VisTHAA

2016 ◽  
pp. 151-177
Author(s):  
Laura Cruz-Reyes ◽  
Mercedes Pérez Villafuerte ◽  
Marcela Quiroz-Castellanos ◽  
Claudia Gómez ◽  
Nelson Rangel Valdez ◽  
...  
Keyword(s):  
Design Theory ◽  
Bin Packing ◽  
Heuristic Algorithms ◽  
Statistical Tests ◽  
Packing Problem ◽  
Point Of View ◽  
Minimum Requirement ◽  
The One ◽  
Standard Sets ◽  
Non Parametric

In this chapter, a scientific tool designed to facilitate fair comparisons of heuristics is introduced. Making a fair comparison of the performance of different algorithms is a general problem for the heuristic community. Most of the works on experimental analysis of heuristic algorithms have been focused on tabular comparisons of experimental results over standard sets of benchmark instances. However, from a statistical point of view, and according to the experimental design theory, a minimum requirement to compare heuristic algorithms is the use of non-parametric tests. Non-parametric tests can be used for comparing algorithms whose results represent average values, in spite of the inexistence of relationships between them, and explicit conditions of normality, among others. The proposed tool, referred to as VisTHAA, incorporates four non-parametric statistical tests to facilitate the comparative analysis of heuristics. As a case study, VisTHAA is applied to analyze the published results for the best state-of-the-art algorithms that solve the one-dimensional Bin Packing Problem.

scholarly journals An Adaptive Fitness-Dependent Optimizer for the One-Dimensional Bin Packing Problem

IEEE Access ◽  
2020 ◽  
Vol 8 ◽  
pp. 97959-97974 ◽  
Author(s):  
Diaa Salama Abdul-Minaam ◽  
Wadha Mohammed Edkheel Saqar Al-Mutairi ◽  
Mohamed A. Awad ◽  
Walaa H. El-Ashmawi
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
One Dimensional ◽  
Bin Packing Problem ◽  
The One

Solving the one-dimensional bin packing problem with a weight annealing heuristic

2008 ◽  
Vol 35 (7) ◽  
pp. 2283-2291 ◽  
Author(s):  
Kok-Hua Loh ◽  
Bruce Golden ◽  
Edward Wasil
Keyword(s):  
Bin Packing ◽  
Packing Problem ◽  
One Dimensional ◽  
Bin Packing Problem ◽  
The One

scholarly journals Point vortex equilibria and optimal packings of circles on a sphere

2010 ◽  
Vol 467 (2129) ◽  
pp. 1468-1490 ◽  
Author(s):  
Paul K. Newton ◽  
Takashi Sakajo
Keyword(s):  
Particle Interaction ◽  
Point Vortex ◽  
Packing Problem ◽  
Point Of View ◽  
Basis Set ◽  
Equilibrium Solutions ◽  
Optimal Packing ◽  
Packing Process ◽  
Point Vortex Equilibria ◽  
The One

We answer the question of whether optimal packings of circles on a sphere are equilibrium solutions to the logarithmic particle interaction problem for values of N =3–12 and 24, the only values of N for which the optimal packing problem (also known as the Tammes problem) has rigorously known solutions. We also address the cases N =13–23 where optimal packing solutions have been computed, but not proven analytically. As in Jamaloodeen & Newton (Jamaloodeen & Newton 2006 Proc. R. Soc. Lond. Ser. A 462 , 3277–3299. ( doi:10.1098/rspa.2006.1731 )), a logarithmic, or point vortex equilibrium is determined by formulating the problem as the one in linear algebra, , where A is a N ( N −1)/2× N non-normal configuration matrix obtained by requiring that all interparticle distances remain constant. If A has a kernel, the strength vector is then determined as a right-singular vector associated with the zero singular value, or a vector that lies in the nullspace of A where the kernel is multi-dimensional. First we determine if the known optimal packing solution for a given value of N has a configuration matrix A with a non-empty nullspace. The answer is yes for N =3–9, 11–14, 16 and no for N =10, 15, 17–24. We then determine a basis set for the nullspace of A associated with the optimally packed state, answer the question of whether N -equal strength particles, , form an equilibrium for this configuration, and describe what is special about the icosahedral configuration from this point of view. We also find new equilibria by implementing two versions of a random walk algorithm. First, we cluster sub-groups of particles into patterns during the packing process, and ‘grow’ a packed state using a version of the ‘yin-yang’ algorithm of Longuet-Higgins (Longuet-Higgins 2008 Proc. R. Soc. A (doi:10.1098/rspa.2008.0219)). We also implement a version of our ‘Brownian ratchet’ algorithm to find new equilibria near the optimally packed state for N =10, 15, 17–24.

Heuristic Algorithms

2012 ◽  
pp. 238-267
Author(s):  
Laura Cruz Reyes ◽  
Claudia Gómez Santillán ◽  
Marcela Quiroz ◽  
Adriana Alvim ◽  
Patricia Melin ◽  
...  
Keyword(s):  
Large Scale ◽  
Bin Packing ◽  
Heuristic Algorithms ◽  
Packing Problem ◽  
Transportation System ◽  
Deterministic Algorithm ◽  
Computational Time ◽  
Routing Problem ◽  
Bin Packing Problem ◽  
Truck Loading

This chapter approaches the Truck Loading Problem, which is formulated as a rich problem with the classic one dimensional Bin Packing Problem (BPP) and five variants. The literature review reveals that related work deals with three variants at the most. Besides, few efforts have been done to combine the Bin Packing Problem with the Vehicle Routing Problem. For the solution of this new Rich BPP a heuristic-deterministic algorithm, named DiPro, is proposed. It works together with a metaheuristic algorithm to plan routes, schedules and loads. The objective of the integrated problem, called RoSLoP, consists of optimizing the delivery process of bottled products in a real application. The experiments show the performance of three version of the Transportation System. The best version achieves a total demand satisfaction, an average saving of three vehicles and a reduction of the computational time from 3 hrs to two minutes regarding their manual solution. For the large scale the authors have develop a competitive genetic algorithm for BPP. As future work, it is intended integrate the approximation algorithm to the transportation system.

Sign in / Sign up

Export Citation Format

Share Document