (2DRGCSP) is minimizing stock cost. However, setup cost is also needed to be considered as an important factor in the real manufacturing process. A sequential pattern generation algorithm with rectangular homogenous strips (SPGA-RHSs) is presented to generate a cutting plan based on each single stock. A better cutting pattern considering both stock cost and setup cost is obtained with the cost balance utilization (CBU). The balanced approach combining SPGA-RHSs and CBU is used to achieve a current optimal cutting plan for 2DRGCSP with the minimum sum of stock and setup cost. The computational results prove that the proposed balanced approach has good optimization performance for 2DRGCSP with setup cost.

Bioinspired Temperature-Responsive Multilayer Films and Their Performance under Thermal Fatigue.

The structure of certain nonliving tissues determines their self-shaping and self-folding capabilities in response to a stimulus. Predetermined movements are realized according to changes in the environmental conditions due to the generated stresses of the multilayer anisotropic structure. In this study, we present bioinspired responsive anisotropic multilayer films and their fabrication process which comprises low-cost techniques. The anisotropic multilayer materials are capable of deforming their geometry caused by small temperature changes (<40 °C). The mismatch in the thermo-mechanical properties between three or more anisotropic thin layers creates responsive materials that alter their shape owing to the developed internal stresses. The movements of the material can be controlled by forming anisotropic homogenous metallic strips over an anisotropic thermoplastic layer. As a result, responsive multilayer films made of common materials can be developed to passively react to a temperature stimulus. We demonstrate the ability of the anisotropic materials to transform their geometry and we present a promising fabrication process and the thermal fatigue resistance of the developed materials. The thermal fatigue performance is strongly related to the fabrication method and the thickness of the strips. We studied the thermal fatigue performance of the materials and how the thermal cycling affects their sensitivity, as well as their failure modes and crack formation.

A deterministic algorithm for generating optimal three-stage layouts of homogenous strip pieces

Purpose: The time required by the algorithms for general layouts to solve the large-scale two-dimensional cutting problems may become unaffordable. So this paper presents an exact algorithm to solve above problems. Design/methodology/approach: The algorithm uses the dynamic programming algorithm to generate the optimal homogenous strips, solves the knapsack problem to determine the optimal layout of the homogenous strip in the composite strip and the composite strip in the segment, and optimally selects the enumerated segments to compose the three-stage layout. Findings: The algorithm not only meets the shearing and punching process need, but also achieves good results within reasonable time. Originality/value: The algorithm is tested through 43 large-scale benchmark problems. The number of optimal solutions is 39 for this paper’s algorithm; the rate of the rest 4 problem’s solution value and the optimal solution is 99.9%, and the average consumed time is only 2.18 seconds. This paper’s pattern is used to simplify the cutting process. Compared with the classic three-stage, the two-segment and the T-shape algorithms, the solutions of the algorithm are better than that of the above three algorithms. Experimental results show that the algorithm to solve a large-scale piece packing quickly and efficiency.

Exact algorithm for generating optimal homogenous strip T-shape layouts

This paper presented an algorithm for generating the homogenous strip T-shape layouts for large-scale rectangular piece packing.The algorithm not only achieved good results within reasonable time,but also met the shearing and punching process need.The algorithm generated optimal homogenous strips,solved knapsack problems to obtain the strip layouts on the sections and the section layouts on the segments,and optimally selected two segments to compose the layouts.The algorithm was tested on 63 benchmark problems,and compared with five famous algorithms(the classic two-stage,the general T shape,the two-stage homogenous block,the general cutting pattern and the heuristic algorithm TABU500).The computational results indicate that the algorithm is efficient in both the computation time and the material utilization rate.

Semi-analytic method for slow light photonic crystal waveguide design

We present a semi-analytic method to calculate the dispersion curves and the group velocity of photonic crystal waveguide modes in two-dimensional geometries. We model the waveguide as a homogenous strip, surrounded by photonic crystal acting as diffracting mirrors. Following conventional guided-wave optics, the properties of the photonic crystal waveguide may be calculated from the phase upon propagation over the strip and the phase upon reflection. The cases of interest require a theory including the specular order and one other diffracted reflected order. The computational advantages let us scan a large parameter space, allowing us to find novel types of solutions.

Fast heuristic for constrained homogenous T-shape cutting patterns

Homogenous T-shape (HTS) cutting patterns are welcomed when the two-phase process is used to produce rectangular pieces from the stock plate, where the plate is cut into homogenous strips at the first phase, and the strips are divided into pieces at the second phase. A heuristic is presented for generating constrained HTS patterns, where the objective is to maximize the pattern value that is equal to the total value of the included pieces, observing the upper bound constraint on the frequency of each piece type. The heuristic is based on dynamic programming and branch-and-bound techniques. It can yield solutions close to optimal with short computation time. By providing good initial solutions, the heuristic can greatly improve the time efficiency of an existing exact branch-and-bound algorithm.

An Algorithm to Optimal Two-Stage Homogenous Strip Patterns of Rectangular Pieces

This paper presents an algorithm for two-stage homogenous strip patterns for rectangular pieces. The algorithm is appropriate for the shearing and punching process. It proposes the two-stage homogenous strip patterns that can be cut into homogenous strips in two stages, with another two stages being required to cut the strips into pieces. Firstly vertical cuts divide the stock sheet into segments, and then horizontal cuts divide the segments into homogenous strips. A homogenous strip contains pieces of the same type. The algorithm uses a dynamic programming recursion to determine the strip layout on each segment, solves knapsack problems to obtain the segment layout on the sheet. The algorithm is tested through benchmark problems, and compares with two famous algorithms. The pattern value and the computation speed of this paper’s algorithm are better than that of the classic two-stage algorithm. What’s more, this paper’s algorithm can give solutions very close to optimality.

A recursive branch-and-bound algorithm for constrained homogenous T-shape cutting patterns

The manufacturing industry often uses the two-phase process to divide stock plates into rectangular items. A guillotine machine cuts the plates into homogenous strips at the first phase, where each strip contains items of the same type. Either a guillotine machine or stamping press cuts the strips into items at the second phase. This paper presents a recursive branch-and-bound algorithm for generating constrained homogenous T-shape (HTS) cutting patterns at the first phase, where the frequency of an item type is constrained by its upper bound. A HTS pattern includes two segments. Each segment contains homogenous strips of the same direction. The strip directions of the two segments are perpendicular to each other. Two versions of the algorithm are presented. The first uses the unconstrained solutions to estimate the upper bounds, and the second uses the constrained solutions. The computational results indicate that the algorithm is much faster than existing algorithms.

An algorithm for generating optimal constrained one-stage homogenous strip cutting patterns

The cutting and stamping process is often used to divide a stock plate into items to make products. It includes two phases. A guillotine machine cuts the plate orthogonally into homogenous strips at the cutting phase; then a stamping press stamps out the items from the strips at the stamping phase. A homogenous strip contains items of the same type. A one-stage homogenous strip cutting pattern (OSHSCP) contains parallel homogenous strips of the same length. The OSHSCP is useful because it can be used independently or as elements to compose other types of cutting patterns. This article presents a dynamic programming algorithm for generating the optimal constrained OSHSCP, where the maximum demand for each item type is specified and the objective is to maximize the total value of items included in the pattern. The computational results indicate that the computation time is reasonable.

An algorithm for the constrained two-dimensional rectangular multiple identical large object placement problem

This paper presents an algorithm for the constrained, two-dimensional, rectangular multiple identical large object placement problem, where a set of small rectangular items must be cut from a specified number of identical plates, so as to maximize the value of the cut items. The algorithm generates optimal homogenous T-shape patterns that contain only homogenous strips. A homogenous strip contains items of the same type. A cut divides the plate into two segments. Each segment consists of strips with the same direction. The strips in the first segment are horizontal, and those in the second segment are vertical. The algorithm is based on the bottom-up tree-search approach. Both lower and upper bounds are used to prune the search tree. The computational results indicate that the algorithm is capable of solving problems of small and medium scales.

T-shape homogenous block patterns for the two-dimensional cutting problem

This paper presents an algorithm for unconstrained T-shape homogenous block cutting patterns of rectangular pieces. A vertical cut divides the stock sheet into two segments. Each segment consists of sections that have the same length and direction. A section contains a row of homogenous blocks. A homogenous block consists of homogenous strips of the same piece type. Each cut on the block produces just one strip. The directions of two strips cut successively from a block are either parallel or orthogonal. The algorithm uses a dynamic programming recursion to generate optimal blocks, solves knapsack problems to obtain the block layouts on the sections and the section layout on segments of various lengths, and optimally selects two segments to compose the cutting pattern. The computational results indicate that the algorithm is efficient in improving material usage, and the computation time is reasonable.

An exact algorithm for generating homogenous two-segment cutting patterns

An exact algorithm is proposed for generating homogenous two-segment patterns for the constrained two-dimensional guillotine-cutting problems of rectangular items. It is a bottom-up approach combined with branch-and-bound techniques. The stock plate is divided into two segments. Each segment consists of strips of the same length and direction. Only homogenous strips are considered, each of which contains items of the same type. The strip directions of the two segments may be either the same or perpendicular to each other. The algorithm uses a tree-search procedure. It starts from an initial lower bound, implicitly generates all possible segments through the assembly of strips, and constructs possible patterns through the combination of two segments. Tighter bounds are established to discard non-promising segments. The computational results indicate that the algorithm is efficient both in computation time and in material utilization, and is able to deal with relatively large-scale problems.

Heuristic and exact algorithms for generating homogenous constrained three-staged cutting patterns

An approach is proposed for generating homogenous three-staged cutting patterns for the constrained two-dimensional guillotine-cutting problems of rectangles. It is based on branch-and-bound procedure combined with dynamic programming techniques. The stock plate is divided into segments. Each segment consists of strips with the same direction. Only homogenous strips are allowed, each of which contains rectangles of the same size. The approach uses a tree-search procedure. It starts from an initial lower bound, implicitly generates all possible segments through the builds of strips, and constructs all possible patterns through the builds of segments. Tighter bounds are established to discard non-promising segments and patterns. Both heuristic and exact algorithms are proposed. The computational results indicate that the algorithms are capable of dealing with problems of larger scale. Finally, the solution to a cutting problem taken from a factory that makes passenger cars is given.

An exact algorithm for generating homogenous T-shape cutting patterns

Both the material usage and the complexity of the cutting process should be considered in generating cutting patterns. This paper presents an exact algorithm for constrained two-dimensional guillotine-cutting problems of rectangles. It uses homogenous T-shape patterns to simplify the cutting process. Only homogenous strips are allowed, each of which contains rectangular blanks of the same size and direction. The sheet is divided into two segments. Each segment consists of strips of the same length and direction. The strip directions of the two segments are perpendicular to each other. The algorithm is based on branch and bound procedure combined with dynamic programming techniques. It is a bottom-up tree-search approach that searches the solution tree from the branches to the root. Tighter bounds are established to shorten the searching space. The computational results indicate that the algorithm is efficient both in computation time and in material usage.

Auftragsgerät für die analytische dünnschichtchromatographie

An apparatus is described for the loading of samples on to thin layer chromatography plates. The dissolved substances are sprayed as a fine homogenous strip (0.5 mm or more thick) without damaging the surface of the plate. The apparatus permits work on an analytical (from 3–4 μl) or on a preparative scale, and has great advantages for the loading of plates for quantitative densitometry.