Comparing several heuristics for a packing problem

Packing problems are in general NP-hard, even for simple cases. Since now there are no highly efficient algorithms available for solving packing problems. The two-dimensional bin packing problem is about packing all given rectangular items, into a minimum size rectangular bin, without overlapping. The restriction is that the items cannot be rotated. The current paper is comparing a greedy algorithm with a hybrid genetic algorithm in order to see which technique is better for the given problem. The algorithms are tested on different sizes data.Comment: 5 figures, 2 tables; accepted: International Journal of Advanced Intelligence Paradigm

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

Processing second-order stochastic dominance models using cutting-plane representations

This is the post-print version of the Article. The official published version can be accessed from the links below. Copyright @ 2011 Springer-VerlagSecond-order stochastic dominance (SSD) is widely recognised as an important decision criterion in portfolio selection. Unfortunately, stochastic dominance models are known to be very demanding from a computational point of view. In this paper we consider two classes of models which use SSD as a choice criterion. The first, proposed by Dentcheva and Ruszczyński (J Bank Finance 30:433–451, 2006), uses a SSD constraint, which can be expressed as integrated chance constraints (ICCs). The second, proposed by Roman et al. (Math Program, Ser B 108:541–569, 2006) uses SSD through a multi-objective formulation with CVaR objectives. Cutting plane representations and algorithms were proposed by Klein Haneveld and Van der Vlerk (Comput Manage Sci 3:245–269, 2006) for ICCs, and by Künzi-Bay and Mayer (Comput Manage Sci 3:3–27, 2006) for CVaR minimization. These concepts are taken into consideration to propose representations and solution methods for the above class of SSD based models. We describe a cutting plane based solution algorithm and outline implementation details. A computational study is presented, which demonstrates the effectiveness and the scale-up properties of the solution algorithm, as applied to the SSD model of Roman et al. (Math Program, Ser B 108:541–569, 2006).This study was funded by OTKA, Hungarian National Fund for Scientific Research, project 47340; by Mobile Innovation Centre, Budapest University of Technology, project 2.2; Optirisk Systems, Uxbridge, UK and by BRIEF (Brunel University Research Innovation and Enterprise Fund)

Application of 2D packing algorithms to the woodwork industry

Esta pesquisa investiga a aplicação de metodologias computacionais na indústria madeireira, com foco no Problema do Corte de Material (PCE) com duas iterações: guilhotinável e não guilhotinável. O estudo aplica um algoritmo evolucionário baseado no Non-dominated Sorting Genetic Algorithm II (NSGA-II) adaptado às complexidades do problema para otimizar o processo de corte. A metodologia tem como objetivo melhorar a eficiência da utilização de material em tarefas de trabalho em madeira, empregando este algoritmo utilizando sobras de peças ao invés de uma nova placa. O relatório fornece dados empíricos e métricas de desempenho do algoritmo, demonstrando a sua eficácia na redução do desperdício e na otimização do trabalho na indústria. Esta abordagem melhora a eficiência operacional e sublinha os benefícios ambientais da utilização mais sustentável dos recursos de madeira, exemplificando o potencial da integração de técnicas computacionais em indústrias tradicionais para atingir este objetivo.This research investigates the application of computational methodologies in the woodworking industry, focusing on the Cutting Stock Problem (CSP) with two iterations: guillotinable and non-guillotinable iterations. The study applies an Evolutionary Algorithm (EA) based on Non-dominated Sorting Genetic Algorithm II (NSGA-II) customized to fit the intricacies of the problem to optimize the cutting process. The methodology aims to enhance material usage efficiency in woodworking tasks by employing this algorithm using leftover parts instead of a new board. The report provides empirical data and performance metrics of the algorithm, demonstrating its effectiveness in reducing waste and optimizing labor in the industry. This approach improves operational efficiency and underscores the environmental benefits of using timber resources more sustainably, exemplifying the potential of integrating computational techniques in traditional industries to achieve this objective