A Multi-Objective Genetic Algorithm with Path Relinking for the p-Median Problem

Multiobjective Optimization for Multimode Transportation Problems

“…The MOO -median problem with an additional facility cost objective is dealt with in [13]. Each facility is weighted by a building cost, and the goal is to minimize the sum of distances to locations ( -median objective) and the sum of costs of the opened locations.…”

“…Each facility is weighted by a building cost, and the goal is to minimize the sum of distances to locations ( -median objective) and the sum of costs of the opened locations. The authors in [13] used two approaches. The first is an -constraint like formulation that is a mix of two-phases algorithms [14] and classical -constraint approach [15].…”

“…However, since the number of nodes varies in our case for the distance count (for instance, pupils going to school by public transportation are not taken into account for the distance of demands from facilities), the method must be adapted, as it will be shown in Section 4. The second approach used in [13] helps to handle large test-cases and is based on MOGA framework, with a path relinking local search procedure for mixing solutions. Problems with uniform demand at each location (unitary problems) and with up to 400 demands and 20 facilities are processed.…”

“…Compared with the previous model, we replace (6b) by (12), (13), and (14), which ensure that demand node cannot be in if there is no school node at distance .…”

Traditional and self-adaptive differential evolution for the p-median problem

“…The methods based on genetic algorithms include a GA for capacitated PMP with a domain specific crossover (based on so-called exchange vectors) and mutation (heuristic hypermutation) [1], a mutation-less GA with greedy solution optimization [4], a GA with fixed-length subset encoding and domain specific heuristics [7], a GA with cut-and-paste crossover operator and hybrid local search [2], and a multiobjective [8] and grouping [9] GA variants. A common property of these approaches is the use of customized genetic operators, problem-specific local search, or heuristic solution optimization steps.…”