Abstract: Aiming at a kind of integrated scheduling problem of distributed production, transportation and assembly(ISPDPTA), which widely exists in real-life applications, the model of the problem is established first. And then, an enhanced three-dimensional estimation of distribution algorithm(E3DEDA) is proposed to solve the model. In global search stage, E3DEDA uses a multi-segment encoding mechanism to represent jobs and productions that contain factory information based on the characteristics of ISPDPTA, in which each vehicle path is determined by applying the shortest path rule. Besides, two three-dimensional probability matrices are adopted to enhance the ability of E3DEDA for finding promising search regions. That is, the matrices separately learn and accumulate the information about the structure and location of job blocks and product blocks stemming from elite individuals found during the search process. Thereby, new individuals are generated by sampling the two matrices. In local search stage, E3DEDA adopts adaptive variable neighborhood local search to improve the local search ability of the algorithm. Especially, ten neighborhood operations are used to form the alternative set based on the characteristics of each stage of ISPDPTA, and a two-dimensional probability matrix is used to learn the information about high-quality neighborhood structures regarding different neighborhood operations. By sampling the matrix, permutations are generated and a series of neighborhood operations are in turn performed on the solutions of E3DEDA, so as to intensively examine promising search regions discovered by the global search stage. Moreover, a probability evaluation updating mechanism of block structure is proposed to improve the efficiency of the algorithm. Finally, simulations and comparisons demonstrate that E3DEDA can effectively solve ISPDPTA.

Key words: distributed production, vehicle transportation, integrated scheduling, three-dimensional estimation of distribution algorithm, block structure