Efficient, robust and effective rank aggregation for massive biological datasets

Integer Linear Programming Reformulations for the Linear Ordering Problem

“…These results offer perspectives for the biological application [1]. Matheuristics can be used in this context, also with the extension ties, and using properties of their easier median of permutation instances allowing specific reduction space operators [1,13]. Perspectives are also to combine matheuristics and local search approaches which are efficient for the problem, as shown by LocalSolver benchmark on this study, and also with [8].…”

“…These results offer perspectives for the biological application [1]. Matheuristics can be used in this context, also with the extension ties, and using properties of their easier median of permutation instances allowing specific reduction space operators [1,13].…”

“…As mentioned by [1,13], characteristics of instances is crucial in the difficulty of instances. In many social choice applications and datasets, N is small, so that exact resolution with the reference ILP formulation is almost instantaneous.…”

“…• aleaSum100 (denoted aSum): uniform generation in [[0, 100]] such that w i,j + w j,i = 100: for i < j w i,j is randomly generated [[0, 100]] and w j,i is then set to w j,i = 100 − w i,j . • aleaShuffle (denoted aShuf): max(N/2, 20) random permutations are generated (with Python function shuffle), w i,j are then computes using Kendallτ distance and Kemeny ranking, as in [1][2][3].…”

“…An extension of LOP considering ties relies on this ILP formulation [2]. Current and recent works focus for consensus ranking in biological datasets, and use specific data characteristics of these median of permutation problems for an efficient resolution [1,13].…”