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Due to the algorithmic simplicity, cellular automata (CA) models are useful and simple methods in structural optimization. In

this paper, a cellular-automaton-based algorithm is presented for simultaneous shape and topology optimization of continuum

structures, using five-step optimization procedure. Two objective functions are considered and the optimization process is

converted to the single objective optimization problem (SOOP) using weighted sum method (WSM). A novel triangle

neighborhood is proposed and the design domain is divided into small triangle elements, considering each cell as the finite

element. The finite element formulation for constant strain triangles using three-node triangular elements is developed in this

article. Topological parameters and shape of the design space are taken as the design variables, which for the purpose of this

paper are continuous variables. The paper reports the results of several design experiments, comparing them with the currently

available results obtained by CA and genetic algorithm in the literature. The outcomes of the developed scheme show the

accuracy and efficiency of the method as well as its timesaving behavior in achieving better results

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Since the 1990’s, network reliability has been considered as a new index for evaluating transportation networks under uncertainty. A large number of studies have been revealed in the literature in this field, which are mostly dedicated to developing relevant measures that can be utilized for the evaluation of vulnerable networks under different sources of uncertainty, such as daily traffic flow fluctuations, natural disasters, weather conditions, and so fourth. This paper addresses the resource allocation problem in vulnerable transportation networks, in which multiple performance reliability measures should be met at their desired levels, while the overall cost of upgrading links’ performances should be minimized simultaneously. For this purpose, a new approach has been considered to formulate the two well-known performance measures, connectivity and capacity reliability, along with their application in a bi-objective nonlinear mixed integer goal programming model. In order to take into account the uncertain conditions of supply, links’ capacities have been assumed to be random variables and follow normal distribution functions. A computationally efficient method has been developed that allows calculating the network-wise performance indices simply by means of a set of functions of links’ performance reliabilities. Using this approach, as the performance reliability of links are themselves functions of the random links’ capacities, they can be simply calculated through numerical integration. To achieve desirable levels for both connectivity reliability and capacity reliability (as network-wise performance reliability measures) two distinct objectives have been considered. One of the objectives seeks to maximize each of the measures regardless of what is happening to the other objective function which minimizes the budget. Since optimization models with two conflicting objectives cannot be solved directly, the well-known goal attainment multi-objective decision-making (MODM) approach has been adapted to formulate the model as a single objective model. Then the resultant single objective model has been solved through the generalized gradient method, which is a straightforward solution algorithm coded in existing commercial software such as MATLAB programming software. To show the applicability of the proposed model, numerical results are provided for a simple network. Also, to show the sensitiveness of the model to decision maker’s direction weights, the results of sensitivity analysis are presented..

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Engineering design usually requires considering multiple variances in a design and integrating them appropriately in order to achieve the most desirable alternative. This consideration takes particular importance in the constructional projects of civil engineering. However, frequently, the structural designer’s considerations in civil engineering teams contrast the stylish and creative novelties of architectures. Then, we should take up new methodologies to yield appropriate alternatives which meet artistic aspects of design and simultaneously satisfy the structural designer’s demands. Consequently, the process of design should incorporate the multi-fold aspects of engineer’s requirements and their personal preference. So, in this study, we preset a systematic approach, so-called desirability based design, to perform a directed multi-objective optimal design considering various aspects of a design, based on soft-computing methods. Fuzzy logic integrated with genetic algorithm is employed to build a decision-making fuzzy system based on expert knowledge. It will be employed to conduct the designing process. Illustrative examples show practicality and efficiency of the presented methodology in structural design of several space structures.