کیوان قصیری

The industry has been faced with the difficulty of Safety level determination for their systems. Safety is one of the most important issues in all environments. In this study, the most important thing is to determine the safety integrity level by the usage of IEC61508 standard in an uncertainty environment. At first, the concept of safety integrity level index is determined in IEC61508 standard and then the uncertainty issues are considered in the input parameters of the model. It should be noted that the uncertainty should be considered in our model because in our real environment, the processes of data gathering has uncertainty, which is clearly explained in our paper. The fault tree analysis is used to determine the fault rate of the system and the dependence of the safety system to each safety integrity level is determined more carefully by implementing the fuzzy approach. This study is implemented on train barking system as a case study and the safety level has been appointed more accuracy.

Data Envelopment Analysis (DEA) is a managerial powerful tool for assess the performance of Decision Making Units (DMUs). Nowadays, multi-objective DEA models are an attractive technique for evaluation quantity and quality aspects of performance analysis. But these models are in static. In this paper, we want to present a proposed fuzzy dynamic multi-objective DEA model in which data are changing sequentially. In this paper is presented to compare with those obtained using the proposed model as well as original DEA models. Results reveal that the new model just needs to solve multiple objective programming once to calculate the efficiency achievement for all DMUs and they are indication for improvement discriminating power of classical DEA models.

Traveling Salesman Problem (TSP) is one of the most well known and applicable problems in combinatorial optimization that transportation makes up the most notable applications of the problem. Its definition is simple and clear while its solving is very hard. In the classic TSP, a salesman wants to find the cheapest way of visiting a number of cities in which each city must be visited exactly once. The TSP can be symmetric or asymmetric. In symmetric one, the distance between each two cities does not depend on the direction. The classic TSP is also known as finding the shortest Hamiltonian tour. In addition to the classic TSP, which is defined so far, the problem has numerous variants from which we can mention traveling salesman problem with time windows, period traveling salesman problem, selective traveling salesman problem, moving object traveling salesman problem and so on.The importance of the TSP lies in two aspects: theoretical and practical aspects. In theoretical aspect, because the TSP is one of the first problems that its NP-Completeness has been proved, i.e. there is no algorithm to solve it in polynomial time; it has become a test bed for new algorithmic ideas. In the practical aspect, its simple definition has resulted to many direct or indirect applications in different problems of various domains like transportation, production planning, and bioinformatics. In transportation domain, as our attention. General routing problems generally deal with transporting of customers/commodities on a given network using an optimal method, from which, we can mention the distribution of services/commodities from depots to customers, vehicle routing problems, production and distribution planning and so on. These problems occur in operational management while the classic TSP is the core of most of them. In fact, although the TSP has direct applications, we can also mention indirect applications of the TSP in many other problems like the vehicle routing problems, crew scheduling, and train scheduling. Because the physical costs of distribution make up a considerable amount of the total distribution costs in each economy, any reduction in these costs through improved solution methods and algorithms of routing problems results in great savings and benefits to the final customers. So, in this paper we develop a successful solution method in solving the TSP and then apply it for the first time to 360 selected cities of Iran to find the shortest Hamiltonian tour. The cities had been chosen based on their economical and political importance. As a solution method, among numerous exact and approximate ones, a new combination of the ant colony system (ACS) and the local search is used. Ant algorithms with inspirations of real ant's foraging behavior are competent in solving hard optimization problems while using a local search can lead to better results. In other words, the ACS section of the proposed algorithm is rather responsible for searching the solution space while the local search part refines the search and directs it to the most promising regions by locally optimizing the solutions of the ACS section. To check for quality of the solutions, results are compared to the results of the well-known ACS. This comparison shows the complete superiority of the suggested method over the ACS. These results also can be used in future for other comparisons of different solution methods for this problem.

This paper aims to solve a locomotive routing through a rail network that is important for railway companies, in view of the high cost of operating locomotives. The locomotive routing problem finds the least cost routes to assign a set of locomotives locating in a central depot to a set of trains in a pre-planned train schedule so as to provide them with sufficient power to haul the trains from the origins to their destinations. In this research the well known vehicle routing problem with time windows is considered to be the basis for modeling the locomotive routing problem. Vehicle routing problem with time windows (VRPTW) is an important variant of vehicle routing problem (VRP) with adding time windows constraints to the model. In this problem the vehicles that are located a depot must serve a number of customers within predefined soft/hard time windows at minimum cost, without violating the capacity and total trip time constraints for each vehicle. This paper first reviews the literature of VRPTW and locomotive routing problem and after defining the locomotive routing model, designs an efficient genetic algorithm with special operators to solve it. In the proposed genetic algorithm part of the initial population is initialized randomly and part is initialized using Push Forward Insertion Heuristic (PFIH) method. Having non-random part of the population greatly reduces the time for the solution to converge, and having a random part prevents sticking to a local optimum and not exploring the complete solution space. Candidate solutions for mating are selected using the tournament selection that in which two identical (through differently ordered) copies of the population is kept and in every generation, adjacent chromosomes are compared in one copy of the population pair by pair, and one chromosome with best fitness value is selected to insert to the mating pool. Then this procedure is proceeding with the second copy of the population to select the other half of the chromosomes. The proposed genetic algorithm employs two kinds of crossover operators namely heuristic and merge crossover that they tries to produced solutions with better time and distance travel cost. Also, the mutation schemes that are used in suggestive algorithm are swap node and swap sequence that they applied on chromosomes with special mutation probability scheme which changes the mutation probability as the standard deviation of the population fitness changes.The suggestive genetic algorithm uses a famous local heuristics namely λ-interchange mechanism to search the neighborhood and larger area of solution space and also make improvements on produced solutions. This mechanism incorporates two strategies namely one-interchange (FB) and two-interchange (GB) to search for better routing solutions. The former tries to find the first better solution in short time and the latter finds the best solutions during some changes. Also at the end of each generation, elitism and recovery strategy is used to keep a few numbers of good individuals. It is notable to mention that the algorithm reduces the exponential computational complexity of the problem to a polynomial one which is an advantage for the solution algorithm. Two different scenarios are presented and their results are compared. To check the validity of the method, results gained by the algorithm are compared with the ones from an optimizer solver. Moreover, a test problem with small size is solved step by step according to suggestive method to clarify the concept of the model. The results indicate good quality and time saving of the method.

Train scheduling problem is one of the severe problems in rail transport planning. Mathematical programming, simulation, expert systems, heuristic and meta-heuristic methods, and combinational methods are amongst techniques for train scheduling. This paper develops an algorithm to train scheduling problem using Ant Colony System meta-heuristic. At first, a kind of train scheduling problem is formulated in a mathematical model and then the algorithm based ACS is presented to solve the problem. The problem is considered as a traveling salesman problem wherein cities represent the trains. ACS determines sequence of trains dispatched on the graph of TSP. According to the sequence as well as removing trains collisions incurred, train scheduling is determined. Numerical examples in small and medium size are solved by using the algorithm and compared to exact optimum solutions to check for the quality and accuracy. To analyze the solution results obtained, they are compared with those of exact optimization method of the train scheduling model. For this purpose, computations are carried out for 45 problems including 3 to 8 trains and 2 to 8 track sections. Comparison of the solutions shows good enough quality and time savings. Sensitivity of the run times of the algorithm with respect to variation of number of track sections as well as with respect to variation of number of trains have been shown and compared with those of exact optimization method. To clarify use of the proposed algorithm, a problem with 30 trains and 4 track sections is solved to illustrate the solution. Structure of the paper is as follows: section 1 presents a hierarchical process of rail transport planning and ant’s behavior which gives inspiration for ant algorithms, is presented. Section 2 reviews the literature of the train scheduling problem and then the manner of creating, developing and applying the ant algorithms is put forward. Section 3 presents the proposed ACS-based model and solution method using ACS for train scheduling. In this section a mathematical model for train scheduling on a single track line is presented. Section 4 illustrates the analysis of the model. This chapter compares the solution results obtained from the model with those of exact optimization method of the train scheduling. Section 5 presents a case study that supports the qualified results of the model. This section describes how to determine the ACS algorithm parameters and section 6 summarizes the paper.