Utility-based Configuration of Learning Factories Using a Multidimensional, Multiple-choice Knapsack Problem

Heuristic algorithms for the multiple-choice multidimensional knapsack problem

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 "reduce and solve" approach for the multiple-choice multidimensional knapsack problem

The multiple-choice multidimensional knapsack problem (MMKP) is a well-known NP-hard combinatorial optimization problem with a number of important applications. In this paper, we present a ”reduce and solve” heuristic approach which combines problem reduction techniques with an Integer Linear Programming (ILP) solver (CPLEX). The key ingredient of the proposed approach is a set of group fixing ...

A best first search exact algorithm for the Multiple-choice Multidimensional Knapsack Problem

In this paper, we propose an optimal algorithm for the Multiple-choice Multidimensional Knapsack Problem MMKP. The main principle of the approach is twofold: (i) to generate an initial feasible solution as a starting lower bound, and (ii) at different levels of the search tree to determine an intermediate upper bound obtained by solving an auxiliary problem called MMKPaux and perform the strate...

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 ...