Heuristics for the 0–1 multidimensional knapsack problem

Abstract

a b s t r a c tTwo heuristics for the 0-1 multidimensional knapsack problem (MKP) are presented. The first one uses surrogate relaxation, and the relaxed problem is solved via a modified dynamic-programming algorithm. The heuristics provides a feasible solution for (MKP). The second one combines a limited-branch-and-cutprocedure with the previous approach, and tries to improve the bound obtained by exploring some nodes that have been rejected by the modified dynamic-programming algorithm. Computational experiences show that our approaches give better results than the existing heuristics, and thus permit one to obtain a smaller gap between the solution provided and an optimal solution.

Solution of multidimensional knapsack problems via cooperation of dynamic programming and branch and bound

“…The reader is referred to [3], [4] and [5] for computational studies related to bounds obtained with surrogate relaxation.…”

“…In the sequel, we propose an efficient algorithm based on dynamic programming in order to find out a good lower bound of (M KP ) by solving surrogate relaxation (see [5]). …”

A procedure-based heuristic for 0-1 Multiple Knapsack Problems

“…Problem (KPC) is solved via the dynamic programming method with dominance techniques (see Ahrens and Finke, 1975;El Baz and Elkihel, 2005;Boyer et al, 2009). In this method, items are considered successively from s − r to s + r − 1.…”

Dense Dynamic Programming on Multi GPU

“…The knapsack problem arises as a sub-problem of many complex problems (see for example [10] - [13]). …”