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In this paper, an algorithm for the bi-objective median path (BMP) problem on a tree network is considered. The algorithm is based on the two-phase method which can compute all Pareto solutions for the BMP problem. The first phase is applied to find supported Pareto solutions by solving the uni-objective problem D(P, λ). The second phase is used to compute the unsupported Pareto solutions by applying a k-best algorithm which computes the k-best Pareto solutions in order of their objective values.

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