Exact solution method to solve large scale integer quadratic multidimensional knapsack problems

Upper Bounds for Large Scale Integer Quadratic Multidimensional Knapsack Problems

We consider the separable quadratic multi-knapsack problem (QMKP) which consists in maximizing a concave separable quadratic integer function subject to m linear capacity constraints. The aim of this paper is to develop an effective method to compute an upper bound for (QMKP) from a surrogate relaxation originally proposed in Djerdjour et al. (1988). The quality of three other upper bounds for...

An Integer Programming-based Local Search for Large-Scale Multidimensional Knapsack Problems

Integer programming-based local search (IPbLS) is a metaheuristic recently proposed for solving linear combinatorial optimization problems. IPbLS is basically the same as the first-choice hillclimbing except for using integer programming for neighbor generation. Meanwhile, the multidimensional knapsack problem (MKP) is one of the most well-known linear combinatorial optimization problems and ha...

Solving the bi-objective multi-dimensional knapsack problem exploiting the concept of core

This paper deals with the bi-objective multi-dimensional knapsack problem. We propose the adaptation of the core concept that is effectively used in single objective multidimensional knapsack problems. The main idea of the core concept is based on the “divide and conquer” principle. Namely, instead of solving one problem with n variables we solve several sub-problems with a fraction of n variab...

A Branch-and-Bound Algorithm to Solve Large Scale Integer Quadratic Multi-Knapsack Problems

A generalized implicit enumeration algorithm for a class of integer nonlinear programming problems

Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...