  Motivated by their success in the single-objective domain, we propose a very
simple linear programming-based matheuristic for tri-objective binary integer
programming. To tackle the problem, we obtain lower bound sets by means of the
vector linear programming solver Bensolve. Then, simple heuristic approaches,
such as rounding and path relinking, are applied to this lower bound set to
obtain high-quality approximations of the optimal set of trade-off solutions.
The proposed algorithm is compared to a recently suggested algorithm which is,
to the best of our knowledge, the only existing matheuristic method for
tri-objective integer programming. Computational experiments show that our
method produces a better approximation of the true Pareto front using
significantly less time than the benchmark method on standard benchmark
instances for the three-objective knapsack problem.
