Multiobjective Capacitated Arc Routing Problem

The Capacitated Arc Routing Problem (CARP) is a very hard vehicle routing problem raised for instance by urban waste collection. In addition to the total route length (the only criterion minimized in the academic problem), waste management companies seek to minimize also the length of the longest trip. A bi-objective genetic algorithm is presented for this more realistic CARP, never studied before in literature. Based on the NSGA-II template, it includes two-key features: use of good constructive heuristics to seed the initial population and hybridization with a powerful local search procedure. This genetic algorithm is appraised on 23 classical CARP instances, with excellent results. Application of NSGA-II with improvements Initial solutions • Path-Scanning [Golden et al. 1983] • Augment-Merge [Golden & Wong, 1981] • Ulusoy' s heuristic [Ulusoy 1985] Chromosome representation • permutation (giant tour) • exact evaluation through a shortest path algorithm in an auxiliary graph Local search • improvement in each direction of the objectives or both • Applied under probability after each crossover operation • five types of moves: inverse the traversal direction of a task in its trip move one task after one other move two adjacent tasks after one other swap two tasks perform 2-opt moves Evaluation of the quality of a solution Distance measure • a front is used as a "reference front" (here a front w/o Local Search) • it is a piecewise linear front • the front is extrapolated • a distance is measured between a solution and its projection to the extrapolated reference front • distances are cumulated • distance can be normalized when dividing by the number of efficient solutions f1 f2 extrapolated front reference front