Solving the irregular strip packing problem via guided local search for overlap minimization

The irregular strip-packing problem (ISP) requires a given set of non-convex polygons to be placed without overlap within a rectangular container having a fixed width and a variable length, which is to be minimized. As a core sub-problem to solve ISP, we consider an overlap minimization problem (OMP) whose objective is to place all polygons into a container with given width and length so that the total amount of overlap between polygons is made as small as possible. We propose to use directional penetration depths to measure the amount of overlap between a pair of polygons, and present an efficient algorithm to find a position with the minimum overlap for each polygon when it is translated in a specified direction. Based on this, we develop a local search algorithm for OMP that translates a polygon in horizontal and vertical directions alternately. Then we incorporate it in our algorithm for OMP, which is a variant of the guided local search algorithm. Computational results show that our algorithm improves the best-known values of some well-known benchmark instances.     

An exact strip packing algorithm based on canonical forms

Given a set of rectangles and a rectangular container with a fixed width, called a strip, the two-dimensional strip packing problem (2SP) requires all the given rectangles to be placed orthogonally without overlap within the strip so as to minimize the height of the strip. 2SP and its variants have many applications in steel and textile industries, including an indirect application in scheduling problems. However, 2SP is known to be NP-hard.     

Full‐color photo‐addressable electronic paper using cholesteric liquid crystals and organic photoconductors

Abstract— Full‐color photo‐addressable electronic paper using cholesteric liquid crystals and organic photoconductors was developed. The electronic paper is comprised of two stacked photo‐addressable elements displaying blue/green and red images, respectively. Each photo‐addressable element was independently controlled by two different color‐addressing lights. Furthermore, blue and green images were selectively switched by one organic photoconductor using the threshold characteristics of cholesteric liquid crystals. A highly reflective polymer‐dispersed cholesteric liquid‐crystal (PDCLC) layer was obtained by a new formation process based on the sol‐gel transition behavior of a gelatin matrix and an agar overcoat layer. The PDCLC layer had a close‐packed honeycomb‐like monolayer structure with a flat surface. The A6‐sized prototype had paper‐like features and showed full‐color bistable images instantly written with a viewer‐type writing apparatus.     

Growth and reproduction of the chinchilla-age at vaginal opening, oestrous cycle, gestation period, litter size, sex ratio, and diseases frequently encountered (author's transl)

The paper deals with observations on growth and reproduction of the chinchilla in recent 4 years started from 1966 at this laboratory. There were large variations in age of vaginal opening (less than 71 days-308 days) with an average of 173.2+/-57.6 days in 45 females. The average length of 100 oestrus cycles in 24 females was 35.7+/-7.9 (15-62) days. The mean period of 5 gestations in 5 females was 110.4 (108-112) days. Eighty-one out of 123 litters were born between March and August during 3 years, and parturition never occurs in December. The most suitable season for reproduction of chinchillas may be from January to April, and a summer anoestrous seems to be present in August to early September as reported by Weir. The litter size ranged from 1 to 4 with a mode of 2 (46.3%) and an average of 1.90+/-0.76. More male kids were produced at birth at this laboratory, and sex ratio was 133.7 (98 females and 131 males). In 1973, 37 chinchillas gave birth to 71 kids with an average litter size of 1.92, and 59 of them were successfully weaned (1.59 per litter). Of these kids, 50 (1.35 per liter) attained 240 days of age (adulthood). Among 91 subjected to investigation for causes of death, 23 (25.3%) were dead during newborn period, and 9 and 5 adults were dead of malocclusion (9.9%) and the prolapse of rectum respectively.