Approaches to cutting stock and strip packing problems

Abstract

Cutting and packing problems are progressively encountered in several manufacturing industries. The growing need for automation that may result in economic saving and better utilization of raw stock, are the major challenges faced by these industries. This thesis presents a number of methods for generating high quality solutions for these cutting and packing challenges. The thesis addresses two problems: (i) one dimensional cutting stock problem that deals with generating patterns for cutting the available raw stock that result in minimum trim loss and, (ii) strip packing problem that involves packing of small items into a large container (called strip) such that the resulting height of packing layout is minimized.A constructive framework to solve large complex problems is presented with methods that lead to high material utilization. The framework is analyzed, and its e ectiveness is illustrated on di erent datasets. We investigate di erent parameters for this framework, like low demand ratio, feasibility for other dimensions, etc. Metaheuristic and heuristic strategies are explored for e ective column generation techniques in order to stabilize and accelerate the solution process, when applied to one dimensional cutting stock problem. Dynamism feature of a genetic algorithm is used to improve the solution convergence rate to a great extent, which controls the random behavior to an acceptable level.A new placement strategy is proposed for the e ective layout of small rectangles into a container. The obtained solution is improved by applying a metaheuristic technique that evolves a better placement sequence for items. Further, the data structure implementation improves the scalability to large problem instances. The main challenge is to develop systems of higher generality, which can intelligently select, evolve or combine search methods (heuristics) to operate upon a wider range of problems and their instances. Hence, we proposeda new search technique that couples genetic algorithm with constructive hyperheuristic approach. It investigates di erent low level heuristics, which are capable of producing good solutions for packing problems. Experimental evidence indicates that the hyper-heuristic can operate on a wide range of problems to produce some competitive results. We also demonstrate the capability of identifying the e ectiveness of the low-level heuristics. This research follows the direction and contributes towards achieving the goal of exploring and automating the design of search systems. These facilitate the design and development of a similar automation system for the same or other domains.