We propose an introduction to the use of incremental preference elicitation methods in the field of multiobjective combinatorial optimization. We consider three different optimization problems in vector-valued graphs, namely the shortest path problem, the minimum spanning tree problem and the assignment problem. In each case, the preferences of the decision-maker over cost vectors are assumed to be representable by a weighted sum but the weights of criteria are initially unknown. We then explain how to interweave preference elicitation and search to quickly determine a near-optimal solution with a limited number of preference queries. This leads us to successively introduce an interactive version of dynamic programming, greedy search, and branch and bound to solve the problems under consideration. We then present numerical tests showing the practical efficiency of these algorithms that achieve a good compromise between the number of queries asked and the solution times.

中文翻译：

---

通过标准权重的增量启发，交互式解决多目标组合优化问题

我们提出了在多目标组合优化领域中使用增量偏好启发方法的介绍。我们考虑向量值图中的三个不同的优化问题，即最短路径问题，最小生成树问题和分配问题。在每种情况下，假定决策者对成本向量的偏好都可以由加权和表示，但准则的权重最初是未知的。然后，我们解释了如何将偏好激发与搜索交织在一起，以快速确定数量有限的偏好查询所产生的接近最优的解决方案。这使我们先后引入了交互式版本的动态编程，贪婪搜索和分支定界，以解决所考虑的问题。