A Repair-based approach for stochastic quadratic multiple knapsack problem

Abstract

In this paper, a new problem called stochastic quadratic multiple knapsack problem (SQMKP) is studied. SQMKP is the extension of the quadratic multiple knapsack problem (QMKP) with stochastic factors. Different from QMKP, the objective of SQMKP is no longer to find a single global optimal solution, but to find a solution with the best expected quality under all possible cases. We use the recoverable robustness technique to tackle these stochastic factors. The idea of the recoverable robustness is to first find a solution that is feasible for the static QMKP, and then adjust the solution through a simple recovery algorithm according to the emerging stochastic scenarios. Following the idea of the recoverable robustness technique, we propose a repair-based approach (RBOA) which involves three key components – an instance generator that is able to create a set of representative scenarios, a static QMKP algorithm that is able to provide a set of potentially robust solutions and a simple fast repair algorithm that can quickly restore the feasibility of a solution with respect to a given stochastic scenario. Experimental results on a set of stochastic instances extended from 90 well-known QMKP benchmarks demonstrate the efficacy of the proposed RBOA.