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.

提出了一种用于解决多目标组合优化问题的交互式遗传算法，能够处理偏好不准确的情况，通过选择集聚函数的参数化表示、遗传算子应用于参数实例、以及利用现有解决方法生成有前景的解决方案，快速给出好的推荐解决方案。