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

Bin Packing and Related Problems: General Arc-flow Formulation with Graph Compression

We present an exact method, based on an arc-flow formulation with side constraints, for solving bin packing and cutting stock problems --- including multi-constraint variants --- by simply representing all the patterns in a very compact graph. Our method includes a graph compression algorithm that usually reduces the size of the underlying graph substantially without weakening the model. As opposed to our method, which provides strong models, conventional models are usually highly symmetric and provide very weak lower bounds. Our formulation is equivalent to Gilmore and Gomory's, thus providing a very strong linear relaxation. However, instead of using column-generation in an iterative process, the method constructs a graph, where paths from the source to the target node represent every valid packing pattern. The same method, without any problem-specific parameterization, was used to solve a large variety of instances from several different cutting and packing problems. In this paper, we deal with vector packing, graph coloring, bin packing, cutting stock, cardinality constrained bin packing, cutting stock with cutting knife limitation, cutting stock with binary patterns, bin packing with conflicts, and cutting stock with binary patterns and forbidden pairs. We report computational results obtained with many benchmark test data sets, all of them showing a large advantage of this formulation with respect to the traditional ones

A genetic algorithm for the one-dimensional cutting stock problem with setups

This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also practical instances from a chemical-fiber company. The computational results show that the method is efficient and obtains positive results when compared to other methods from the literature. © 2014 Brazilian Operations Research Society

On the use of biased-randomized algorithms for solving non-smooth optimization problems

Soft constraints are quite common in real-life applications. For example, in freight transportation, the fleet size can be enlarged by outsourcing part of the distribution service and some deliveries to customers can be postponed as well; in inventory management, it is possible to consider stock-outs generated by unexpected demands; and in manufacturing processes and project management, it is frequent that some deadlines cannot be met due to delays in critical steps of the supply chain. However, capacity-, size-, and time-related limitations are included in many optimization problems as hard constraints, while it would be usually more realistic to consider them as soft ones, i.e., they can be violated to some extent by incurring a penalty cost. Most of the times, this penalty cost will be nonlinear and even noncontinuous, which might transform the objective function into a non-smooth one. Despite its many practical applications, non-smooth optimization problems are quite challenging, especially when the underlying optimization problem is NP-hard in nature. In this paper, we propose the use of biased-randomized algorithms as an effective methodology to cope with NP-hard and non-smooth optimization problems in many practical applications. Biased-randomized algorithms extend constructive heuristics by introducing a nonuniform randomization pattern into them. Hence, they can be used to explore promising areas of the solution space without the limitations of gradient-based approaches, which assume the existence of smooth objective functions. Moreover, biased-randomized algorithms can be easily parallelized, thus employing short computing times while exploring a large number of promising regions. This paper discusses these concepts in detail, reviews existing work in different application areas, and highlights current trends and open research lines

A branch-and-price-and-cut algorithm for the pattern minimization problem

n cutting stock problems, after an optimal (minimal stockusage) cutting plan has been devised, one might want to further reducethe operational costs by minimizing the number of setups. A setupoperation occurs each time a different cutting pattern begins to beproduced. The related optimization problem is known as the PatternMinimization Problem, and it is particularly hard to solve exactly. Inthis paper, we present different techniques to strengthen a formulationproposed in the literature. Dual feasible functions are used for thefirst time to derive valid inequalities from different constraints of themodel, and from linear combinations of constraints. A new arc flowformulation is also proposed. This formulation is used to define thebranching scheme of our branch-and-price-and-cut algorithm, and itallows the generation of even stronger cuts by combining the branchingconstraints with other constraints of the model. The computationalexperiments conducted on instances from the literature show that ouralgorithm finds optimal integer solutions faster than other approaches.A set of computational results on random instances is also reported.info:eu-repo/semantics/publishedVersio

A pattern enumeration approach to the trim loss problem

This thesis examines the characteristics of practical one dimensional trim loss problems. As a result of the wide range of these characteristics, previous scheduling methods have only had a limited range of applicability. A heuristic approach is proposed, based on pattern enumeration, which can be used to develop scheduling methods for a reasonably wide class of trim loss problems. The effectiveness of the approach depends on its ability to avoid the intractable residual problems which normally arise towards the end of a heuristic scheduling procedure. The approach is used in three case studies, and the efficiency of the schedules generated is compared with that yielded by other methods

Shadow Price Guided Genetic Algorithms

The Genetic Algorithm (GA) is a popular global search algorithm. Although it has been used successfully in many fields, there are still performance challenges that prevent GA’s further success. The performance challenges include: difficult to reach optimal solutions for complex problems and take a very long time to solve difficult problems. This dissertation is to research new ways to improve GA’s performance on solution quality and convergence speed. The main focus is to present the concept of shadow price and propose a two-measurement GA. The new algorithm uses the fitness value to measure solutions and shadow price to evaluate components. New shadow price Guided operators are used to achieve good measurable evolutions. Simulation results have shown that the new shadow price Guided genetic algorithm (SGA) is effective in terms of performance and efficient in terms of speed