A genetic algorithm for the one-dimensional cutting stock problem with setups

This paper investigates the one-dimensional cutting stock problem considering two conflicting objective functions: minimization of both the number of objects and the number of different cutting patterns used. A new heuristic method based on the concepts of genetic algorithms is proposed to solve the problem. This heuristic is empirically analyzed by solving randomly generated instances and also practical instances from a chemical-fiber company. The computational results show that the method is efficient and obtains positive results when compared to other methods from the literature. © 2014 Brazilian Operations Research Society

Advanced manufacturing development of a composite empennage component for L-1011 aircraft

This is the final report of technical work conducted during the fourth phase of a multiphase program having the objective of the design, development and flight evaluation of an advanced composite empennage component manufactured in a production environment at a cost competitive with those of its metal counterpart, and at a weight savings of at least 20 percent. The empennage component selected for this program is the vertical fin box of the L-1011 aircraft. The box structure extends from the fuselage production joint to the tip rib and includes front and rear spars. During Phase 4 of the program, production quality tooling was designed and manufactured to produce three sets of covers, ribs, spars, miscellaneous parts, and subassemblies to assemble three complete ACVF units. Recurring and nonrecurring cost data were compiled and documented in the updated producibility/design to cost plan. Nondestruct inspections, quality control tests, and quality acceptance tests were performed in accordance with the quality assurance plan and the structural integrity control plan. Records were maintained to provide traceability of material and parts throughout the manufacturing development phase. It was also determined that additional tooling would not be required to support the current and projected L-1011 production rate

One-dimensional cutting stock problems and solution procedures

This paper provides an introduction to one-dimensional cutting stock problems and solution procedures. The first problem considered requires that both trim loss and pattern changes be controlled. Both linear programming and sequential heuristic procedures are discussed along with the ways they can be used jointly to generate the best possible solutions to this type of problem. Two other important classes of one-dimensional problems are discussed along with ways in which they can be solved.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/30249/1/0000644.pd

A branch-and-price-and-cut algorithm for the pattern minimization problem

n cutting stock problems, after an optimal (minimal stockusage) cutting plan has been devised, one might want to further reducethe operational costs by minimizing the number of setups. A setupoperation occurs each time a different cutting pattern begins to beproduced. The related optimization problem is known as the PatternMinimization Problem, and it is particularly hard to solve exactly. Inthis paper, we present different techniques to strengthen a formulationproposed in the literature. Dual feasible functions are used for thefirst time to derive valid inequalities from different constraints of themodel, and from linear combinations of constraints. A new arc flowformulation is also proposed. This formulation is used to define thebranching scheme of our branch-and-price-and-cut algorithm, and itallows the generation of even stronger cuts by combining the branchingconstraints with other constraints of the model. The computationalexperiments conducted on instances from the literature show that ouralgorithm finds optimal integer solutions faster than other approaches.A set of computational results on random instances is also reported.info:eu-repo/semantics/publishedVersio

Cutting stock problems and solution procedures

This paper discusses some of the basic formulation issues and solution procedures for solving one- and two- dimensional cutting stock problems. Linear programming, sequential heuristic and hybrid solution procedures are described. For two-dimensional cutting stock problems with rectangular shapes, we also propose an approach for solving large problems with limits on the number of times an ordered size may appear in a pattern.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/29128/1/0000167.pd

Study of different setup costs in SingleGA to solve a one-dimensional cutting stock problem

This paper presents the application of new costs for one recent approach, called SingleGA, in solving One-Dimensional cutting stock problem. The cutting problem basically consists in finding the best way to obtain parts of distinct sizes (items) from the cutting of larger parts (objects) with the purpose of minimizing a specific cost or maximizing the profit. The obtained results of SingleGA are compared to the following methods: SHP, Kombi234, ANLCP300 and Symbio, found in literature, verifying its capacity to find feasible and competitive solutions. The computational results show that variations of SingleGA posses good results, improving as setup cost increases

A case for heuristic optimization methods in forestry

With rising competition for scarce resources, forest managers are increasingly concerned with estimating optimal solutions to complex problems. Heuristic procedures are often useful in solving such problems

Shadow Price Guided Genetic Algorithms

The Genetic Algorithm (GA) is a popular global search algorithm. Although it has been used successfully in many fields, there are still performance challenges that prevent GA’s further success. The performance challenges include: difficult to reach optimal solutions for complex problems and take a very long time to solve difficult problems. This dissertation is to research new ways to improve GA’s performance on solution quality and convergence speed. The main focus is to present the concept of shadow price and propose a two-measurement GA. The new algorithm uses the fitness value to measure solutions and shadow price to evaluate components. New shadow price Guided operators are used to achieve good measurable evolutions. Simulation results have shown that the new shadow price Guided genetic algorithm (SGA) is effective in terms of performance and efficient in terms of speed

The use of geometric information in heuristic optimization

The trim-loss, or cutting stock, problem arises whenever material manufactured continuously or in large pieces has to be cut into pieces of sizes ordered by customers. The problem is so to organize the cutting as to minimize the amount of waste (trim-loss) resulting from it. Brown (1971) remarks that no practical solution method has been found for the generalized 2-dimensional trim-loss problem. This thesis discusses the applicability of heuristic search methods as solution techniques for this and other problems. Chapter 2 describes three types of combinatorial search method, state-space search, problem reduction, and branch-and-bound. There is a discussion of the ways in which heuristic information can be incorporated into these methods, and descriptions of the versions of the methods used in the work described in succeeding chapters. In the 1-dimensional trim-loss problem order lengths of some material such as steel bars must be cut from stock lengths held by the supplier. Gilmore and Gomory (1961, 1963) have formulated a mathematical programming solution of this problem, which also arises with the slitting of steel rolls, cutting of metal pipe and slitting of cellophane rolls. Their approach has been developed by Haessler (1971,1975) who is particularly concerned with problems arising in the paper industry. In the 1½-dimensional case the material is manufactured as a continuous sheet of constant width and it is required to minimize the length produced to satisfy orders for rectangular pieces. In the 2-dimensional case the orders are again for rectangular pieces, but here the stock is held as large rectangular sheets. In both cases there may be restrictions as to the way in which the material may be cut; the generalized problem in each case occurs when no such restrictions exist. The 1½-dimensional problem appears to be easier of solution than the 2-dimensional case since in the latter it is necessary not only to determine the relative positions of the required pieces in a cutting pattern, but also to partition the pieces into sets to be cut from separate stock sheets. A solution method for the easier problem might provide some insight into possible methods of solution of the more difficult. In chapter 3, a state-space search method for the solution of generalized 1½-dimensional problems where the number of pieces in the order list is fairly small and the dimensions are small integers is described. This method can be developed to solve 2-dimensional problems in which the order list is fairly small and the size of stock sheets variable but affecting the cost of the material. This development is described in chapter 4. A similarly structured state-space search can be used for finding solutions to optimal network problems. Such searches do not prove the solutions they find to be optimal, so it is of interest also to develop a method for finding solutions to the problems that proves them to be optimal. In chapter 5 the state-space search method is compared with one using branch-and-bound.problems change when large numbers of identical pieces are ordered, so a solution method with a different structure is required. Chapter 6 describes a problem reduction method for generalized 2-dimensional problems in which the order lists are large and the dimensions are small integers. Even when there are restrictions on the way in which the material may be cut, the presence of other constraints may make a mathematical formulation of the 2-dimensional trim-loss problem intractable, so again a heuristic solution method may be desirable. In a problem where there are sequencing constraints on the design of successive cutting patterns, problem reduction is again found to provide a useful solution method. This is described in chapter 7. Some conclusions about the efficacy and potential of the methods used are drawn in chapter 8. The remainder of the present chapter is concerned with setting the work described in this thesis in the context of other work on the same and related problems