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A new variant of two-echelon routing problem is investigated, where the truck and the drone are used to cooperatively complete the deliveries of all parcels. The truck not only acts as a tool for parcel delivery, but also serves as a moving depot for the drone. The drone can carry several parcels and take off from the truck, while returning to the truck after completing the delivery. The energy consumption model for the routing process of the drone is analyzed, when it is utilized to deliver multiple parcels. A two-stage route-based modelling approach is proposed to optimize both the truck’s main route and the drone’s adjoint flying routes. A hybrid heuristic integrating nearest neighbor and cost saving strategies is developed to quickly construct a feasible solution. The simulated annealing algorithm is applied to improve the quality of the solution, where a Tabu list is employed to improve the search efficiency. Random instances at different scales are used to test the performance of the proposed algorithm. A case study based on the practical road network in Changsha, China, is presented, through which the sensitivity analysis is conducted with respect to some critical factors.
We are concerned with the granular representation of mappings (or experimental data) coming in the form R:R/spl rarr/[0,1] (for one-dimensional cases) and R:R/sup n//spl rarr/[0,1] (for multivariable cases) with R being a set of real numbers. As the name implies, a granular mapping is defined over information granules and maps them into a collection of granules expressed in some output space. The design of the granular mapping is discussed in the case of set and fuzzy set-based granulation. The proposed development is regarded as a two-phase process that comprises: 1) a definition of an interaction between information granules and experimental evidence or existing numeric mapping and 2) the use of these measures of interaction in building an explicit expression for the granular mapping. We show how to develop information granules in case of multidimensional numeric data by resorting to fuzzy clustering (fuzzy C-means). Experimental results serve as an illustration of the proposed approach.
G-images refer to image data defined on irregular graph domains. This work\nelaborates a similarity-preserving Fuzzy C-Means (FCM) algorithm for G-image\nsegmentation and aims to develop techniques and tools for segmenting G-images.\nTo preserve the membership similarity between an arbitrary image pixel and its\nneighbors, a Kullback-Leibler divergence term on membership partition is\nintroduced as a part of FCM. As a result, similarity-preserving FCM is\ndeveloped by considering spatial information of image pixels for its robustness\nenhancement. Due to superior characteristics of a wavelet space, the proposed\nFCM is performed in this space rather than Euclidean one used in conventional\nFCM to secure its high robustness. Experiments on synthetic and real-world\nG-images demonstrate that it indeed achieves higher robustness and performance\nthan the state-of-the-art FCM algorithms. Moreover, it requires less\ncomputation than most of them.\n
There exist various categories of uncertain information, and their corresponding methods of aggregation may also vary. At present, there exists a dearth of specifically tailored techniques for aggregating basic uncertain information (BUI). The present study introduces a two-step aggregation frame that is applicable to inputs of both real-valued and BUI-valued inputs. In the process of constructing such a frame, several novel notions and definitions are introduced. These comprise of extended aggregation operators with respect to a finite set and to a collection of subsets of the set, some certainty independent BUI aggregation and some certainty dependent BUI aggregation, BUI merging operators and BUI aggregation operators, BUI-valued min operator, and BUI-valued Sugeno integral. Some corresponding deductions, necessary reasoning and numerical examples are presented.
