An Application of an Unequal-Area Facilities Layout Problem with Fixed-Shape Facilities

The unequal-area facility layout problem (UA-FLP) is the problem of locating rectangular facilities on a rectangular floor space such that facilities do not overlap while optimizing some objective. The objective considered in this paper is minimizing the total distance materials travel between facilities. The UA-FLP considered in this paper considers facilities with fixed dimension and was motivated by the investigation of layout options for a production area at the Toyota Motor Manufacturing West Virginia (TMMWV) plant in Buffalo, WV, USA. This paper presents a mathematical model and a genetic algorithm for locating facilities on a continuous plant floor. More specifically, a genetic algorithm, which consists of a boundary search heuristic (BSH), a linear program, and a dual simplex method, is developed for an UA-FLP. To test the performance of the proposed technique, several test problems taken from the literature are used in the analysis. The results show that the proposed heuristic performs well with respect to solution quality and computational time

An Application of an Unequal-Area Facilities Layout Problem with Fixed-Shape Facilities

The unequal-area facility layout problem (UA-FLP) is the problem of locating rectangular facilities on a rectangular floor space such that facilities do not overlap while optimizing some objective. The objective considered in this paper is minimizing the total distance materials travel between facilities. The UA-FLP considered in this paper considers facilities with fixed dimension and was motivated by the investigation of layout options for a production area at the Toyota Motor Manufacturing West Virginia (TMMWV) plant in Buffalo, WV, USA. This paper presents a mathematical model and a genetic algorithm for locating facilities on a continuous plant floor. More specifically, a genetic algorithm, which consists of a boundary search heuristic (BSH), a linear program, and a dual simplex method, is developed for an UA-FLP. To test the performance of the proposed technique, several test problems taken from the literature are used in the analysis. The results show that the proposed heuristic performs well with respect to solution quality and computational time

Two-dimensional placement compaction using an evolutionary approach: a study

The placement problem of two-dimensional objects over planar surfaces optimizing given utility functions is a combinatorial optimization problem. Our main drive is that of surveying genetic algorithms and hybrid metaheuristics in terms of final positioning area compaction of the solution. Furthermore, a new hybrid evolutionary approach, combining a genetic algorithm merged with a non-linear compaction method is introduced and compared with referenced literature heuristics using both randomly generated instances and benchmark problems. A wide variety of experiments is made, and the respective results and discussions are presented. Finally, conclusions are drawn, and future research is defined

Moldable Items Packing Optimization

This research has led to the development of two mathematical models to optimize the problem of packing a hybrid mix of rigid and moldable items within a three-dimensional volume. These two developed packing models characterize moldable items from two perspectives: (1) when limited discrete configurations represent the moldable items and (2) when all continuous configurations are available to the model. This optimization scheme is a component of a lean effort that attempts to reduce the lead-time associated with the implementation of dynamic product modifications that imply packing changes. To test the developed models, they are applied to the dynamic packing changes of Meals, Ready-to-Eat (MREs) at two different levels: packing MRE food items in the menu bags and packing menu bags in the boxes. These models optimize the packing volume utilization and provide information for MRE assemblers, enabling them to preplan for packing changes in a short lead-time. The optimization results are validated by running the solutions multiple times to access the consistency of solutions. Autodesk Inventor helps visualize the solutions to communicate the optimized packing solutions with the MRE assemblers for training purposes

A heuristic for solving the irregular strip packing problem with quantum optimization

We introduce a novel quantum computing heuristic for solving the irregular strip packing problem, a significant challenge in optimizing material usage across various industries. This problem involves arranging a set of irregular polygonal pieces within a fixed-height, rectangular container to minimize waste. Traditional methods heavily rely on manual optimization by specialists, highlighting the complexity and computational difficulty of achieving quasi-optimal layouts. The proposed algorithm employs a quantum-inspired heuristic that decomposes the strip packing problem into two sub-problems: ordering pieces via the traveling salesman problem and spatially arranging them in a rectangle packing problem. This strategy facilitates a novel application of quantum computing to industrial optimization, aiming to minimize waste and enhance material efficiency. Experimental evaluations using both classical and quantum computational methods demonstrate the algorithm's efficacy. We evaluate the algorithm's performance using the quantum approximate optimization algorithm and the quantum alternating operator ansatz, through simulations and real quantum computers, and compare it to classical approaches.Comment: 30 pages, 12 figure

The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect

In this paper, a two-dimensional cutting problem is considered in which a single plate (large object) has to be cut down into a set of small items of maximal value. As opposed to standard cutting problems, the large object contains a defect, which must not be covered by a small item. The problem is represented by means of an AND/OR-graph, and a Branch & Bound procedure (including heuristic modifications for speeding up the search process) is introduced for its exact solution. The proposed method is evaluated in a series of numerical experiments that are run on problem instances taken from the literature, as well as on randomly generated instances.Two-dimensional cutting, defect, AND/OR-graph, Branch & Bound

Greedy seeding procedure for GAs solving a strip packing problem

In this paper, the two-dimensional strip packing problem with 3-stage level patterns is tackled using genetic algorithms (GAs). We evaluate the usefulness of a greedy seeding procedure for creating the initial population, incorporating problem knowledge. This is motivated by the expectation that the seeding will speed up the GA by starting the search in promising regions of the search space. An analysis of the impact of the seeded initial population is offered, together with a complete study of the influence of these modifications on the genetic search. The results show that the use of an appropriate seeding of the initial population outperforms existing GA approaches on all the used problem instances, for all the metrics used, and in fact it represents the new state of the art for this problem.Red de Universidades con Carreras en Informática (RedUNCI

Greedy seeding procedure for GAs solving a strip packing problem

In this paper, the two-dimensional strip packing problem with 3-stage level patterns is tackled using genetic algorithms (GAs). We evaluate the usefulness of a greedy seeding procedure for creating the initial population, incorporating problem knowledge. This is motivated by the expectation that the seeding will speed up the GA by starting the search in promising regions of the search space. An analysis of the impact of the seeded initial population is offered, together with a complete study of the influence of these modifications on the genetic search. The results show that the use of an appropriate seeding of the initial population outperforms existing GA approaches on all the used problem instances, for all the metrics used, and in fact it represents the new state of the art for this problem.Red de Universidades con Carreras en Informática (RedUNCI

A comparison of different recombination operators for the 2-dimensional strip packing problem

In this paper, the three-stage two-dimensional rectangular strip packing problem is tackled using genetic algorithms. A new problem dependent recombination operator, called best inherited levels recombination (BIL), is introduced. A comparison of its performance is carried out with respect to four classical recombination operators. A complete study of the influence of the recombination operators on the genetic search, including the trade-off between exploration and exploitation in the search process, is presented. The results show that the use of our specialized BIL recombination outperforms the others more generic on all problem instances for all the metrics testedVII Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Two-Dimensional Cutting Problem

This paper deals with two-dimensional cutting problems. Firstly the complexity of the problem in question is estimated. Then, several known approaches for the regular (rectangular) and irregular (not necessarily rectangular) cutting problems are described. In the second part, a decision support system for cutting a rectangular sheet of material into pieces of arbitrary shapes, is presented. The system uses two earlier described methods which prefer different types of data and the user may decide which one is more suitable for the problem in question. After brief description of system data files and its manual, some experimental results are presented