A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming

We present a new heuristic algorithm to approximately generate the nondominated frontier of bi-objective pure integer linear programs. The proposed algorithm employs a customized version of several existing algorithms in the literature of both single-objective and bi-objective optimization. Our proposed method has two desirable characteristics: (1) there is no parameter to be tuned by users other than the time limit; (2) it can naturally exploit parallelism. An extensive computational study shows the efficacy of the proposed method on some existing standard test instances in which the true frontier is known, and also some large randomly generated instances. We show that even a basic version of our algorithm can significantly outperform the Nondominated Sorting Genetic Algorithm II (Deb et al. 2002), and the sophisticated version of our algorithm is competitive with Multidirectional Local Search (Tricoire 2012). We also show the value of parallelization on the proposed approach.