Abstract: Motivated by the collaborative operations of the manufacturing alliances in industries such as aviation and automobiles, the joint optimization problem of member selection of virtual alliance and collaborative production among alliance enterprises under the public service platform are mainly studied in this paper. This problem involves two levels of virtual alliance, namely strategic alliance and operational level. It aims to achieve collaborative optimization in three stages including virtual alliance member selection, order allocation and production sequencing. Based on the analysis of the optimal properties of the order production in a single enterprise, the structured properties of customer order allocation and alliance member selection are given. Considering the complexity of the joint optimization problem, the Tree-Seed algorithm for solving the continuous optimization problem is introduced and extended. The discrete tree algorithm embedded in the two-dimensional discrete coding strategy and discrete seed generation rule is developed, and the calculation method of fitness is carried out based on the above-mentioned structuring properties.In addition, a benchmark simulation data for this problem are given, and a series of simulation comparison experiments are further conducted. The experimental results show that the proposed algorithm has certain superiority in solving quality and robustness compared with others discrete intelligent optimization algorithms such as Discrete Firefly Algorithm (DFA) and Shuffled Frog Leapfrog Algorithm (SFLA).The main innovation of this paper is to propose a virtual alliance collaboration model across strategic and operational levels, and develop a novel discrete Tree-Seed algorithm, which can provide some guiding significance for the formation and operation of virtual manufacturing alliance.

Key words: virtual alliance, member selection, collaborative production, discrete Tree-Seedalgorithm