Heuristic algorithms for the multiple-choice multidimensional knapsack problem

Heuristic algorithms for the multiple-choice multidimensional knapsack problem

Modified Choice Function Heuristic Selection for the Multidimensional Knapsack Problem

Hyper-heuristics are a class of high-level search methods used to solve computationally difficult problems, which operate on a search space of low-level heuristics rather than solutions directly. Previous work has shown that selection hyper-heuristics are able to solve many combinatorial optimisation problems, including the multidimensional 0-1 knapsack problem (MKP). The traditional framework ...

Heuristic Algorithms for the Fixed-Charge Multiple Knapsack Problem

In a previous paper we formulated the fixed-charge multiple knapsack problem (FCMKP), and developed an exact algorithm to solve this problem to optimality by combining pegging test and branch-and-bound technique. Although the developed algorithm was quite successful for instances with small number of knapsacks (m), for larger m the problem was hard to solve by this method. Here we present some ...

The Multiple-choice Knapsack Problem

This paper treats the multiple-choice (continuous) knapsack problem P: n mi n mi maximize L .L cijxijsubjectto(l) I I aij x ij";b,(2)0,,;xij";1,i=I,2, i=l J=l i=l J=1 ... , n, j = 1,2, .... mi and (3) at most one of x il, x i2' ... , x im. is positive for i = 1,2, ., ., n, , where n, mi are positive integers and aij' Cij' bare nonnegative real numbers. Two approximate algorithms and an exact br...

A Heuristic for the Multidimensional 0-1 Knapsack Problem

This paper deals with the concepts of core and core problems for multidimensional 0-1 knapsack (MKP) problems. Core problems were introduced by Balas and Zemel (1980) and have been widely studied in the literature. The core refers to the seet of variables for which it is hard to decide what their value will be in an optimal solution; and the core problem is a reduction of the original problem i...