Professor Nooshin et al. defined structural regularity indicators quantitatively three decades ago and used various methods for improving the regularity of some structures, such as stepping projection, sphere Packing concept, recursive techniques, etc, to create a special category of space structures (domes and flats) and grid shells that were designed in a multifaceted manner, and depending on the type of project, they used one or more of these indicators to analyze and compare the regularity of the structures The regularity studied in this research is related to increase of equal lengths or almost equal lengths, the reduction the count of elements with different lengths, the reduction of the number of length intervals and different shapes of faces while maintaining the geometric form. The aim of this research is to study the previous regularity indicators,  investigate and analyze the improving regularity of  Delaunay triangulation obtained from the points of the single layer dome of Bidboland Khuzestan with the proposed Algorithm: using the Circle Packing Algorithm and genetic optimization (using the minimization of different regularity indicators) to reach a suitable pattern. To analyze the improving regularity. we have presented Algorithms for calculating the regularity indicators, we have calculated the numerical results of these indices and we have suggested a general definition for regularity degree. we show that each of these indices alone is not criteria for measuring and comparing the regularity of two structures. The results of this research are effective in improving the regularity of structures, form finding, and creating the optimal design of a structure.

We provide a complete description of the edge-to-edge tilings with a regular triangle and a shield-shaped hexagon with no right angle. The case of a hexagon with a right angle is also briefly discussed.

Given a container of fixed width, infinite height and a set of rectangular block, the 2D-strip Packing problem consists of orthogonally placing all the rectangles such that the height is minimized. The position is subject to confinement of no overlapping of blocks. The problem is a complex NP-hard combinatorial optimization, thus a heuristic based on genetic Algorithm is proposed to solve it. In this paper, we give a hybrid approach which combined genetic encoding and evolution scheme with the proposed placement approach. Such a combination resulted in better population evolution and faster solution convergence to optimal. The approach is subjected to a comprehensive test using benchmark instances. The computation results validate the solution and the effectiveness of the approach.

Packing is one of the well-known problems in operation research, especially in production planning. The main objective of studying the Packing problem is to reduce the wastes of cutting through optimization of Packing of pieces. Packing is a kind of NP-hard problem that the precise methods are not able to solve it. In this paper, in order to achieve an optimal Packing of Non-guillotine cutting problems, the meta-heuristic emerging Imperialist Competitive Algorithm was used and the results were compared with the output of the genetic Algorithm, which is the typical Algorithm in solving Packing problems. To achieve better solutions, the parameters of all meta-heuristics were calibrated with Taguchi experiment method. The efficacy of the proposed approach was tested on a set of instances, taken from the literature, and the results of the proposed Algorithm were tested statistically by ANOVA. The results of this study showed that the meta-heuristic emerging Imperialist Competitive Algorithm is more efficient and faster in solving Packing problems.

The Bin Packing Problem (BPP) is to find the minimum number of bins needed to pack a given set of objects of known sizes so that they do not exceed the capacity of each bin. This problem is known to be NP-Hard [5], hence many heuristic procedures for its solution have been suggested. In this paper we propose a new representation scheme and solve the problem by a Genetic Algorithm. Limited computational results show the efficiency of this scheme.

Shape detection in digital images is one of the most effective subjects in image processing. This paper introduces a method for Circle detection in digital images using genetic Algorithm. Circle is expressed by a quadratic relation in coordinates screen. For Circle detection, finding coefficients of this quadratic relation is the challenge. In the proposed method, three random points are selected on the edges of image. Because of each three points that do not locate on a straight line express a Circle in coordinates screen, the quadratic relation coefficients of the Circle are considered as the chromosome of genetic Algorithm. After finding the coefficients and drawing the Circle, fitness function is calculated by computing amount of overlapping this Circle with the edge of image. Then, the polynomial coefficients of new generations are generated by using crossover and mutation operators. Genetic Algorithm continues until reaching the final conditions. Results of experiments on some of the images show that the proposed method can find Circles on images. Increasing of the success rate in Circle detection on image and exact detection of center and radius of Circle are the contribution of this article in comparison with studied methods.

Wireless sensor networks, as an up-to-date technology, are one of the fastest growing technologies in the world today. Since these networks are used in military and agricultural environments as well as for observation of inaccessible environments, these networks need to be organized to achieve goals such as successful and timely sending of data to the main station. Clustering of wireless sensor networks is one of the most widely used methods for organizing these networks. Various ways to cluster these networks are provided, most of which are aimed at preventing energy loss and increasing the lifetime of sensor nodes. The thesis attempts to present a new geometric method for clustering the nodes of wireless sensor networks. In this geometric method, Apollonius Circle is used to draw the abstract shape of the clusters and to assemble the nodes around the cluster head. Due to the high accuracy that it has in determining the fit of node distances, this Circle can accurately assign nodes to cluster heads and prevent large single-node clusters or faraway nodes. In this Algorithm, a main station, a number of nodes are used as a cluster header and a number of nodes as routers. The goal is to find the most accurate cluster heads and create clusters of high coverage in the network. The proposed method is implemented in MATLAB software and comparison of the results obtained from the view of successful data transmission, clustering accuracy, network lifetime and number of coverage areas, is showing accuracy of this method compared to optimal Leach Algorithms and K-means presented in this field.

One of the most important devices in poem is the repeatation of vowels and consonants is named alliteration. Important is that alliteration has two functions, sound function and meaning function. In this article an attempt has been made to present a modle for analyzation of alliteration.

In textile industry, marker planning is one of the main operations in the cutting fabric stage. Marker Packing is usually used to maximize cloth exploitation and minimize its waste. In this research, a method is used based on new found meta-heuristic imperialist competitive Algorithm (ICA) and Bottom-Left-Fill Algorithm (BLF) to achieve optimal marker Packing. Function of the proposed method was compared with other evolutionary Algorithm based marker Packing methods. The results indicate that the performance of presented method is 6.5% higher than other evolutionary marker Packing methods.