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A relation of dominance for the bicriterion bus routing problem

Widuch J.

International Journal of Applied Mathematics and Computer Science

2017

Vol. 27, no. 1

133--155

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.

A Label Correcting Algorithm for the Bus Routing Problem

Widuch J.

Fundamenta Informaticae

2012

Vol. 118, nr 3

305-326

This paper proposes a label correcting algorithm for solving the bus routing problem (BRP). The goal of the BRP is finding a route from the start stop to the final stop minimizing the time and the cost of travel. Additionally the time of starting travel at the start stop is given. The problem belongs to the group of multicriteria optimization problems (MOP), whose the solution is a set of non-dominated solutions. 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.