Critical path method plays an important role on managing medium to large-scale problems. It is often difficult to determine the critical path for different reasons such as the existing uncertainties in processing tasks. One alternative to handle the uncertainty associated with the processing time is to use fuzzy techniques. We present a new method to calculate the critical path method when the processing times follow trapezoidal fuzzy numbers. The proposed model of this paper does not use any defuzzification technique to find the final processing time. The implementation of the proposed model is compared with other techniques using a well-known example from the literature.

Traffic congestion is a major concern for many cities throughout the world. In a general traffic light controller, the traffic lights change at a constant cycle time. Hence it does not provide an optimal solution. Many traffic light controllers in current use are based on the “time-of-the-day” scheme, which use a limited number of predetermined traffic light patterns and implement these patterns depending upon the time of the day. These automated systems do not provide an optimal control for fluctuating traffic volumes. In this paper, the fuzzy traffic light controller is used to optimize the control of fluctuating traffic volumes such as oversaturated or unusual load conditions. The problem is solved by genetic algorithm, and a new defuzzification method is introduced. The performance of the new defuzzification method (NDM) is compared with the centroid point defuzzification method (CPDM) by using ANOVA. Finally, an illustrative example is presented to show the competency of proposed algorithm.

Flow-shop problems, as a typical manufacturing challenge, have become an interesting area of research. The primary concern is that the solution space is huge and, therefore, the set of feasible solutions cannot be enumerated one by one. In this paper, we present an efficient solution strategy based on a genetic algorithm (GA) to minimize the makespan, total waiting time and total tardiness in a flow shop consisting of n jobs and m machines. The primary objective is to minimize the job waiting time before performing the related operations. This is a major concern for some industries such as food and chemical for planning and production scheduling. In these industries, there is a probability of the decay and deterioration of the products prior to accomplishment of operations in workstation, due to the increase in the waiting time. We develop a model for a flowshop scheduling problem, which uses the planner-specified weights for handling a multi-objective optimization problem. These weights represent the priority of planning objectives given by managers. The results of the proposed GA and classic GA are analyzed by the analysis of variance (ANOVA) method and the results are discussed

Traffic jam is a daily problem in nearly all major cities in the world and continues to increase with population and economic growth of urban areas. Traffic lights, as one of the key components at intersections, play an important role in control of traffic flow. Hence, study and research on phase synchronization and time optimization of the traffic lights could be an important step to avoid creating congestion and rejection queues in a urban network. Here, we describe the application of NSGA-II, a multi-objective evolutionary algorithm, to optimize both vehicle and pedestrian delays in an individual intersection. Results show that parameters found by improved NSGA-II can be superior to those defined by a traffic engineer with respect to several objectives, including total queue length of vehicles and pedestrians.In this paper, we improve NSGA-II algorithm based to the regression line to find a Pareto-optimal solution or a restrictive set of Pareto-optimal solutions based on our solution approaches to the problem, named PDNSGA (Non-dominated Sorting Genetic Algorithm based on Perpendicular Distance). In this paper, our purpose is to present a solution methodology to obtain all Pareto-optimal solutions to optimize traffic signal timing and enable the decision-makers to evaluate a greater number of alternative solutions. The proposed algorithm has the capability of searching Pareto front of the multi-objective problem domain. Further jobs should be concerned on the signal timing optimization method for the oversaturated coordinated intersections or small-scale road network and real-field applications with the traffic signal controller. The high speed of the proposed algorithm and its quick convergence makes it desirable for large scheduling with a large number of phases. Furthermore, we have used the mean deviation from the ideal point (MDI) measure to compare the performance of the MOGA, PDNSGA, NSGA-II, and WBGA by the ANOVA method. It is demonstrated that the our proposed algorithm (PDNSGA) gives better outputs than those of MOGA, NSGA-II, and WBGA in traffic signal optimization problem, statistically .