Solving the two dimensional cutting problem using evolutionary algorithms with penalty functions

In this work a solution using evolutionary algorithms with penalty function for the non-guillotine cutting problem is presented. In this particular problem, the rectangular pieces have to be cut from an unique large object, being the goal to maximize the total value of cut pieces. Some chromosomes can hold pieces to be cut, but some pieces cannot be arranged into the object, generating infeasible solutions. A way to deal with this kind of solutions is to use a penalizing strategy. The used penalty functions have been originally developed for the knapsack problem and they are adapted for the cutting problem in this paper. Moreover, the effect on the algorithm performance to combine penalty functions with two different selection methods (binary tournament and roulette wheel) is studied. The algorithm uses a binary representation, one-point crossover, big-creep mutation and in order to evaluated the quality of solutions a placement routine is considered (Heuristic with Efficient Management of Holes). Experimental comparisons of the performance of the resulting algorithms are carried out using publicly available benchmarks to the non-guillotine cutting problem. We report on the high performance of the proposed models at similar (or better) accuracy with respect to existing algorithms.VI Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Solving the two dimensional cutting problem using evolutionary algorithms with penalty functions

In this work a solution using evolutionary algorithms with penalty function for the non-guillotine cutting problem is presented. In this particular problem, the rectangular pieces have to be cut from an unique large object, being the goal to maximize the total value of cut pieces. Some chromosomes can hold pieces to be cut, but some pieces cannot be arranged into the object, generating infeasible solutions. A way to deal with this kind of solutions is to use a penalizing strategy. The used penalty functions have been originally developed for the knapsack problem and they are adapted for the cutting problem in this paper. Moreover, the effect on the algorithm performance to combine penalty functions with two different selection methods (binary tournament and roulette wheel) is studied. The algorithm uses a binary representation, one-point crossover, big-creep mutation and in order to evaluated the quality of solutions a placement routine is considered (Heuristic with Efficient Management of Holes). Experimental comparisons of the performance of the resulting algorithms are carried out using publicly available benchmarks to the non-guillotine cutting problem. We report on the high performance of the proposed models at similar (or better) accuracy with respect to existing algorithms.VI Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

An anytime tree search algorithm for two-dimensional two- and three-staged guillotine packing problems

[libralesso_anytime_2020] proposed an anytime tree search algorithm for the 2018 ROADEF/EURO challenge glass cutting problem (https://www.roadef.org/challenge/2018/en/index.php). The resulting program was ranked first among 64 participants. In this article, we generalize it and show that it is not only effective for the specific problem it was originally designed for, but is also very competitive and even returns state-of-the-art solutions on a large variety of Cutting and Packing problems from the literature. We adapted the algorithm for two-dimensional Bin Packing, Multiple Knapsack, and Strip Packing Problems, with two- or three-staged exact or non-exact guillotine cuts, the orientation of the first cut being imposed or not, and with or without item rotation. The combination of efficiency, ability to provide good solutions fast, simplicity and versatility makes it particularly suited for industrial applications, which require quickly developing algorithms implementing several business-specific constraints. The algorithm is implemented in a new software package called PackingSolver

Bun splitting: a practical cutting stock problem

We describe a new hierarchical 2D-guillotine Cutting Stock Problem. In contrast to the classic cutting stock problem, waste is not an issue. The problem relates to the removal of a defective part and assembly of the remaining parts into homogeneous size blocks. The context is the packing stages of cake manufacturing. The company's primary objective is to minimise total processing time at the subsequent, packing stage. This objective reduces to one of minimising the number of parts produced when cutting the tray load of buns. We offer a closed form optimization approach to this class of problems for certain cases, without recourse to mathematical programming or heuristics. The methodology is demonstrated through a case study in which the number of parts is reduced by almost a fifth, and the manufacturer's subsidiary requirement to reduce isolated single bun parts and hence customer complaints is also satisfied

2 stage guillotine cutting

Modello 1, modello di sezione 3.

Aplicação do Algoritmo Genético em um Problema de Engenharia Logística

The research work described in this paper main aim to investigate the effectiveness of the Genetic Algorithm applied in solving a problem of Logistics Engineering. In addition, the paper presents a dense theory on the subject in order to contribute to researchers in this area. With this clear objectives, the composition of this paper will initially clarify the technical concepts used. Subsequently, the problem that will be solved as well as its modeling is presented, so that at the end an algorithm is presented, focusing on the construction of the logic of the algorithm, as well as the data obtained that prove the effectiveness tool as a way of solving the defined problem. The concepts behind the algorithm used here, are derived from the most recent studies on Artificial Intelligence and are based on biological studies of the theory of evolution and genetics.El trabajo de investigación descrito en este artículo tiene como objetivo principal investigar la efectividad del Algoritmo Genético aplicado en la resolución de un problema de Ingeniería Logística. Además, el artículo presenta una teoría densa sobre el tema con el fin de contribuir a los investigadores en esta área. Con estos objetivos claros, la composición de este trabajo permitirá aclarar inicialmente los conceptos técnicos utilizados. Posteriormente se presenta el problema que se resolverá así como su modelado, de manera que al final se presenta un algoritmo, enfocándose en la construcción de la lógica del algoritmo, así como los datos obtenidos que comprueban la efectividad de la herramienta como herramienta. forma de resolver el problema definido. Los conceptos detrás del algoritmo utilizado aquí, se derivan de los estudios más recientes sobre Inteligencia Artificial y se basan en estudios biológicos de la teoría de la evolución y la genética.O trabalho de pesquisa descrito neste artigo tem como objetivo principal investigar a eficácia do Algoritmo Genético aplicado na solução de um problema de Engenharia Logística. Além disso, o artigo apresenta uma densa teoria sobre o assunto a fim de contribuir com pesquisadores da área. Com estes objetivos claros, a composição deste artigo irá inicialmente esclarecer os conceitos técnicos utilizados. Posteriormente, é apresentado o problema que será resolvido bem como sua modelagem, de forma que ao final seja apresentado um algoritmo, com foco na construção da lógica do algoritmo, bem como os dados obtidos que comprovam a eficácia da ferramenta como uma forma de resolver o problema definido. Os conceitos por trás do algoritmo aqui utilizado são derivados dos estudos mais recentes em Inteligência Artificial e são baseados em estudos biológicos da teoria da evolução e da genética

Algorithms for two-dimensional guillotine packing problems

The Guillotine Two-Dimensional Packing Problems are a class of optimization problems that require to pack rectangular items into rectangular containers with the constraint that every packed item should be possibly retrieved with a series of vertical and horizontal cuts that divide the container into 2 parts without cutting items. 2 exact and 2 heuristic algorithms have been developed, to solve respectively the Guillotine Two-Dimensional Knapsack and the Guillotine Two-Dimensional Bin Packingope

Models and Solutions of Resource Allocation Problems based on Integer Linear and Nonlinear Programming

In this thesis we deal with two problems of resource allocation solved through a Mixed-Integer Linear Programming approach and a Mixed-Integer Nonlinear Chance Constraint Programming approach. In the first part we propose a framework to model general guillotine restrictions in two dimensional cutting problems formulated as Mixed-Integer Linear Programs (MILP). The modeling framework requires a pseudo-polynomial number of variables and constraints, which can be effectively enumerated for medium-size instances. Our modeling of general guillotine cuts is the first one that, once it is implemented within a state of-the-art MIP solver, can tackle instances of challenging size. Our objective is to propose a way of modeling general guillotine cuts via Mixed Integer Linear Programs (MILP), i.e., we do not limit the number of stages (restriction (ii)), nor impose the cuts to be restricted (restriction (iii)). We only ask the cuts to be guillotine ones (restriction (i)). We mainly concentrate our analysis on the Guillotine Two Dimensional Knapsack Problem (G2KP), for which a model, and an exact procedure able to significantly improve the computational performance, are given. In the second part we present a Branch-and-Cut algorithm for a class of Nonlinear Chance Constrained Mathematical Optimization Problems with a finite number of scenarios. This class corresponds to the problems that can be reformulated as Deterministic Convex Mixed-Integer Nonlinear Programming problems, but the size of the reformulation is large and quickly becomes impractical as the number of scenarios grows. We apply the Branch-and-Cut algorithm to the Mid-Term Hydro Scheduling Problem, for which we propose a chance-constrained formulation. A computational study using data from ten hydro plants in Greece shows that the proposed methodology solves instances orders of magnitude faster than applying a general-purpose solver for Convex Mixed-Integer Nonlinear Problems to the deterministic reformulation, and scales much better with the number of scenarios