Many real-world combinatorial optimization problems have both expensive objective and constraint functions. Although surrogate models for the discrete decision variables can be trained to replace the expensive fitness evaluations in evolutionary algorithms, the approximation errors of the surrogate models for the constraint function easily misguide the search. The classic genetic algorithm, which is often applied straightforwardly to the combinatorial optimization problems, gradually exposes its inefficiency in the search process. Therefore, we proposed a random forest assisted evolutionary algorithm using a new competitive neighborhood search, where random forest is used as the surrogate models to approximate both the objective and constraint functions and the competitive neighborhood search is to improve the search efficiency. Moreover, competitive neighborhood search shows a natural adaptability to the surrogate model, which helps to reduce the impact of approximation errors. The proposed algorithm is tested on 01 knapsack problems and quadratic knapsack problems with various dimensions and constraints. The experimental results demonstrate that the proposed algorithm is able to solve the expensive constrained combinatorial optimization problems efficiently.

许多现实世界中的组合优化问题都有昂贵的目标和约束功能。尽管可以训练用于离散决策变量的替代模型来替代进化算法中昂贵的适应性评估，但是用于约束函数的替代模型的近似误差很容易误导搜索。传统的遗传算法通常直接应用于组合优化问题，逐渐暴露出其在搜索过程中的低效率。因此，我们提出了一种使用新的竞争邻域搜索的随机森林辅助进化算法，该算法以随机森林作为替代模型来近似目标和约束函数，而竞争邻域搜索则是为了提高搜索效率。此外，竞争性邻域搜索显示出对代理模型的自然适应性，这有助于减少近似误差的影响。该算法在具有各种尺寸和约束的01背包问题和二次背包问题上进行了测试。实验结果表明，该算法能够有效解决昂贵的约束组合优化问题。