Two-phase algorithm for solving the preference-based multicriteria optimal path problem with reference points

Multiobjective Path Problems and Algorithms in Telecommunication Network Design—Overview and Trends

“…Concerning the works [46,79], the first paper addresses the 'resource-constrained shortest path problem', the aim of which is to obtain the shortest path under constraints corresponding to upper bounds on resource consumption along the path. A new resolution method, based on the reference point methodology, is described.…”

“…We consider five types of MOSPP algorithms, namely, generalizations of labeling techniques for the single-objective shortest path problem (ls, label setting, and lc, label correcting); parametric methods which compute nondominated supported solutions based on the scalarization of the objective functions depending on a varying parameter (par); ranking methods which list paths in order of cost and eliminate solutions dominated by others (ran); two-phase algorithms which generate the nondominated supported solutions of the problem and afterwards swap duality gap regions to find those that are unsupported nondominated (2p); and recursive algorithms (rec) which extend node labels recursively, therefore following a depth-search policy and generating labels implicitly until a certain point. [11] 2 ran APO [12] k ls APO (Corley and Moon 1985) [13] k lc APO (Mote et al, 1991) [14] 2 2p APO (Stewart and White 1991) [15] k ls APO (Tung and Chew, 1992) [16] k ls APO (Santos 1999) [9] k ls/lc APO (Guerriero and Musmanno 2001) [17] k ls/lc APO (Clímaco et al, 2003) [42] k lc APR (Fouchal et al, 2011) [43] k ls APR (Pulido et al, 2014) [44] k ls APR (Shirdel and Ramezani-Tarkhorani 2018) [45] k ls APR (Pugliese et al, 2020) [46] k 2p/lc APR * ls: label setting; lc: label correcting; par: parametric; ran: ranking; rec: recursive; 2p: two phases.…”