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In the paper we describe the bus routing problem (BRP), which the goal is to find a route from the start stop to the final stop minimizing the time and the cost of travel and the length of the route. Additionally the time of starting travel at the start stop is given. Analysis of the problem is presented and in particular we point at properties of routes. The BRP is an example of multicriteria optimization problem (MOP), which the solution is the set of non-dominated solutions. This paper proposes a label correcting algorithm with storing partial solutions for solving the BRP. The algorithm makes possible to find all routes which belong to the set of non-dominated solutions. Apart from that the results of experimental tests are presented. Additionally the results are compared with results for the BRP where the goal is to minimize only the time and the cost of travel and the length of the route is not taken into consideration.

A bicriterion bus routing (BBR) problem is described and analysed. The objective is to find a route from the start stop to the final stop minimizing the time and the cost of travel simultaneously. Additionally, the time of starting travel at the start stop is given. The BBR problem can be resolved using methods of graph theory. It comes down to resolving a bicriterion shortest path (BSP) problem in a multigraph with variable weights. In the paper, differences between the problem with constant weights and that with variable weights are described and analysed, with particular emphasis on properties satisfied only for the problem with variable weights and the description of the influence of dominated partial solutions on non-dominated final solutions. This paper proposes methods of estimation a dominated partial solution for the possibility of obtaining a non-dominated final solution from it. An algorithm for solving the BBR problem implementing these estimation methods is proposed and the results of experimental tests are presented.

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