Hamiden Ahmed

This paper introduces a time efficient deep learning-based solution to the traveling salesman problem with time window (TSPTW). Our goal is to reduce the total tour length traveled by -*the agent without violating any time limitations. This will aid in decreasing the time required to supply any type of service, as well as lowering the emissions produced by automobiles, allowing our planet to recover from air pollution emissions. The proposed model is a variation of the pointer networks that has a better ability to encode the TSPTW problems. The model proposed in this paper is inspired from our previous work that introduces a hybrid context encoder and a multi attention decoder. The hybrid encoder primarily comprises the transformer encoder and the graph encoder; these encoders encode the feature vector before passing it to the attention decoder layer. The decoder consists of transformer context and graph context as well. The output attentions from the two decoders are aggregated and used to select the following step in the trip. To the best of our knowledge, our network is the first neural model that will be able to solve medium-size TSPTW problems. Moreover, we conducted sensitivity analysis to explore how the model performance changes as the time window width in the training and testing data changes. The experimental work shows that our proposed model outperforms the state-of-the-art model for TSPTW of sizes 20, 50 and 100 nodes/cities. We expect that our model will become state-of-the-art methodology for solving the TSPTW problems.

The Delphi method is a process where subjective data are transformed into quasi-objective data using statistical analysis and are converged to stable points. The Delphi method was developed by the RAND Corporation at Santa Monica, California, and is widely used for long-range forecasting in management science. It is a method by which the subjective data of experts are made to converge using some statistical analyses. This article proposes a variation of the Delphi method using triangular fuzzy numbers, where the communication method with the experts is the same, but the estimation procedure is different. The utility of the method is illustrated by a numerical example.

This paper deals with constrained multistage machines flow-shop (FS) scheduling model in which processing times, job weights, and break-down machine time are characterized by fuzzy numbers that are piecewise as well as quadratic in nature. Avoiding to convert the model into its crisp, the closed interval approximation for the piecewise quadratic fuzzy numbers is incorporated. The suggested method leads a noncrossing optimal sequence to the considered problem and minimizes the total elapsed time under fuzziness. The proposed approach helps the decision maker to search for applicable solution related to real-world problems and minimizes the total fuzzy elapsed time. A numerical example is provided for the illustration of the suggested methodology.