This book investigates in detail the two-dimensional packing and cutting problems in the field of operations research and management science. It introduces the mathematical models and intelligent solving algorithms for these problems, as well as their engineering applications. Most intelligent methods reported in this book have already been applied in reality, which can provide reference for the engineers. The presented novel methods for the two-dimensional packing problem provide a new way to solve the problem for researchers interested in operations research or computer science. This book also introduces three new variants of packing problems and their solving methods, which offer a different research direction. The book is intended for undergraduate and graduate students who are interested in the solving methods for packing and cutting problems, researchers investigating the application of intelligent algorithms, scientists studying the theory of the operations research and CAM software developers working on integration of packing and cutting problem.
Author(s): Yunqing Rao, Qiang Luo
Series: Engineering Applications of Computational Methods, 10
Publisher: Springer
Year: 2022
Language: English
Pages: 338
Preface
Contents
1 Introduction to the Packing and Cutting Problem
1.1 Problem Definition
1.1.1 Packing Problem
1.1.2 Cutting Problem
1.2 Literature Review
1.2.1 Review for 2DRSP
1.2.2 Review for 2DISP
1.2.3 Review for CSP
1.3 Development Trends
References
2 Intelligent Algorithms for Rectangular Packing Problem
2.1 Problem Description
2.2 Memetic Algorithm for the Problem
2.2.1 Introduction
2.2.2 The Placement Strategy
2.2.3 The Memetic Algorithm
2.2.4 Implementation of Memetic Algorithm
2.2.5 Experimental Results
2.3 Discrete Grey Wolf Optimization
2.3.1 Introduction
2.3.2 Improved Best-Fit Heuristic Algorithm
2.3.3 Discrete Grey Wolf Optimization
2.3.4 Experimentation and Results
2.4 Conclusions
References
3 Intelligent Algorithms for Irregular Packing Problem
3.1 Problem Description
3.2 The Geometrical Technique
3.3 Memetic Algorithm for the Problem
3.3.1 Introduction
3.3.2 The Memetic Algorithm
3.3.3 The Realization of the Adaptive Memetic Algorithm
3.3.4 Experimental Study and Discussions
3.4 Beam Search Hybridized with Tabu Search for the Problem
3.4.1 Introduction
3.4.2 Placement Principle Based on Improved NFP
3.4.3 The Hybrid Algorithm for Searching Sequence
3.4.4 Experimental Results and Discussions
3.5 Biased Genetic Algorithm Hybridized with VNS for the Problem
3.5.1 Introduction
3.5.2 Placement Method
3.5.3 Biased Genetic Algorithm Hybridized with VNS
3.5.4 Experimental Results and Discussions
3.6 Conclusions
Appendix
References
4 Novel Algorithms for 2DRSP and 2DISP
4.1 Reinforcement Learning Algorithm for 2DRPP
4.1.1 Introduction and Problem Description
4.1.2 Lowest Centroid Placement Method
4.1.3 Sequence Optimization Based on Q-learning
4.1.4 Computational Packing Experiments
4.2 Reinforcement Learning Algorithm for 2DIPP
4.2.1 Introduction
4.2.2 Description of Packing Problem
4.2.3 Positioning Strategy Based on BL
4.2.4 Sequence Optimization Strategy
4.2.5 Computational Experiment
4.3 Sequential Transfer-Based PSO for 2DIPP
4.3.1 Introduction
4.3.2 Novel Positioning Strategy Based on NFP
4.3.3 Description of Sequence Transfer
4.3.4 Computational Experiments
References
5 Solutions for New Variants of Packing Problem
5.1 Knapsack Packing Problem with Defects
5.1.1 Introduction and Literature Review
5.1.2 Problem Description
5.1.3 The Approach for the Problem
5.1.4 Numerical Experiments and Conclusions
5.2 Irregular Packing Problem with Defects
5.2.1 Introduction and Problem Description
5.2.2 Literature Review
5.2.3 Genetic Algorithm and Grey Wolf Optimization
5.2.4 Heuristic Placement Algorithm
5.2.5 Computational Results and Conclusions
5.3 Rectangular Packing Problem with Divisible Items
5.3.1 Introduction and Problem Description
5.3.2 Related Work
5.3.3 The Heuristic Placement Method
5.3.4 Integration with Metaheuristic
5.3.5 Numerical Experiments and Conclusions
Appendix
References
6 Integration of Packing and Cutting
6.1 An Integrated Approach on Packing and Cut Planning
6.1.1 Introduction
6.1.2 The Three-Stage Solution
6.1.3 Mathematical Modeling
6.1.4 The Solving Approach
6.1.5 Computational Experiments and Discussion
6.2 An Integrated System for Packing and Cutting-Punching
6.2.1 Introduction
6.2.2 The Overall Structure
6.2.3 The Data Structure of IKBS
6.2.4 The Knowledge Base of IKBS
6.2.5 Case Study and Discussion
6.3 An Integrated System for Packing and Sheet Metal Cutting
6.3.1 Introduction
6.3.2 The System Overall Structure
6.3.3 Nest Planning
6.3.4 CAD/CAPP/CAM
6.3.5 Case Study
References
7 Intelligent Algorithms for Cutting Scheduling Problem
7.1 Problem Description
7.2 Improved Hierarchical Genetic Algorithm for the CSP
7.2.1 Introduction
7.2.2 Problem Statement and Mathematical Modeling
7.2.3 Ant Colony—Hierarchical Genetic Algorithm
7.2.4 Computational Experiments
7.2.5 Conclusions
7.3 Hybrid Genetic Algorithm for the Bi-Objective CSP
7.3.1 Introduction
7.3.2 Problem Description and Formulation
7.3.3 VNSGA III Based on Reference Points
7.3.4 Evaluation Metric
7.3.5 Experimental Design and Results
7.4 GWO Algorithm for the Bi-Objective CSP
7.4.1 Introduction
7.4.2 Problem Description and Formulation
7.4.3 Reference-Point-Based GWO Algorithm
7.4.4 Experimental Design and Results
References
8 Application on Laser Cutting of Metal Sheets
8.1 Introduction to LaserCAM Software
8.1.1 Graphics Module
8.1.2 Packing Module
8.1.3 Laser Cutting Module
8.1.4 NC and Report Module
8.2 Case 1: Rectangular Packing and Cutting
8.3 Case 2: Irregular Packing and Cutting
