scholarly journals A Reinforced Tabu Search Approach for 2D Strip Packing

2010 ◽  
Vol 1 (3) ◽  
pp. 20-36 ◽  
Author(s):  
Giglia Gómez-Villouta ◽  
Jean-Philippe Hamiez ◽  
Jin-Kao Hao
Keyword(s):  
Tabu Search ◽  
Search Algorithm ◽  
Fitness Function ◽  
Packing Problem ◽  
Local Search Algorithm ◽  
Strip Packing ◽  
Benchmark Instances ◽  
Finite Set ◽  
Infinite Height ◽  
Search Approach

This paper discusses a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied considers regular items, rectangular to be precise, that must be packed without overlap, not allowing rotations. The objective is to minimize the height of the resulting packing. In this regard, the authors present a local search algorithm based on the well-known tabu search metaheuristic. Two important components of the presented tabu search strategy are reinforced in attempting to include problem knowledge. The fitness function incorporates a measure related to the empty spaces, while the diversification relies on a set of historically “frozen” objects. The resulting reinforced tabu search approach is evaluated on a set of well-known hard benchmark instances and compared with state-of-the-art algorithms.

A Reinforced Tabu Search Approach for 2D Strip Packing

2012 ◽  
pp. 171-188
Author(s):  
Giglia Gómez-Villouta ◽  
Jean-Philippe Hamiez ◽  
Jin-Kao Hao
Keyword(s):  
Tabu Search ◽  
Search Algorithm ◽  
Fitness Function ◽  
Packing Problem ◽  
Two Dimensional ◽  
Strip Packing ◽  
Benchmark Instances ◽  
Finite Set ◽  
Infinite Height ◽  
Search Approach

This paper discusses a particular “packing” problem, namely the two dimensional strip packing problem, where a finite set of objects have to be located in a strip of fixed width and infinite height. The variant studied considers regular items, rectangular to be precise, that must be packed without overlap, not allowing rotations. The objective is to minimize the height of the resulting packing. In this regard, the authors present a local search algorithm based on the well-known tabu search metaheuristic. Two important components of the presented tabu search strategy are reinforced in attempting to include problem knowledge. The fitness function incorporates a measure related to the empty spaces, while the diversification relies on a set of historically “frozen” objects. The resulting reinforced tabu search approach is evaluated on a set of well-known hard benchmark instances and compared with state-of-the-art algorithms.

CONSTRUCTION OF MIXED COVERING ARRAYS OF STRENGTHS 2 THROUGH 6 USING A TABU SEARCH APPROACH

2012 ◽  
Vol 04 (03) ◽  
pp. 1250033 ◽  
Author(s):  
LORETO GONZALEZ-HERNANDEZ ◽  
NELSON RANGEL-VALDEZ ◽  
JOSE TORRES-JIMENEZ
Keyword(s):  
Tabu Search ◽  
Search Algorithm ◽  
Fine Tuning ◽  
Optimal Size ◽  
Software System ◽  
Covering Arrays ◽  
Combinatorial Structures ◽  
Finite Set ◽  
Best Parameter ◽  
Search Approach

The development of a new software system involves extensive tests of the software functionality in order to identify possible failures. Also, a software system already built requires a fine tuning of its configurable options to give the best performance in the environment where it is going to work. Both cases require a finite set of tests that avoids testing all the possible combinations (which is time consuming); to this situation mixed covering arrays (MCAs) are a feasible alternative. MCAs are combinatorial structures having a case per row. MCAs are small, in comparison with exhaustive search, and guarantee a level of interaction among the involved parameters (a difference with random testing). We present a tabu search algorithm (TSA) for the construction of MCAs. Also, we report the fine tuning process used to identify the best parameter values for TSA. The analyzed TSA parameters were three different initialization functions, five different tabu list sizes and the mixture of four neighborhood functions. The performance of TSA was evaluated with two benchmarks previously reported. The results showed that TSA improved the algorithms IPOG-F, ITCH, Jenny, TConfig, and TVG in relation with the size of the constructed matrices. Particularly, TSA found the optimal size in 20 of the 23 cases tested.

scholarly journals GASAT: A Genetic Local Search Algorithm for the Satisfiability Problem

2006 ◽  
Vol 14 (2) ◽  
pp. 223-253 ◽  
Author(s):  
Frédéric Lardeux ◽  
Frédéric Saubion ◽  
Jin-Kao Hao
Keyword(s):  
Tabu Search ◽  
Local Search ◽  
Hybrid Algorithm ◽  
State Of The Art ◽  
Search Algorithm ◽  
Satisfiability Problem ◽  
Local Search Algorithm ◽  
Overall Performance ◽  
Genetic Local Search ◽  
Search Stage

This paper presents GASAT, a hybrid algorithm for the satisfiability problem (SAT). The main feature of GASAT is that it includes a recombination stage based on a specific crossover and a tabu search stage. We have conducted experiments to evaluate the different components of GASAT and to compare its overall performance with state-of-the-art SAT algorithms. These experiments show that GASAT provides very competitive results.

On Local Search for Bi-objective Knapsack Problems

2013 ◽  
Vol 21 (1) ◽  
pp. 179-196 ◽  
Author(s):  
Arnaud Liefooghe ◽  
Luís Paquete ◽  
José Rui Figueira
Keyword(s):  
Experimental Study ◽  
Local Search ◽  
Search Algorithm ◽  
Exact Algorithms ◽  
Knapsack Problems ◽  
Optimal Solutions ◽  
Local Search Algorithm ◽  
Property A ◽  
Total Profit ◽  
Search Approach

In this article, a local search approach is proposed for three variants of the bi-objective binary knapsack problem, with the aim of maximizing the total profit and minimizing the total weight. First, an experimental study on a given structural property of connectedness of the efficient set is conducted. Based on this property, a local search algorithm is proposed and its performance is compared to exact algorithms in terms of runtime and quality metrics. The experimental results indicate that this simple local search algorithm is able to find a representative set of optimal solutions in most of the cases, and in much less time than exact algorithms.

GREEDY ALGORITHMS FOR PACKING UNEQUAL SPHERES INTO A CUBOIDAL STRIP OR A CUBOID

2011 ◽  
Vol 28 (06) ◽  
pp. 739-753 ◽  
Author(s):  
TIMO KUBACH ◽  
ANDREAS BORTFELDT ◽  
THOMAS TILLI ◽  
HERMANN GEHRING
Keyword(s):  
Knapsack Problem ◽  
Greedy Algorithms ◽  
Three Dimensional ◽  
Packing Problem ◽  
Variable Length ◽  
Strip Packing ◽  
Finite Set

Given a finite set of spheres of different sizes, we study the three-dimensional Strip Packing Problem (3D-SPP) as well as the three-dimensional Knapsack Problem (3D-KP). The 3D-SPP asks for a placement of all spheres within a cuboidal strip of fixed width and height so that the variable length of the cuboidal strip is minimized. The 3D-KP requires packing of a subset of the spheres in a given cuboid so that the wasted space is minimized. To solve these problems two greedy algorithms were developed which adapt the algorithms proposed by Huang et al. (2005) to the 3D case with some important enhancements. The resulting methods were tested using the instances provided by Stoyan et al. (2003). Additionally, two series of 12 instances each for the 3D-SPP and for the 3D-KP are introduced and results for these new instances are also reported.

scholarly journals Exact solutions for the 2d-strip packing problem using the positions-and-covering methodology

PLoS ONE ◽  
2021 ◽  
Vol 16 (1) ◽  
pp. e0245267
Author(s):  
Nestor M. Cid-Garcia ◽  
Yasmin A. Rios-Solis
Keyword(s):  
Exact Solutions ◽  
Optimal Solution ◽  
Packing Problem ◽  
Set Covering ◽  
Medium Size ◽  
Strip Packing ◽  
Fixed Weight ◽  
Np Hard Problem ◽  
Minimum Height ◽  
Infinite Height

We use the Positions and Covering methodology to obtain exact solutions for the two-dimensional, non-guillotine restricted, strip packing problem. In this classical NP-hard problem, a given set of rectangular items has to be packed into a strip of fixed weight and infinite height. The objective consists in determining the minimum height of the strip. The Positions and Covering methodology is based on a two-stage procedure. First, it is generated, in a pseudo-polynomial way, a set of valid positions in which an item can be packed into the strip. Then, by using a set-covering formulation, the best configuration of items into the strip is selected. Based on the literature benchmark, experimental results validate the quality of the solutions and method’s effectiveness for small and medium-size instances. To the best of our knowledge, this is the first approach that generates optimal solutions for some literature instances for which the optimal solution was unknown before this study.

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