Ant colony optimisation and local search for bin-packing and cutting stock problems

The Bin Packing Problem and the Cutting Stock Problem are two related classes of NP-hard combinatorial optimization 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 optimization (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 compete with existing evolutionary methods, whereas the hybrid approach can outperform the best-known hybrid evolutionary solution methods for certain problem classes. The hybrid ACO approach is also shown to require different parameter values from the pure ACO approach and to give a more robust performance across different problems with a single set of parameter values. The local search algorithm is also run with random restarts and shown to perform significantly worse than when combined with ACO

A study on exponential-size neighborhoods for the bin packing problem with conflicts

We propose an iterated local search based on several classes of local and large neighborhoods for the bin packing problem with conflicts. This problem, which combines the characteristics of both bin packing and vertex coloring, arises in various application contexts such as logistics and transportation, timetabling, and resource allocation for cloud computing. We introduce $O(1)$ evaluation procedures for classical local-search moves, polynomial variants of ejection chains and assignment neighborhoods, an adaptive set covering-based neighborhood, and finally a controlled use of 0-cost moves to further diversify the search. The overall method produces solutions of good quality on the classical benchmark instances and scales very well with an increase of problem size. Extensive computational experiments are conducted to measure the respective contribution of each proposed neighborhood. In particular, the 0-cost moves and the large neighborhood based on set covering contribute very significantly to the search. Several research perspectives are open in relation to possible hybridizations with other state-of-the-art mathematical programming heuristics for this problem.Comment: 26 pages, 8 figure

OPTIMIZING SERVER CONSOLIDATION FOR ENTERPRISE APPLICATION SERVICE PROVIDERS

In enterprise application environments, hardware resources show averagely low utilization rates due to a provisioning practice that is based on peak demands. Therefore, the consolidation of orthogonal workloads can improve energy efficiency and reduce total cost of ownership. In this paper, we address existing workload consolidation potential by solving a bin packing problem, where the number of servers is to be minimized. Since dynamic workloads, gathered from historical traces, and priorities of running services are considered, we formulate the Dynamic Priority-based Workload Consolidation Problem (DPWCP) and develop solution algorithms using heuristics and metaheuristics. Relevance is pointed out by an analysis of service resource demands and server capacities across four studied cases from productively operating enterprise application service providers. After a classification of related work, seven algorithms were developed and evaluated regarding their exploited optimization potential and computing time. Best results were achieved by a best-fit approach that uses a genetic algorithm to optimize its input sequence (GA_BF). When applying the GA_BF onto the four studied cases, average utilization rates could be increased from 23 to 63 percent within an average computing time of 22.5 seconds. Therefore, the overall server capacity was reduced significantly by up to 83%

Optimal Recombination in Genetic Algorithms

This paper surveys results on complexity of the optimal recombination problem (ORP), which consists in finding the best possible offspring as a result of a recombination operator in a genetic algorithm, given two parent solutions. We consider efficient reductions of the ORPs, allowing to establish polynomial solvability or NP-hardness of the ORPs, as well as direct proofs of hardness results