Ant colony optimization and local search for bin packing and cutting stock problems

Abstract

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimisation problems. Exact solution methods can only be used for very small instances, so for real-world problems we have to rely on heuristic methods. In recent years, researchers have started to apply evolutionary approaches to these problems, including Genetic Algorithms and Evolutionary Programming. In the work presented here, we used an ant colony optimisation (ACO) approach to solve both Bin Packing and Cutting Stock Problems. We present a pure ACO approach, as well as an ACO approach augmented with a simple but very effective local search algorithm. It is shown that the pure ACO approach can outperform some existing solution methods, whereas the hybrid approach can compete with the best known solution methods. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO.

Virtual Machine Consolidation in Cloud Data Centers Using ACO Metaheuristic

“…Levine et al [13] first proposed an ACO-based solution for bin packing problem combined with a local search algorithm. Later, Brugger et al [14] used a later version of the ACO metaheuristic that demonstrated superior performance over genetic algorithm for large problem instances.…”

“…16) using a probabilistic decision rule (Eq. 15) [line [11][12][13][14][15][16][17][18][19][20][21][22]. If the current PM is fully utilized or there are no feasible VMs left to assign to the PM, a new empty PM is taken to fill in [line [14][15][16].…”

An Analogy between Bin Packing Problem and Permutation Problem: A New Encoding Scheme

“…It uses the classical encoding scheme. [12] uses a hybrid ant colony optimization, inspired by Falkenauer's works. It does not individualize the items, they are designated by their size and not their index: S = (w i ) i∈N with w i the size of item i.…”

An investigation into two bin packing problems with ordering and orientation implications

“…We specifically choose this method as its execution times are very fast, but yet it is still able to produce solutions of equal quality to those achieved by other well-known packing algorithms such as the hybrid grouping genetic algorithm of Falkenauer (1998) and the ant-based algorithm of Levine and Ducatelle (2003). The former attribute is particularly useful because of the extra time that is consumed in determining groups' membership of F, a task that inevitably has to be performed many times during a run.…”

“…1) is then applied to S and T . This is a modified version of a procedure previously used with the BPP (Falkenauer, 1998;Levine and Ducatelle, 2003;Lewis, 2009) and is based on the concepts of dominance, defined by Martello and Toth (1990b). The idea is that items are interchanged between groups in S and groups in T such that the number of items in each group in S remains the same or decreases, while the total size of the items within these groups increases.…”