The combinatorial auction is one of the important methods used for multi-item auctions, and the solution to the winner determination problem (WDP) is the key factor in the widespread application of combinatorial auctions. This paper explores the use of the cross-entropy method to solve the WDP, which is an NP problem. The performance of the proposed approach is evaluated on the basis of two well-known benchmark test cases. The experimental results show that, compared with the genetic algorithm and the particle swarm optimization algorithm, the cross-entropy（CE）method has the advantages of a higher success rate and a shorter time for solving the WDP. Therefore, the CE method provides a high-quality solution for the effective solution of the problem of determining winning bids in combined auctions.

中文翻译：

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组合拍卖中获奖者确定问题的交叉熵方法

组合拍卖是用于多项目拍卖的重要方法之一，解决赢家确定问题（WDP）是组合拍卖广泛应用的关键因素。本文探讨了使用交叉熵方法求解WDP的问题，这是一个NP问题。在两个众所周知的基准测试案例的基础上，对所提出方法的性能进行了评估。实验结果表明，与遗传算法和粒子群优化算法相比，交叉熵（CE）方法具有更高的成功率和更短的时间求解WDP的优点。因此，CE方法为有效解决组合拍卖中确定中标的问题提供了高质量的解决方案。