Approximate solutions to the multiple-choice knapsack problem by multiobjectivization and Chebyshev scalarization

Abstract

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.