  The method BISSA, proposed by Bednarczuk, Miroforidis, and Pyzel, provides
approximate solutions to the multiple-choice knapsack problem. To fathom the
optimality gap that is left by BISSA, we present a method that starts from the
BISSA solution and it is able to provide a better approximation and in
consequence a tighter optimality gap. Like BISSA, the new method is based on
the multiobjectivization of the multiple-choice knapsack but instead of the
linear scalarization used in BISSA, it makes use of the Chebyshev
scalarization. We validate the new method on the same set of problems used to
validate BISSA.
