https://www.mansci.ovgu.de/mansci_media/publikationen/2007/typology-EGOTEC-5t0pvr6fjifln4r4oav60tt612.pdf

An improved typology of cutting and packing problems

Random-key genetic algorithms were introduced by Bean (ORSA J. Comput. 6:154---160, 1994) for solving sequencing problems in combinatorial optimization. Since then, they have been extended to handle a wide class of combinatorial optimization problems. This paper presents a tutorial on the implementation and use of biased random-key genetic algorithms for solving combinatorial optimization problems. Biased random-key genetic algorithms are a variant of random-key genetic algorithms, where one of the parents used for mating is biased to be of higher fitness than the other parent. After introducing the basics of biased random-key genetic algorithms, the paper discusses in some detail implementation issues, illustrating the ease in which sequential and parallel heuristics based on biased random-key genetic algorithms can be developed. A survey of applications that have recently appeared in the literature is also given.

Biased random-key genetic algorithms for combinatorial optimization

This paper presents a new best-fit heuristic for the two-dimensional rectangular stock-cutting problem and demonstrates its effectiveness by comparing it against other published approaches. A placement algorithm usually takes a list of shapes, sorted by some property such as increasing height or decreasing area, and then applies a placement rule to each of these shapes in turn. The proposed method is not restricted to the first shape encountered but may dynamically search the list for better candidate shapes for placement. We suggest an efficient implementation of our heuristic and show that it compares favourably to other heuristic and metaheuristic approaches from the literature in terms of both solution quality and execution time. We also present data for new problem instances to encourage further research and greater comparison between this and future methods.

http://www.cs.nott.ac.uk/~pszgxk/papers/gxwor2004.pdf

A New Placement Heuristic for the Orthogonal Stock-Cutting Problem

Swarm intelligence (SI) and bio-inspired computing in general have attracted great interest in almost every area of science, engineering, and industry over the last two decades. In this chapter, we provide an overview of some of the most widely used bio-inspired algorithms, especially those based on SI such as cuckoo search, firefly algorithm, and particle swarm optimization. We also analyze the essence of algorithms and their connections to self-organization. Furthermore, we highlight the main challenging issues associated with these metaheuristic algorithms with in-depth discussions. Finally, we provide some key, open problems that need to be addressed in the next decade.

Swarm Intelligence and Bio-Inspired Computation: An Overview

We consider the problem of orthogonally packing a given set of rectangular items into a given strip, by minimizing the overall height of the packing. The problem is NP-hard in the strong sense, and finds several applications in cutting and packing. We propose a new relaxation that produces good lower bounds and gives information to obtain effective heuristic algorithms. These results are used in a branch-and-bound algorithm, which was able to solve test instances from the literature involving up to 200 items.

An Exact Approach to the Strip-Packing Problem

http://www.inf.utfsm.cl/~mcriff/EA/eva-space-planning/ht00.pdf

E Hopper

Papers

An Empirical Investigation of Meta-heuristic and Heuristic Algorithms for a 2D Packing Problem