This paper develops an efficient non-dominated sorting genetic algorithm (NSGA-II) to solve the redundancy allocation problem (RAP) of series-parallel systems. The system consists of subsystem in series, where components are used in parallel for each subsystem. Both the system and its subsystems can only take two states of complete perfect and complete failure. Identical redundant components are included to achieve a desirable reliability. The components of each subsystem, which are chosen from a list that is available in the market, are characterized by their cost, weight, and reliability. To find the optimum combination of the number of components for each subsystem, the mathematical formulation for the maximal reliability and minimal cost of the system configuration under cost constraint is first obtained. Then, a modified NSGA-II is proposed to solve the model. In this algorithm, a heuristic method of generating a primary solution is integrated to achieve better solutions. Moreover, design of experiment approach is employed to calibrate the parameters of the algorithm. At the end, some numerical examples are used to validate the solution, to assess the performance of the proposed methodology under different configurations, and to compare the performance with the ones of two other meta-heuristic algorithms. The results of experiments are generally in favor of the proposed solution algorithm. پرونده مقاله

‎The problem of resource-constrained project scheduling(RCPSP) and the problem of time-cost tradeoff (DTCTP) are two mathematical optimization problems that have long mattered in project management in such a way that reducing the completion time of a project, which is achieved through increasing the resources required for executing the activities, usually turns into a necessity in practice. The existing methods and algorithms for solving this problem, considering the cost-slope of the activities as a pivotal index, have been defined differently to date. Yet, this paper aims to present a framework whereby project scheduling and time-cost tradeoff can be addressed under the circumstances that several modes of execution exist for each activity. Apart from the renewable resources, the non-renewable resources have also been taken into consideration for each activity. Hence, initially, a mathematical optimization model based on the assumptions of the problems is proposed, and then, via changing the variables and other mathematical modelling techniques, the problems are integrated and developed in form of a mixed-integer linear mathematical programming model. Eventually, the model is solved using the branch and bound method and the results are studied with sensitivity ‎analysis.‎ پرونده مقاله

In This paper we discuss about the redundancy allocation problem when uncertainty exists in the problem. The innovation of this paper is the use of fuzzy universal generating function for calculating the availability of system. The system consists of component in series and for each component, elements are used in parallel. The system has the range of levels for performance from complete perfect to complete failure. Identical redundant elements are included in order to achieve a desirable reliability. The elements of each component are characterized by their cost, weight and availability. These elements are chosen from a list that available in market. To find optimum combination of elements for each component we calculate the system availability and then use proposed NSGA-III. The proposed NSGA-III heuristic determines the maximal availability system configuration base on weight constrain. پرونده مقاله