提出多项目集中采购或大型工程项目招标的逆向组合拍卖中的标的物打包优化的问题和数学模型.由于该优化问题实质上是一种自变量为集合的、非解析的多目标优化问题,提出一种基于量子进化算法的求解方法.方法中采用基于价格互补系数矩阵中非零变量的0-1编码,以及一种有利于好的量子位(Q-bit)胜出的β-旋转门.大量数值例子的对比计算的结果表明,β-旋转门明显优于现有的α-旋转门；而对比遗传算法这种新算法对于中小规模的打包优化问题有明显的计算优势.%The object bundling optimization problem in reverse combinatorial auctions for online procurements and large project tenders is addressed. A mathematical model with multi-objectives is proposed to solve the problem. Because of its nonlinear and non-analytic properties with variable sets, it is very difficult to solve. Thus, a Quantum Evolutionary Algorithm (QEA) is developed for its solution. It adopts the 0-1 encoding scheme with nonzero elements in the cost complementarity matrix, and the β-based rotation gate to enlarge the probability of selecting the better Q-bits. Numerical results from a number of examples show that the p-based rotation gate is evidently better than the α-based one. Compared with a contrastive genetic algorithm, QEA can achieve better computational performances for small- and middle-sized problems.
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