On Bin Packing with Conflicts

Heuristics for Solving the Bin-Packing Problem with Conflicts

This paper deals to solve the one dimensional bin-packing problem with conflicts. The conflicts are represented by a graph whose nodes are the items, and adjacent items cannot be packed into the same bin. We propose an adaptation of Minimum Bin Slack heuristic also with a combination of heuristics based on the uses of the classical bin-packing methods to packing items of maximal-stable-subsets ...

Approaches to Bin Packing with Clique-Graph Conflicts

The problem of bin packing with arbitrary conflicts was introduced in [3]. In this paper, we consider a restricted problem, bin packing with clique-graph conflicts. We prove bounds for several approximation algorithms, and show that certain onand off-line algorithms are equivalent. Finally, we present an optimal polynomial-time algorithm for the case of constant item sizes, and analyze its perf...

A new lower bound for bin-packing problem with general conflicts graph

We propose a new lower bound for the one dimensional bin-packing problem with conflicts. The conflicts are represented by a graph whose nodes are the items, and adjacent items cannot be packed into the same bin. The lower bound is based on an iterative search of maximal cliques in the conflict graph using Johnson's heuristic. At each step we delete from the graph the items of the last clique fo...

An Approximation Scheme for Bin Packing with Conflicts

A heuristic algorithm for the Bin Packing Problem with Conflicts on Interval Graphs

In this paper we deal with the Bin Packing Problem with Conflicts on interval graphs: given an interval graph, a nonnegative integer weight for each vertex, and a nonnegative integer B, find a partition of the vertex set of the graph into k subsets such that the sum of the weights of the vertices assigned to same subset is less than or equal to B, two vertices connected by an edge do not belong...

Extending Two-Dimensional Bin Packing Problem: Consideration of Priority for Items

In this paper a two-dimensional non-oriented guillotine bin packing problem is studied when items have different priorities. Our objective is to maximize the total profit which is total revenues minus costs of used bins and wasted area. A genetic algorithm is developed to solve this problem where a new coding scheme is introduced. To evaluate the performance of the proposed GA, first an upper b...