In this paper, we propose an interactive genetic algorithm for solving multi-objective combinatorial optimization problems under preference imprecision. More precisely, we consider problems where the decision maker's preferences over solutions can be represented by a parameterized aggregation function (e.g., a weighted sum, an OWA operator, a Choquet integral), and we assume that the parameters are initially not known by the recommendation system. In order to quickly make a good recommendation, we combine elicitation and search in the following way: 1) we use regret-based elicitation techniques to reduce the parameter space in a efficient way, 2) genetic operators are applied on parameter instances (instead of solutions) to better explore the parameter space, and 3) we generate promising solutions (population) using existing solving methods designed for the problem with known preferences. Our algorithm, called RIGA, can be applied to any multi-objective combinatorial optimization problem provided that the aggregation function is linear in its parameters and that a (near-)optimal solution can be efficiently determined for the problem with known preferences. We also study its theoretical performances: RIGA can be implemented in such way that it runs in polynomial time while asking no more than a polynomial number of queries. The method is tested on the multi-objective knapsack and traveling salesman problems. For several performance indicators (computation times, gap to optimality and number of queries), RIGA obtains better results than state-of-the-art algorithms.

翻译：本文提出了一种交互式遗传算法，用于解决偏好不精确条件下的多目标组合优化问题。具体而言，我们考虑决策者对解的偏好可由参数化聚合函数（如加权和、OWA算子、Choquet积分）表示的问题，并假设推荐系统初始时未知这些参数。为快速生成优质推荐，我们通过以下方式将偏好获取与搜索相结合：1）采用基于遗憾的偏好获取技术高效缩减参数空间；2）对参数实例（而非解）应用遗传算子以更充分地探索参数空间；3）利用针对已知偏好问题设计的现有求解方法生成有前景的解（种群）。我们的算法称为RIGA，可应用于任何聚合函数关于参数线性、且已知偏好下能高效确定（近似）最优解的多目标组合优化问题。我们还研究了其理论性能：RIGA可通过多项式时间实现，且无需超过多项式数量级的查询次数。该方法在背包问题和旅行商问题的多目标版本上进行了测试。在计算时间、最优性差距和查询次数等多个性能指标上，RIGA均获得了优于现有最优算法的结果。