Algorithmic improvements on dynamic programming for the bi‐objective {0,1} knapsack problem

This paper presents several methodological and algorithmic improvements over a state‐of‐the‐art dynamic programming algorithm for solving the bi‐objective {0,1} knapsack problem. The variants proposed make use of new definitions of lower and upper bounds, which allow a large number of states to be discarded. The computation of these bounds are based on the application of dichotomic search, definition of new bound sets, and bi‐objective simplex algorithms to solve the relaxed problem. Although these new techniques are not of a common application for dynamic programming, we show that the best variants tested in this work can lead to an average improvement of 10 to 30 % in CPU‐time and significant less memory usage than the original approach in a wide benchmark set of instances, even for the most difficult ones in the literature.