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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In this paper, two-dimensional cutting stock problem with demand has been studied.In this problem, cutting of large rectangular sheets into specific small pieces should be carried out hence, the waste will be minimized. Solving this problem is important to decrease waste materials in any industry that requires cutting of sheets. In most previus studies, the demand of pieces has not been usually considered. The cutting problems belong to the category of Np-hard problems. So finding a desirable solution in a suitable time is practically impossible and heuristic methods must be used. A meta-heuristic algorithm using SA approach is presented.Then attempt will be made to regulate the SAs parameters. Initial solutions are produced with a rule based algorithm and two internal and main SAs are used that lead to better performance of the algorithm. Due to lack of benchmark or test problems, two procedures for generating random problems is presented and are used to study efficiency of the algorithm. For this purpose, problems about 10 to 50 types of pieces with maximum demands of 2400 are generated and solved using the proposed algorithm. The results indicate that the algorithm capable of finding a solution with less than 6% of waste for problems with 30 types of pieces and total demands of 500.