Route optimization is an important problem for single agents and multi-agent systems. In route optimization tasks, the considered challenges generally belong to the family of shortest path problems. Such problems are solved using optimization algorithms, such as the A∗algorithm, which is based on tree search and dynamic programming. In several practical cases, cost values should be as evenly minimized for individual parts of paths as possible. These situations are also considered as multi-objective problems for partial paths. Since dynamic programming approaches are employed for the shortest path problems, different types of criteria which can be decomposed with dynamic programming might be applied to the conventional solution methods. For this class of problems, we employ a leximax-based criterion, which considers the bottlenecks and unfairness among the cost values of partial paths. This criterion is based on a similar criterion called leximin for multiobjective maximization problems. It is also generalized for objective vectors which have variable lengths. We address an extension of the conventional A∗search algorithm and investigate an issue concerning on-line search algorithms. The influence of the proposed approach is experimentally evaluated.