A Graph Theoretic Approach for Minimizing Storage Space using Bin Packing Heuristics (original) (raw)

A NOVEL GRAPH BASED ALGORITHM FOR ONE DIMENSIONAL BIN PACKING PROBLEM

The Bin Packing Problem (BPP) is one of the most known combinatorial optimization problems. The main objective of the problem is to minimize the number of bins used and pack the items with different sizes in finite number of bins efficiently. This paper introduces a new graph based algorithm for one dimensional bin packing problem. The proposed algorithm is implemented and tested with the well known benchmark instances and a comparison with existing First-Fit Decreasing (FFD) algorithm is given with respect to number of bins and waste space. In most of the cases the new algorithm produces near optimal solutions and performs better than FFD.

Efficient algorithms for the offline variable sized bin-packing problem

Journal of Global Optimization, 2012

We addresses a variant of the classical one dimensional bin-packing problem where several types of bins with unequal sizes and costs are presented. Each bin-type includes limited and/or unlimited identical bins. The goal is to minimize the total cost of bins needed to store a given set of items, each item with some space requirements. Four new heuristics to solve this problem are proposed, developed and compared. The experiments results show that higher quality solutions can be obtained using the proposed algorithms.

A Fast Scalable Heuristic for Bin Packing

2019

In this paper we present a fast scalable heuristic for bin packing that partitions the given problem into identical sub-problems of constant size and solves these constant size sub-problems by considering only a constant number of bin configurations with bounded unused space. We present some empirical evidence to support the scalability of our heuristic and its tighter empirical analysis of hard instances due to improved lower bound on the necessary wastage in an optimal solution.

New heuristics for one-dimensional bin-packing

Computers & Operations Research, 2002

Several new heuristics for solving the one-dimensional bin packing problem are presented. Some of these are based on the minimal bin slack (MBS) heuristic of Gupta and Ho. A different algorithm is one based on the variable neighbourhood search metaheuristic. The most effective algorithm turned out to be one based on running one of the former to provide an initial solution for the latter. When tested on 1370 benchmark test problem instances from two sources, this last hybrid algorithm proved capable of achieving the optimal solution for 1329, and could find for 4 instances solutions better than the best known. This is remarkable performance when set against other methods, both heuristic and optimum seeking.

A pr 2 01 9 A Fast Scalable Heuristic for Bin Packing

2019

Heuristics for the variable sized bin-packing problem

Computers & Operations Research, 2009

We investigate the one-dimensional variable-sized bin-packing problem. This problem requires packing a set of items into a minimum-cost set of bins of unequal sizes and costs. Six optimization-based heuristics for this problem are presented and compared. We analyze their empirical performance on a large set of randomly generated test instances with up to 2000 items and seven bin types. The first contribution of this paper is to provide evidence that a set covering heuristic proves to be highly effective and capable of delivering very-high quality solutions within short CPU times. In addition, we found that a simple subset-sum problem-based heuristic consistently outperforms heuristics from the literature while requiring extremely short CPU times.

Worst-Case Analysis of Heuristics for the Bin Packing Problem with General Cost Structures

Operations Research, 1994

We consider the famous bin packing problem where a set of items must be stored in bins of equal capacity. In the classical version, the objective is to minimize the number of bins used. Motivated by several optimization problems that occur in the context of the storage of items, we study a more general cost structure where the cost of a bin is a concave function of the number of items in the bin. The objective is to store the items in such a way that total cost is minimized. Such cost functions can greatly alter the way the items should be assigned to the bins. We show that some of the best heuristics developed for the classical bin packing problem can perform poorly under the general cost structure. On the other hand, the so-called next-fit increasing heuristic has an absolute worst-case bound of no more than 1.75 and an asymptotic worst-case bound of 1.691 for any concave and monotone cost function. Our analysis also provides a new worst-case bound for the well studied next-fit decreasing heuristic when the objective is to minimize the number of bins used. Subject classifications. Analysis of algorithms: heuristics and worst-case analysis. Mathematics: bin packing and combinatorial optimization. Area of review: OPTIMIZATION.

An Analysis of Solutions to the 2D Bin Packing Problem and Additional Complexities

2021

The Bin Packing problem in 2 space is an NP-Hard combinatorial problem in optimization of packing and arrangement of objects in a given space. It has a wide variety of applications ranging from logistics in retail industries to resource allocation in cloud computing. In this paper, we discuss the mathematical formulation of this problem. Furthermore, we analyse its time complexity, its NP-Hardness and some of its stochastic solutions with their efficiencies. We then propose additional complexities that would make the problem more fit for industrial use and discuss in depth the domains in which it might prove to be useful. We conclude while suggesting areas of improvement in operations research on this subject.

Better-Fit Heuristic for One-Dimensional Bin-Packing Problem

2009 IEEE International Advance Computing Conference

This paper reports a study on better-fit heuristic for Time complexity of NF is 0(n) while those of FF and BF classical bin-packing problem, proposed in [1]. Better-fit replaces is 0 (n log n). NF produces a worst packing of 2 * optimum. an existing object from a bin with the next object in the list, if it FF and BF produce a worst packing of 1.7 * optimum. can fill the bin better than the object replaced. It takes O(n2m) time~whr n.stenme fojct n stenme Off-line algorithms have all the objects available before the time whlere n IS thle number of objects and m IS thle number of distinct object sizes in the list. It behaves as off-line as well packing starts. Two common off-line algorithms are described as on-line heuristic with the condition of permanent assignment below. of objects to a bin removed. Experiments have been conducted First-Fit Decreasing (FFD): After sorting the list of objects in on representative problem instances in terms of expected waste rates. It outperforms off-line best-fit-decreasing heuristic on most non-increasing of the instances. It always performs better than the on-line best-fit to the FF heuristic. heuristic. Best-Fit Decreasing (BFD): After sorting the list of objects in Keywords: Bin Packing Problem, Combinatorial Optimiza-non-increasing order of sizes, the BFD packs objects according tion, Heuristics.

Heuristics for Solving the Bin-Packing Problem with Conflicts

Applied Mathematical Sciences, 2011

This paper deals to solve the one dimensional bin-packing problem with conflicts. The conflicts are represented by a graph whose nodes are the items, and adjacent items cannot be packed into the same bin. We propose an adaptation of Minimum Bin Slack heuristic also with a combination of heuristics based on the uses of the classical bin-packing methods to packing items of maximal-stable-subsets (MSS) which founded through two ways from the conflicts graph. Computational results on benchmark instances taken from the literature show the effectiveness of the proposed procedures.

A Graph Theoretic Approach for Minimizing Storage Space using Bin Packing Heuristics (original) (raw)

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