Computational Methods in Engineering

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Bus network design is an important problem in public transportation. A main step to this design is determining the number of required terminals and their locations. This is a special type of facility location problem, which is a time-consuming, large scale, combinatorial problem. In a previous attempt by the authors, this problem had been solved by GAMS, based on a branch and bound algorithm. In this research, different techniques for solving the problem are investigated to choose the best one. One of these methods is Simulated Annealing (SA), which is an efficient algorithm for solving complex optimization problems. SA’s parameters vary from one problem to another. Here, for the bus terminal location problem, SA’s parameters are determined, then the problem is solved. Another algorithm is the Implicit Enumeration method. In this paper, the results obtained from the above 3 techniques are compared. The criteria for this comparison are the CPU time and the accuracy of the solution. In all the cases studied, SA gave the most accurate results. Its CPU time is lower than the others, too. Solving the bus terminal location problem for the Mashhad network shows that SA is about 150 times faster than GAMS and 50 times faster than Implicit Enumeration. Moreover, bus terminal location problem for the network of the city of Tehran, which is a more difficult problem, has been solved by the SA algorithm successfully. Keywords: Bus network, Lacation problem, Heuristic, Simulated Annealing, Implicit Enumeration

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A Two-phase model for configuring a cellular manufacturing system is proposed. In phase (I), for the first time, number of cells is considered as a decision variable. In phase (II), pursing two different objectives, one minimization of underload and the other, maximization of similarity of parts within a group, the design procedure is performed. As one cannot have these two objects together, a heuristic algorithm based on cellular similarity coefficient and integration of two objects is proposed. The results confirmed that the proposed heuristic procedure has reasonable outcomes. Keywords: manufacturing cell, cellular similarity coefficient, two-phase model, heuristic algorithm

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In this paper, a new algorithm for solving the single loop routing problem is presented. The purpose of the single loop routing problem(SLRP) is to find the shortest loop for an automated guided vehicle covering at least one edge of each department of a block layout. First it shown that this problem can be represented as a graph model. Then a meta-heuristic algorithm based on and colony system is developed for ALRP by using the properties of the graph model. Computational results show the efficiency of the proposed algorithm in comparison with other techniques for solving SLRP.

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A novel version of Ant Colony Optimization (ACO) algorithms for solving continuous space problems is presented in this paper. The basic structure and concepts of the originally reported ACO are preserved and adaptation of the algorithm to the case of continuous space is implemented within the general framework. The stigmergic communication is simulated through considering certain direction vectors which are memorized. These vectors are normalized gradient vectors that are calculated using the values of the evaluation function and the corresponding values of object variables. The proposed Gradient-based Continuous Ant Colony Optimization (GCACO) method is applied to several benchmark problems and the results are compared and contrasted with other population-based algorithms such as Evolutionary Strategies (ES), Evolutionary Programming (EP), and Genetic Algorithms (GA). The results obtained from GCACO compare satisfactorily with those of other algorithms and in some cases are superior in terms of accuracy and computational demand.

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In this paper, the problem of batch scheduling in a flexible flow shop environment is studied. It is assumed that machines in some stages are able to process a number of jobs simultaneously. The applications of this problem can be found in various industries including spring and wire manufacturing and in auto industry. A mixed integer programming formulation of the problem is presented and it is shown that the problem is NP-Hard. Three heuristics will then be developed to solve the problem and a lower bound is also developed for evaluating the performance of the proposed heuristics. Results show that heuristic H3 gives better results compared to the others.

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While a great portion of the scheduling literature focuses on time-based criteria, the most important goal of management is maximizing the profitability of the firm. In this paper, the net preset value criterion is studied taking account of linear time-dependent cash flows in single machine and flow shop scheduling problems. First, a heuristic method is presented for the single machine scheduling problem with NPV criterion. Second, the permutation flow shop scheduling problem is studied with NPV criterion. An efficient Branch & Bound algorithm is accordingly presented using strong lower and upper bounds and dominace rules which are expanded for this problem. Finally, three heuristic methods are presented and compared to find appropriate solutions over short periods. By generating random problems of different sizes, it has been shown that the Branch & Bound method is efficient in solving small and medium sized problems, and also that the presented heuristic algorithm is efficient in tackling problems of any size.

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The purpose of this research is to deal with the problem of two-stage assembly flow shop scheduling. A number of single-item products (identical) each formed of several different parts are ordered. Each part has m operations done at the first  stage with m different machines. After manufacturing the parts, they are assembled into a final product with some non-identical machines. The purpose of the problem is to find the optimal sequence of the parts in the manufacturing stage, allocation and the optimal sequence of the products in the assembly stage. A mixed integer linear programming model and two metaheuristic algorithms, which are particle swarm with local search (MPSO) and simulated annealing (SA), are presented to solve this problem. Computational experiments are conducted to evaluate the performance of the proposed model and algorithms. The results show that the MPSO algorithm performs better than the SA one.
 

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This paper aims at optimizing the finite isotropic plates with the hexagonal cutout subjected to  plane loading using metaheuristic optimization algorithms. This research uses Differential Evolution Algorithm (DE) and Harmony Search Algorithm (HSA) from the evolutionary algorithm category, Big Bang- Big Crunch Algorithm (BB-BC) from the physics-based algorithm category, and Grey Wolf Optimizer Algorithm (GWO) and Particle Swarm Optimization (PSO) from the SI algorithm category; then the results of these algorithms are compared with each other. The results indicate that the grey wolf optimizer has the complete performance, short solution time and the ability to avoid local optimums. In the analysis of finite isotropic plate, the effective parameters on stress distribution around the  hexagonal cutouts are cutout bluntness, cutout orientation, plate’s aspect ratio, cutout size, and type of loading. In this study, with the assumption of plane stress conditions, the analytical solution of Muskhelishvili’s complex variable method and conformal mapping is utilized. The plate is considered to be finite (the proportion ratio of the  diameter of circle circumscribing to the longest plate side should be more than 0.2), isotropic, and linearly elastic. The finite element method has been used to check the accuracy of the  results. Numerical results are in a  good agreement with those of the present analytical solution. The results show that by selecting the aforementioned parameters properly, less amounts of stress could achieve around the cutout can lead  to an increase in the load-bearing capacity of the structure.

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One of the most important issues in engineering is to find the optimal global points of the functions used. It is not easy to find such a point in some functions due to the reasons such as large number of dimensions or inability to derive them from the function. Also in engineering modeling, we do not have the relationships of many functions, but we can input and output them as a black box. Therefore, the meta-heuristic algorithms are presented.
In this paper, a meta-heuristic algorithm based on the behavior of vortices in fluid physics is presented. Technically, the algorithm is made up of vortices. Each vortex contains some particles. The particles move by the presented rotation matrix. This movement causes the local search. Also by selecting another vortex through the selection algorithm, each vortex attempts to escape the local optima and reach the global optima. The algorithm will explore and exploit the given function using its operators. Another innovation of this paper is the introduction of two new evaluation criteria for optimization algorithms. These two criteria show the behavior and convergence of algorithms along the way to reach the global optimal point or fall into the local optima. The proposed algorithm has been implemented, evaluated and compared with the numerical optimization state of the art algorithms. It was observed that the proposed method was able to achieve better results than most of the other methods in the major of twenty-four standard functions in different dimensions.  (All codes available at http://web.nit.ac.ir/ h.omranpour/.).