Shunji Umetani

One-dimensional cutting stock problem to minimize the number of different patterns

Abstract As the cost associated with the change of cutting patterns become more important in recent industry, we consider 1D-CSP in which the number of different cutting patterns is constrained within a given bound. The proposed approach is based on metaheuristics, and incorporates an adaptive pattern generation technique. According to our computational experiments, it is observed that the proposed algorithm provides comparable solutions to other existing heuristic approaches for 1D-CSP.

One-Dimensional Cutting Stock Problem with a Given Number of Setups: A Hybrid Approach of Metaheuristics and Linear Programming

One-dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems, which arises in many industrial applications. Since the setup costs for switching different cutting patterns become more dominant in recent cutting industry, we consider a variant of 1D-CSP, called the pattern restricted problem (PRP), to minimize the number of stock rolls while constraining the number of different cutting patterns within a bound given by users. For this problem, we propose a local search algorithm that alternately uses two types of local search processes with the 1-add neighborhood and the shift neighborhood, respectively. To improve the performance of local search, we incorporate it with linear programming (LP) techniques, to reduce the number of solutions in each neighborhood. A sensitivity analysis technique is introduced to solve a large number of associated LP problems quickly. Through computational experiments, we observe that the new algorithm obtains solutions of better quality than those obtained by other existing approaches.

Solving the irregular strip packing problem via guided local search for overlap minimization

The irregular strip-packing problem (ISP) requires a given set of non-convex polygons to be placed without overlap within a rectangular container having a fixed width and a variable length, which is to be minimized. As a core sub-problem to solve ISP, we consider an overlap minimization problem (OMP) whose objective is to place all polygons into a container with given width and length so that the total amount of overlap between polygons is made as small as possible. We propose to use directional penetration depths to measure the amount of overlap between a pair of polygons, and present an efficient algorithm to find a position with the minimum overlap for each polygon when it is translated in a specified direction. Based on this, we develop a local search algorithm for OMP that translates a polygon in horizontal and vertical directions alternately. Then we incorporate it in our algorithm for OMP, which is a variant of the guided local search algorithm. Computational results show that our algorithm improves the best-known values of some well-known benchmark instances.

On the one-dimensional stock cutting problem in the paper tube industry

The one-dimensional cutting stock problem (1D-CSP) is one of the representative combinatorial optimization problems which arises in many industrial applications. Although the primary objective of 1D-CSP is to minimize the total length of used stock rolls, the efficiency of cutting processes has become more important in recent years. The crucial bottleneck of the cutting process often occurs at handling operations in semiautomated manufacturers such as those in the paper tube industry. To reduce interruptions and errors at handling operations in the paper tube industry, we consider a variant of 1D-CSP that minimizes the total length of used stock rolls while constraining (C1) the number of setups of each stock roll type, (C2) the combination of piece lengths occurring in open stacks simultaneously, and (C3) the number of open stacks. For this problem, we propose a generalization of the cutting pattern called the “cutting group,” which is a sequence of cutting patterns that satisfies the given upper bounds of setups of each stock roll type and open stacks. To generate good cutting groups, we decompose the 1D-CSP into a number of auxiliary bin packing problems. We develop a tabu search algorithm based on a shift neighborhood that solves the auxiliary bin packing problems by the first-fit decreasing heuristic algorithm. Experimental results show that our algorithm improves the quality of solutions compared to the existing algorithm used in a paper tube factory.

Local Search Algorithms for the Two-Dimensional Cutting Stock Problem with a Given Number of Different Patterns

We consider the two-dimensional cutting stock problem that arises in many applications in industries. In recent industrial applications, it is argued that the setup cost for changing patterns becomes more dominant and it is impractical to use many different cutting patterns. Therefore, we consider the pattern restricted two-dimensional cutting stock problem, in which the total number of applications of cutting patterns is minimized while the number of different cutting patterns is given as a parameter n. For this problem, we develop local search algorithms. As the neighborhood size plays a crucial role in determining the efficiency of local search, we propose to use linear programming techniques for the purpose of restricting the number of solutions in the neighborhood. In this process, to generate a cutting pattern, it is required to place all the given products (rectangles) into the stock sheet (two-dimensional area) without mutual overlap. For this purpose, we develop a heuristic algorithm using an existing rectangle packing algorithm with the sequence pair coding scheme. Finally, we generate random test instances of this problem and conduct computational experiments, to evaluate the effectiveness of the proposed algorithms.

A Heuristic Algorithm for the Set Multicover Problem with Generalized Upper Bound Constraints

We consider an extension of the set covering problem SCP introducing i multicover and ii generalized upper bound GUB constraints that arise in many real applications of SCP. For this problem, we develop a 2-flip neighborhood local search algorithm with a heuristic size reduction algorithm, in which a new evaluation scheme of variables is introduced taking account of GUB constraints. According to computational comparison with the latest version of a mixed integer programming solver, our algorithm performs quite effectively for various types of instances, especially for very large-scale instances.

Optimal Electric Power Management in a Residential Building Using Photovoltaic and Storage Battery

We consider the electric power management system facilitated the photovoltaic and storage battery. The total energy cost is derived by solving 0-1 mixed integer programming problem for several scenarios.Copyright

Relaxation heuristics for the set multicover problem with generalized upper bound constraints

We consider an extension of the set covering problem (SCP) introducing (i)~multicover and (ii)~generalized upper bound (GUB)~constraints. For the conventional SCP, the pricing method has been introduced to reduce the size of instances, and several efficient heuristic algorithms based on such reduction techniques have been developed to solve large-scale instances. However, GUB constraints often make the pricing method less effective, because they often prevent solutions from containing highly evaluated variables together. To overcome this problem, we develop heuristic algorithms to reduce the size of instances, in which new evaluation schemes of variables are introduced taking account of GUB constraints. We also develop an efficient implementation of a 2-flip neighborhood local search algorithm that reduces the number of candidates in the neighborhood without sacrificing the solution quality. In order to guide the search to visit a wide variety of good solutions, we also introduce a path relinking method that generates new solutions by combining two or more solutions obtained so far. According to computational comparison on benchmark instances, the proposed method succeeds in selecting a small number of promising variables properly and performs quite effectively even for large-scale instances having hard GUB constraints.

Exploiting variable associations to configure efficient local search algorithms in large-scale binary integer programs ☆

We present a data mining approach for reducing the search space of local search algorithms in a class of binary integer programs including the set covering and partitioning problems. The quality of locally optimal solutions typically improves if a larger neighborhood is used, while the computation time of searching the neighborhood increases exponentially. To overcome this, we extract variable associations from the instance to be solved in order to identify promising pairs of flipping variables in the neighborhood search. Based on this, we develop a 4-flip neighborhood local search algorithm that incorporates an efficient incremental evaluation of solutions and an adaptive control of penalty weights. Computational results show that the proposed method improves the performance of the local search algorithm for large-scale set covering and partitioning problems.

A Combined Approach for Production Scheduling and Routing of Automated Guided Vehicles With Layered Time-Space Network

Automated guided vehicles (AGVs) are useful for material handling in case that a working area is narrow and layout changes frequently in a factory, such as container terminals and semiconductor fabrications. In the conventional studies, routing of AGVs is usually considered under a given optimal production schedule [1]. However, for the efficient processing operation in overall factory, it is necessary to consider the influence between production scheduling and transportation planning of AGVs.Copyright